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CHEMISTRY 59-240
PHYSICAL CHEMISTRY
LABORATORY MANUAL
FALL 2008
8th Edition - Version 1.2DEPARTMENT OF CHEMISTRY & BIOCHEMISTRY
UNIVERSITY OF WINDSOR
TABLE OF CONTENTS
Emergency Procedures............................................................................................................ 2
Safety Regulations................................................................................................................... 4
Safety Quiz............................................................................................................................... 7
Policy on Plagiarism................................................................................................................ 9
Student Contract...................................................................................................................... 12
Marking Scheme and Outline................................................................................................. 13
EXPERIMENTS
Experiment 1: Determination of ∆cH: Bomb Calorimetry...................................................... 15
Experiment 2: Vapour Pressure of Pure Liquids..................................................................... 23
Experiment 3: Surface Tension of n-Butanol and Amount Adsorbed..................................... 29
Experiment 4: Heat of Reaction in Solution: Constant Pressure Calorimeter......................... 34
Experiment 5: Liquid-Vapour Equilibrium in a Binary System.............................................. 38
2
EMERGENCY PROCEDURES
Campus Police 4444
Fire Department 911 or pull wall alarm
Ambulance Dispatch 911
Medical Office 7002
Poison Control 9-800-268-9017
First Aid Kits Rooms 172-2, 175, and 274-2
Eye Baths are in each hallway, 173-3 (Lab E), 173-6 (Lab F)
Safety Showers are in each laboratory
EMERGENCY PROCEDURES
Discovery of a Fire
1. Shout, “Fire”. Turn off all equipment. Close the windows and doors as youleave the room.
2. Activate the nearest fire alarm.
3. Evacuate the building via the nearest exit. Do NOT use elevators.
4. Report the fire to Campus Police.
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1. Advise students to remain calm and to stay away from the fire.
2. Do not attempt to fight fires that cannot be easily handled.
3. If you put out a fire with a fire extinguisher, NEVER WALK AWAY. Back away and standby in case the fire ignites.
Sounding of Evacuation Alarm
1. It is MANDATORY for University buildings to be evacuated during any fire alarm.
2. Place all flammable materials into safety cabinets.
3. Shut off all heat sources including lit Bunsen burners.
4. Close all doors and windows.
5. Ensure any handicapped persons are given assistance.
6. Evacuate the building quickly by walking out the nearest exit. DO NOT use the elevators.(If smoke is encountered in a stairwell or corridor, use an alternate route.)
7. The Building Fire Plan Managers and Fire Wardens (Orange Vests) will assume lead rolesin building evacuation and direct you the Assembly Area.
8. DO NOT re-enter the building until the Fire Department or Campus Police authorize it.
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SAFETY REGULATIONSSafety is a matter of the greatest importance to everyone in the Department. The principaldanger is fire, but others (toxic fumes, sharp objects, etc.) are also of concern. GraduateStudents have a double responsibility of concern as laboratory workers and teaching assistants.Most safety procedures derive from common sense. The basic rule of safety is “If you areunsure of the consequences of an action, DON’T DO IT!” The following sets outregulations, which apply in teaching laboratories. Strict adherence to these is a MUST. Defaulters may be excluded from the lab and course.
One of the most common accidents to occur in the laboratory is a chemical spill. Any chemicalspilled on yourself or on your clothing must be washed off with LARGE AMOUNTS OF WATER.The incident MUST be reported to the TA. If acid is spilled on floors or laboratory benches, it mustbe neutralized immediately (solid sodium bicarbonate) and then cleaned up with water after thegeneration of all gas (carbon dioxide) ceases. Obtain the assistance of the TA.
The following rules are strictly enforced:
Cell phones or any other electronic device are not permitted during scheduledlaboratory time. If a student is observed using any electronic device, the devicewill be confiscated until the laboratory session has been concluded.“Turn it off orturn it over!”
# Safety glasses must be worn at all times in the laboratory. Students refusing to wearsafety glasses (or shatterproof spectacles) will be refused permission to perform theexperiment. Never wear contact lenses in the laboratory.
# It is mandatory that a laboratory coat be worn in the laboratory.
# Laboratory work is only permitted on assigned laboratory periods in the assignedlaboratory room and in the presence of a TA. Unauthorized experimental workconducted outside of stipulated laboratory hours is prohibited and forbidden bydepartmental regulations on grounds of safety. Severe disciplinary action will be takenagainst anyone attempting unauthorized experiments in the laboratory.
# Only those people directly involved in the laboratory experiment are allowed in thelaboratory. Visitors are not permitted to enter the laboratory.
# Smoking, eating, and drinking are not permitted in the laboratory.
# Extraneous items (coats, books, etc.) should remain in the area designated for coatsand schoolbags. These items are not permitted at the workbenches.
# No open-toed shoes or sandals may be worn. Students not wearing the proper footwearwill not be permitted to enter the laboratory and perform the scheduled experiment.
# Long hair is a fire hazard and must be tied back at all times.
# Perform all reactions with toxic or poisonous reagents in the fume hood.
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# Transfer harmful reagents in the fume hood to eliminate the dispersion of toxic fumesthroughout the lab. Handle all solid reagents with a spatula and wear gloves asprotection if necessary.
# Never deliberately purposefully inhale (smell) or taste any chemical. The propertechnique to identify an odour is to fan across the top of the container with your hand towaft very dilute vapours towards you.
# Never place your face directly over the top of a container which is being heated or pointit at a neighbour. The contents may “bump” and be violently ejected from the container. This can happen even after the heat has been removed.
# Never use a Bunsen burner for ANY purpose unless instructed to do so by the TA.
# Adhere to the rules when disposing glassware and reagents. Use the containerdesignated for glass when disposing broken glassware and sharp objects, such asPasteur pipets. Use ONLY the properly labelled waste containers for disposal of liquidand solid chemical waste. Never dispose of ANY chemical into the sink.
# Keep working space clean and free of apparatus and/or other materials. This isparticularly important when flammable materials are in use. Wipe up spilled materialsimmediately.
# If products need to be stored for the next lab period, place products and intermediates inthe labelled desiccators. Never store any chemicals in the student lockers!
# Notify the TA of any accident, cut, or burn no matter how trivial it appears.
Accidents and Injuries
In the event of a fire in the laboratory, turn off all gas, and shut down the fume hoods if possiblebefore leaving the room. Do not hesitate to shout “FIRE” or sound the building alarm for anysizable fire. Close the doors and get out of the building through the nearest exit.
If a student’s clothes catches on fire, lie down and roll over repeatedly to smother the flames. Donot run about, which includes running any distance for a safety shower. Use the safety shower orfire blanket if very close by.
Chemical spills on bench tops, fume hoods, etc., should be cleaned up with paper towels andwashed. Treatment with an appropriate neutralising reagent, if necessary, should be based onconsultation with the TA and/or lab co-ordinator.
Dangerous chemicals that come into contact with skin or clothing should be washed off, followedby prolonged washing for 5 to 10 minutes. Do not be concerned with neutralization, just wash. Ifa sizable quantity of corrosive material is on the clothes, prevent skin contact by quickly removingthe clothing.
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Two eye baths are available in the laboratory for washing out eyes. Be sure to ask for help, nomatter how slight the eye injury is.
Internal contact with chemicals can occur through a cut from broken glass, or by inhalation oringestion. Wash out cuts and allow free bleeding to occur for a few minutes. The laboratory co-ordinator, who is trained in First Aid, can treat cuts. If shattered glass was involved, inspect forfragments still in the wound before bandaging. Move into fresh air for inhalation problems and donot exert oneself until breathing has become normal. Report at once if any chemicals may haveentered the mouth, whether or not if any chemical has been swallowed. Delay will not make anynecessary treatment less unpleasant or less necessary.
Burns should be immersed in very cold water for about 5 minutes and, if necessary, dressingshould be applied afterwards.
In general, remember the locations of the alarm box, showers, hoses, and extinguishers in caseof emergencies.
Important: MSDS (Material Safety Data Sheets) for all chemicals used inthe labs can be found in a binder at the back of the lab by thebalances.
Conduct, House Rules, and Safety
Anyone who does not conduct themselves responsibly in the lab (i.e., who persistently exhibitsthoughtlessness or silly behaviour) may, at the discretion of the TA, be asked to leave thelaboratory, and the professor and laboratory coordinator will be notified. Students who are askedto leave will not be able to make up the experiment nor will they be able to submit a lab report forthat experiment. A grade of zero for that experiment will result.
Experiments should be completed by the stated closing hour. Experimental work conductedoutside of stipulated laboratory hours or in the absence of a TA is prohibited by departmentalregulations on grounds of safety. Students are not competent and experienced enough to judgethe hazards, or lack of them, that may permit them to overrule this decision.
Good laboratory etiquette (e.g. noxious fumes contained in the hood, slippage and drippagemopped up, etc.) is expected from anyone working in the lab. Reasonably tidy bench tops andlockers are a sign of ordered activity and also make matters easier in case of water floods, benchfires, etc. Burners not in use must be turned off as their invisible flames are a distinct hazard.
The University of Windsor has a Policy and Procedure on Sexual Harassment. The followingstatement is drawn from the policy:
“The University of Windsor is committed to providing an environment for study, teaching, researchwork, and play for all members of the University community that is supportive of professional andpersonal development and free from sexual harassment.”
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SAFETY QUIZ
Please take a few moments to answer these questions.
1. Where is the location of the fire alarm pull?
___________________________________________________________________________
2. How many fire extinguishers are in the lab? Where is its/their location(s)?
___________________________________________________________________________
3. Where is the nearest eyewash?
___________________________________________________________________________
4. Where is the safety shower in the lab?
___________________________________________________________________________
5. Where is the fire blanket in the lab?
___________________________________________________________________________
Circle the correct answer to each question.
6. What type of footwear is required in the lab?(a) Dress shoes (b) Sandals(c) Shoes that cover toes and protect feet from spills
7. The main routes of exposure to chemicals are:(a) Eyes, nose, mouth and ears (b) Inhalation, ingestion and skin/eye contact(c) Through open-toed shoes
8. The known hazards related to chemicals used in the lab are found in:(a) PCM - Poison Control Manual (b) MSDS - Material Safety Data Sheets(c) Chemical Safety Data Sheets
9. What should be done if a chemical gets in your eye?(a) Rinse your eyes with water from the eyewash fountain for at least 15 minutes(b) Rinse under the safety shower for 5 minutes(c) Nothing, unless the chemical causes discomfort
10. Why should contact lenses never be worn in the lab?(a) They could inadvertently fall out of the eye(b) They are too hard to find if they fall out (c) Chemical vapour could react with or become trapped between the eye and the lens
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11. Why should you wear goggles in the lab even if you personally are not working with anychemicals?(a) Discomfort is a part of science (b) They make you look smart(c) Someone at another workstation may be working with chemicals and splash you
12. Broken glass and sharp objects must be disposed of:(a) In the trash can (b) In the yellow glass container at the back of the lab(c) In the back of someone else’s locker when they are not looking
13. What precautions are needed with long hair and beards?(a) Must be shampooed (b) No long hair and beards allowed in the lab(c) Keep long hair tied back and away from flames and chemicals
14. To dispose of waste chemicals:(a) Pour them down the sink & flush with lots of water(b) Hide them in the back of your locker(c) Put them in the designated waste containers provided
15. When heating with a burner or hot plate in the lab, NEVER:(a) Put hot glass on a cold counter top (b) Leave it unattended(c) Heat a closed container (d) a, b and c
19. If you spill a small amount of chemical on your skin or clothing you should:(a) Evacuate the lab immediately (b) Take a shower when you get home(c) Flush with water for 5 minutes and notify your TA immediately
20. If a large chemical spill occurs on your skin or clothing you should:(a) Remove the clothing, rinse under the safety shower and notify your TA(b) Run madly about the lab until it dries (c) Call 911
21. You must report any form of personal injury incurred in the lab to your TA.(a) True (b) False
22. The person ultimately responsible for your safety in the lab is:(a) The safety committee (b) Your lab partner (c) Your TA (d) Yourself
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POLICY ON PLAGIARISM
Below are the guidelines that outline the policy on plagiarism for the University of Windsor. TA’swill address this issue with students during the first week of the laboratories and discuss theoutcomes that are of a result of plagiarism.
THE COPYING OF WEB PAGES IS CONSIDERED PLAGIARISM AND IS NOT ACCEPTABLE.
ACADEMIC INFORMATIONUndergraduate Degree Regulations
2.4.22 POLICY ON PLAGIARISM
Plagiarism is defined as: "The act of appropriating the literary composition of another, orparts of passages of his or her writing, or the ideas or language of the same, and passingthem off as the products of one's own mind." (Black's Law Dictionary).
It is expected that all students will be evaluated and graded on their individual merit andall work submitted for evaluation should clearly indicate that it is the student's own contribution.
Students often have to use the ideas of others as expressed in written or published workin preparing essays, papers, reports, theses and publications. It is imperative that both thedata and ideas obtained from any and all published or unpublished material be properlyacknowledged and their sources disclosed. Failure to follow this practice constitutesplagiarism and is considered to be a serious offence. Thus, anyone who knowingly orrecklessly uses the work of another person and creates an impression that it is his or herown, is guilty of plagiarism.
Plagiarism also includes submitting one's own essay, paper, or thesis on more than oneoccasion. Accordingly, it is expected that a thesis, essay, paper or a report has not beenand is not concurrently being submitted for credit for any other course. In exceptionalcircumstances and with the prior agreement of the instructor, a student may use researchcompleted for one course as part of his or her written work for a second course.
A confirmed incident of plagiarism will result in a sanction ranging from a verbal warning,to a loss of credit in the course, to expulsion.
Source: 2004/2006 Undergraduate Academic Calendar, Paragraph 2.4.22
For additional information on this topic, please visit the University of Windsor’s websitededicated to student integrity at http://www.uwindsor.ca/aio
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SENATE BY-LAW 31
UNIVERSITY POLICY IN RESPECT TO JUDICIAL PROCEDURESARTICLE I. SANCTIONS AND DEFINITIONS
Proscriptions StatedUniversity discipline is limited to student misconduct which adversely affects the Universitycommunity's pursuit of its educational objectives. Students are expected to conductthemselves in a manner compatible with the objectives and purposes of the University ofWindsor. Any student at the University of Windsor whose conduct is improper in that itexhibits a lack of integrity touching upon the educational objectives and requirements ofthe University must be disciplined appropriately in the interest of safeguarding andupholding these standards.
It is desirable to define and identify further the standards demanded of each student at theUniversity of Windsor in the interest of educational integrity. Enumerated below areillustrations of improper conduct which would lead to an inference of lack of integrity. Theseare illustrative only and shall not be taken as in any way limiting the generality of the highstandards of conduct required by the objectives and purposes of the University of Windsor.
Examples of misconduct for which students are subject to university discipline are definedas follows:
a. Dishonesty, such as cheating, plagiarism, impersonation at an examination, orknowingly furnishing false information to the University.
b. Forgery, alteration, or use of University documents, records, or instruments ofidentification with intent to defraud.
c. Intentional obstruction or disruption of teaching, research, administration,disciplinary proceedings, or other University activities, including public servicefunctions, and other authorized activities on University premises.
d. Malicious abuse of any person on University premises or at University sponsoredor University supervised functions or malicious conduct which threatens, endangersor harasses any such person.
e. Theft from or deliberate damage to University premises or theft of or deliberatedamage to property of a member of the University community on Universitypremises.
f. Failure to comply with directions of members of the University administration or ofthe teaching staff acting in the proper performance of their particular duties.
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g. Violation of published University regulations, including regulations relating to entryand use of University facilities.
h. Violation of published rules governing University residence halls.
i. Deliberate alteration or misappropriation of computer records, data, software, etc.of the University or member of the University community.
j. Breach or misuse of the Code of Computing Practice for the University of WindsorComputer Centre user.
Sanctions Defined
a. Admonition. Notice to the student, orally or in writing, that s/he has violatedstudent rules and that continuation or repetition of the conduct found wrongful,within a period of time stated in the warning, may be cause for more severedisciplinary action.
b. Censure. Written reprimand for violation of a specified regulation, including thepossibility of more severe disciplinary sanction in the event of conviction for theviolation of any University regulation within a period of time stated in the letter ofreprimand.
c. Disciplinary Probation. Exclusion from participation in privileges or extracurricularUniversity activities as set forth in the notice of disciplinary probation for a specifiedperiod of time.
d. Restitution. Reimbursement for damage or misappropriation of property.Reimbursement may take the form of appropriate service to repair or otherwisecompensate for damages.
e. Suspension. Exclusion from classes and other privileges or activities as set forthin the notice of suspension for a definite period of time.
f. Expulsion. Termination of student status for an indefinite period. The conditionsof readmission, if any is permitted, shall be stated in the order of expulsion.
g. Exclusion from Campus. Denial of access to the campus for an indefinite periodfor non-academic misconduct. The conditions for removing this ban, if any, shall beincluded in the exclusion order.
Source: http://athena.uwindsor.ca/units/senate/senate.nsf/Bylaws?OpenView
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STUDENT CONTRACT
I, ___________________________________, have read and understood the
Laboratory Safety and Plagiarism Policy sections of this manual and agree to abide
by the dictates of these documents. I realize that failure to do so may result in my
dismissal from the lab with no opportunity to make-up missed work. I, also, understand
the serious consequences that are to be taken if I have been caught with plagiarism
and I will take full responsibility for my actions. In addition, I have successfully
completed the Safety Quiz.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Course: 59-_________ Section: ________ Date: _______________________
TA’s Name: __________________________________________________________
Student’s Name (please print): __________________________________________
ID # ___________________ Signature ___________________________________
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MARKING SCHEME AND OUTLINEAll labs are marked out of 20.Abstract (3 marks)
The abstract is a crucial part of your laboratory report. It is a clear written paragraphwhich briefly conveys the intent of the laboratory exercise, mentions the methodology utilizedduring the laboratory period, summarizes important experimental observations, findings andconclusions. The abstract length must be between 200 to 300 words.
Procedure (0 marks)No marks are given for this section. You may indicate “as outlined in the 59–240 lab
manual”, quoting the relevant pages. However, if there is a major deviation from experimentalprocedure or significant problem with the data arising from experimental error, you must statethese differences in this section, as these deviations could influence the marks you receive in latersections (i.e., see Results and Calculations below).
Results and Calculations (Labs 1-4, 8 marks & Lab 5, 6 marks)Present your data in neatly laid out tables. Always include units and estimated errors
arising from experimental errors, instrumental readings, etc. Include a comparison of yourexperimental data with literature values where appropriate. Show a sample calculation for eachtype of calculation required, including the equation used, the numbers substituted into theequation, unit analysis and the final answer.
Discussion (Labs 1-4, 7 marks & Lab 5, 9 marks)This section is meant to convey your understanding of the experiment. Discuss all
important results, where trends and anomalies are discussed with reference to the underlyingtheory of the experiment. Important results should be compared with those found in theliterature, and reasons for differences between experimental and literature data should bediscussed. When there are several sources of possible error, indicate to what extent each mayhave affected the final results. You may also choose to include in your discussion possibleapplications of the experiment, suggested improvements or extensions to the experiment, and/oralternative methods of measurement. Answer the lab questions at the end of each experiment!
Conclusions (1 mark)Write a brief statement summarizing the most important results of the experiment,
including numerical final results and per cent errors (if applicable).
References (1 mark)Make a list of all reference material, using the same format as the lab manual. References
should appear in the order they appear in the text. References in the text should appear as super-scripted arabic numerals. For example: The boiling point of benzene is 80.1 oC.3
Reference format: 1. Atkins, P.W. Physical Chemistry, 7th Edition, Oxford University Press, Oxford, 2001.
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GENERAL LABORATORY OUTLINE1. Lab attendance is compulsory.2. Laboratory reports must be turned in at the start of the next lab period. In the final week,
reports must be handed in exactly one week after the completion of the lab.3. Each laboratory report is marked out of 20, and accounts for a maximum possible 3
marks towards your final grade (the five laboratories have a total weight of 15 % in thiscourse).
4. Laboratories which are not completed receive a grade of zero. A completed laboratoryrefers to both attendance and performance in the lab, as well as handing in a completedreport.
5. If the laboratory is not completed due to illness or family tragedy, the student may presenta doctor’s note or some other documentation to the upper year lab coordinator in order tobe excused from the laboratory. In this case, the student will receive a mark on this“excused laboratory” equal to the average mark on all other laboratory reports.
6. No make-up labs are offered.7. If there is any evidence of plagiarism or duplication in lab reports among lab partners,
friends or other students, all parties will receive a grade of zero and be subject toacademic discipline, as per the University of Windsor Undergraduate Calendar.
Prelab PreparationRead your laboratory manual carefully. You must be prepared to answer questions asked
by your TA about the experiment and for surprise quizzes. You must know, or have writtendown, the physical constants of the chemicals you will be using. MSDS sheets are readilyavailable for those who wish to consult them. You must also know how to prepare solutionsrelevant to your experiment (e.g. 4M HCl from concentrated HCl) before you come to the lab. Ifthere is any procedure, or equipment operation, with which you are not familiar, PLEASE ASKYOUR TA FOR HELP. This will help to prevent accidents and waste of valuable time.
DISPUTES, COMPLAINTS, AND POLICYAny disputes or complaints arising from the laboratory course should, in the first
instance, be drawn to the attention of the TA. Should his/her decision be deemed unjust,representations may be made, in turn, to the Professor instructing the course, the Head of theDepartment of Chemistry and Biochemistry, and the Dean of Students.
ACKNOWLEDGEMENTSThe current edition of this manual was prepared by Robert W. Schurko. Previous
editions of this manual, as well as development and refinement of the experiments are credited toPaul Goulet, Cory Widdifield and Robert W. Schurko.
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C6H5CO2H(s)%
152
O2 (g)ÿ 7 CO2 (g)
% 3 H2O(l) [1]
Fig. 1.1
EXPERIMENT 1DETERMINATION OF ∆cH: BOMB CALORIMETRY
IntroductionThe Bomb Calorimeter
The calorimeter utilized in this laboratory experiment is composed of several parts andyou must be familiar with many of them prior to starting this experiment (see Figure 1.1).
1 – High–precision Thermometer 2 – Thermometer Bracket 3 – Thermometer Support Bracket 4 – Reading Lens 5 – Thermometer Support Rod 6 – Motor 7 – Motor Pulley 8 – Stirrer Drive Belt 9 – Stirrer Pulley 10 – Stirrer Bearing Assembly 11 – Ignition Wire 12 – Stirrer Shaft with Propeller 13 – Bucket 14 – Calorimeter Jacket and Cover 15 – Oxygen Combustion Bomb
In addition to these items, onemust also recognize the oxygen fillingconnection and the ignition unit. Beyondthis (i.e., much of the fine structure of theoxygen combustion bomb), a TA willhelp you to understand how the differentparts work and will also lead you throughsome of the important first steps (seeProcedure).
Measuring the Heat Evolved in a Combustion Reaction and Relation to ∆cHThe change in enthalpy associated with burning a sample is defined as its enthalpy of
combustion, ∆cH, and is expressed in units of kilojoules per gram (kJ g-1). Oftentimes, a sampleof benzoic acid is used to standardize a given bomb calorimeter, as its enthalpy of combustion iswell-defined. When benzoic acid combusts, it can be described by the following chemicalequation:
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dU 'MUMT V
dT %MUMV T
dV [2]
dU ' dq 'MUMT V
dT ' CV dT [3]
dH ' dU % d(pV) ' dw % dq % d(pV) ' CV dT % RTi dn [4]
∆c H – ∆cU ' & C (Tf & Ti ) ' & C∆T [5]
For the following discussion, the system is defined as anything that is chemicallyinvolved in the combustion of the sample. According to the first law of thermodynamics, thechange in internal energy of a system, ∆U, is related to the work done on the system, w, and theheat energy transferred to the system, q, and may be expressed algebraically as ∆U = w + q. Using temperature and volume as independent system variables, small changes in internal energycan be expressed as:
If it is assumed that (i) no work is done on the system and (ii) the system will alwaysoccupy the same volume, then w = 0 and [2] simplifies accordingly:
By experimental design, the measurement of the change in internal energy of the systemoccurs indirectly, by determining the temperature change of the surroundings. This fact becomesimportant when considering the sign (i.e., ±) associated with the internal energy change of thesystem.
Enthalpy is defined as H = U + pV. Small changes in enthalpy can be representedalgebraically:
Where dn represents the change in the number of moles of gaseous species in the system.Here, it is assumed that the gaseous components of the system may be described by the ideal gaslaw. Note that only the change in internal energy is measured experimentally and a smallcorrection (the RTi dn term) is applied to find ∆cH. Normally, the difference between thechanges in the two state functions is very small and may be neglected.
Thus, if all of the heat evolved in the combustion reaction can be measured and if all thework done upon the surroundings is assumed to be negligible, then the internal energy change ofthe system due to combustion can be measured:
Where C is understood to be the heat capacity of the calorimeter, in units of kJ K-1 (as thesurroundings are not in the gas phase, the V subscript may be neglected). This heat capacity willbe determined in the first part of the lab experiment by burning benzoic acid.
Refining the ModelIf ∆cH is to be determined in a fairly accurate manner, the model proposed above must be
refined in order to account for additional factors.As one may suspect, the calorimeter is not truly adiabatic and work is done upon the
surroundings in the form of mechanical stirring. In an effort to account for these items, a
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∆T ' Tf & Ti & rα ( t60 & ti ) & rβ ( tf & t60 ) [6]
radiation correction to the observed temperature change is made, and is represented by thefollowing equation:
Where Ti /ti and Tf /tf are the corrected temperatures (EC) and the times (min) associatedwith the system at ignition and at the start of equilibrium, respectively, rα and rβ are the rates oftemperature change (EC min-1) before ignition and during equilibrium, and where t60 is the time atwhich 60% of the overall temperature change has occurred. The state of equilibrium is said tooccur when, after ignition, the change in the observed temperature becomes constant for a periodof 5 minutes. Corrected temperature values are to be applied according to the table below:
Table 1.1.Range (EC) Correction (EC) Range (EC) Correction (EC)
19.0 – 20.3 – 0.013 24.9 – 25.3 – 0.007
20.4 – 22.7 – 0.012 25.4 – 25.7 – 0.006
22.8 – 23.3 – 0.011 25.8 – 26.0 – 0.005
23.4 – 23.8 – 0.010 26.1 – 26.3 – 0.004
23.9 – 24.3 – 0.009 26.4 – 26.6 – 0.003
24.4 – 24.8 – 0.008 26.7 – 27.8 – 0.002
Although the thermometer can read temperatures up to 35.000 EC, it is not expected thatreadings above those listed will be made. If required, a TA will provide you with the correctionsoutside this range.
The final correction that must be done concerns the ignition wire. In order to ignite thesample, a small amount of nickel/chromium fuse wire is used and is partially consumed. Thecorrection that is to be applied can be found simply by collecting all remaining portions of thefuse wire and measuring their length. For every 1.0 cm of fuse wire burned, a correction of 9.6joules is applied (as an exercise, determine if this correction is to be positive or negative andmake sure to point out your reasoning in your discussion of results).
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Materials
• 2000 mL volumetric flask• oxygen tank• Parr oxygen bomb calorimeter,
ignition unit, oxygen filling adaptor & accessories
• 2 – benzoic acid pellets• 2 – unknown sample pellets• distilled water• nickel/chromium wire • wire cutters• cloth (for drying items)
ProcedureParts A and B are each to be conducted in duplicate. If your results differ by more than 5 %, athird experiment should be conducted, time permitting.A. Bomb Standardization1. The TA will provide you with two benzoic acid pellets (0.7 – 1.0 g) (or you will help
prepare pellets) and introduce you to some important aspects of the bomb calorimeter.2. Determine the mass of a sample pellet and then transfer it to a fuel capsule.3. Place the oxygen bomb head on the bomb head support stand, then put the fuel capsule
with the sample in the electrode loop.4. Cut about 10 cm of nickel/chromium wire and affix to the bomb
head by placing the ends of the wire through the eyelets in eachelectrode (see right). Make sure that (i) the wire touches the topof the sample pellet and (ii) does not touch the sides of the fuelcapsule.
5. Add approximately 1 mL of distilled water to the bottom of thebomb and fill the 2000 mL volumetric flask with distilled water.
6. Open the gas valve on the top of the bomb head, carefully transferthe bomb head into the oxygen combustion bomb, screw on thelid until it is hand tight, then close the gas valve.
7. Fill the bomb with about 25 atm of O2 (ask the TA to show youhow to do this the first time). Slowly purge the O2 and refill the bomb to a pressure ofabout 25 atm once more.
8. Place the bomb into the calorimeter bucket and connect the ignition wires to the terminalsockets.
9. Slowly fill the calorimeter bucket, using all of the distilled water in the volumetric flask.Once done, place the lid on the calorimeter and attach the drive belt.
10. Let the system stand for about 2 minutes, then turn on the stirring motor and begin to taketemperature readings (see Data Sheet).
11. Attach the unconnected lead wire to the common terminal (the other should already be inthe 10 cm binding post of the ignition unit).
12. When t = 3.0 min, depress the black button on the ignition unit for 3 – 4 seconds. The redlight should come on for about half a second.
13. Continue to take measurements as outlined on the data sheet until the equilibrium periodhas been established (i.e., you can stop once the temperature change becomes constantover a period of 5 minutes).
19
14. Disconnect the lead wire from the common terminal, take off the calorimeter lid, wipe theend of the thermometer with the cloth provided and place lid onto appropriate stand.
15. Using the lifting handle, take the bomb partially out of the bucket (enough to expose theoutsides of the terminal sockets to air), disconnect the ignition wires from the terminalsockets, and place the bomb on the counter top.
16. Without directly touching the bucket (you can touch the handle, for anything else use acloth), dump the water out of it, and dry it and everything else that is wet with a cloth.
17. Slowly vent the gases from the bomb, then disassemble it, placing the bomb head on theappropriate stand.
18. Measure the amount of unburned wire, dry the insides of the bomb and remove any metaloxide deposits from the bomb interior, electrodes and fuel capsule by gentlysnipping/rubbing them with the wire cutters.
NOTE: If the sample did not completely combust, the TA will instruct you on how to dispose ofthe remainder.
B. Determination of Unknown Sample1. The TA will provide you with one unknown sample, which you will press into two pellets
(record the code number). Repeat the steps above using the unknown sample.
Results1. Complete the data sheets on pages 20 – 21.2. Create plots of temperature versus time and determine the parameters in [6].3. Determine the corrected values for Ti and Tf according to Table 1.1.4. Calculate and then tabulate: ∆T and the correction for consumed fuse wire for all trials, C
for part A, and ∆cH for part B. You may assume that ∆cU – ∆cH.5. Determine average values for C and ∆cH. For each, calculate the percent difference
between your two best readings.6. Determine the identity of the unknown sample (see Table 1.2). Determine the percent
error of your experiment.
Table 1.2.Compound Formula M (g mol-1) ∆cHE (kJ g-1)
Benzoic Acid C6H5COOH 122.12 – 26.43
Salicylic Acid C6H4(OH)COOH 138.12 – 21.90
Dibenzil (C6H5CH2)2 182.26 – 41.47
Hexamethylbenzene C6(CH3)6 162.27 – 43.95
Naphthoic Acid C11H8O2 172.18 – 29.68
Naphthalene C10H8 128.17 – 40.26
20
Lab Questions 1. After filling the bomb to a pressure of about 25 atm, why was the gas vented and refilled?
What possible side reaction does this action help reduce? Explain.2. What was the purpose of adding 1 mL of distilled water to the bottom of the bomb?3. A student uses a bomb calorimeter and obtains the following data:
Run Compound Sample Weight Initial T (oC) Final T (oC)
Calibration benzoic acid (s) 0.3182 g 24.43 25.67
Sample phenol (s) 0.5118 g 24.61 27.06
(a) Determine the specific heat of the calorimeter.(b) Calculate the molar enthalpy of combustion of adipic acid, and compare (% difference) to
the most recent literature values.
References1. Atkins, Peter. Physical Chemistry, 7th edition Chapters 2 and 3 (or 8th edition Chapter 2).2. Shoemaker, David P. and Garland, Carl W. (1970). Experiments in Physical Chemistry.
(McGraw Hill).3. The Parr Instrument Company, Manuals 204M, 205M, and 207M4. NIST Chemistry WebBook. http://webbook.nist.gov/chemistry/
Recommended ReadingSmall sections on calorimetry and thermochemistry in Lectures 6-8; corresponding sections inAtkins. See the back of the book for useful tables of thermodynamic constants.
21
Dat
a Sh
eets
A.
Mas
s of b
enzo
ic a
cid
pelle
t: tri
al #
1 __
____
____
g
trial
#2
____
____
__ g
trial
#3
____
____
__ g
Tria
l #1
Tria
l #2
Tria
l #3
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
06.
50
6.5
06.
5
17
17
17
27.
52
7.5
27.
5
38
38
38
3.25
8.5
3.25
8.5
3.25
8.5
3.5
93.
59
3.5
9
3.75
9.5
3.75
9.5
3.75
9.5
410
410
410
4.25
10.5
4.25
10.5
4.25
10.5
4.5
114.
511
4.5
11
4.75
124.
7512
4.75
12
513
513
513
5.5
145.
514
5.5
14
615
615
615
22
Dat
a Sh
eets
B.
Mas
s of u
nkno
wn
sam
ple
pelle
t:tri
al #
1 __
____
____
gtri
al #
2 __
____
____
gtri
al #
3 __
____
____
g
Tria
l #1
Tria
l #2
Tria
l #3
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
t (m
in)
T (E
C)
06.
50
6.5
06.
5
17
17
17
27.
52
7.5
27.
5
38
38
38
3.25
8.5
3.25
8.5
3.25
8.5
3.5
93.
59
3.5
9
3.75
9.5
3.75
9.5
3.75
9.5
410
410
410
4.25
10.5
4.25
10.5
4.25
10.5
4.5
114.
511
4.5
11
4.75
124.
7512
4.75
12
513
513
513
5.5
145.
514
5.5
14
615
615
615
23
dpdT
'∆S∆V [1]
dpdT
'∆HT∆V [2]
EXPERIMENT 2VAPOUR PRESSURE OF PURE LIQUIDS
IntroductionIn this experiment, the relationship between the vapour pressure of pure liquids (methanol
and ethanol) and temperature is studied. From careful experiments measuring the vapourpressure with respect to temperature, the molar enthalpies of vaporization (in kJ mol-1) can bedetermined for both methanol and ethanol.
When a pure liquid is placed in an evacuated bulb, molecules leave the liquid phase andenter the gas phase until the vapour pressure in the bulb reaches a definite value. This isdetermined by the nature of the liquid and its temperature. This pressure is called the vapourpressure of the liquid at a given temperature. The vapour pressure of a pure liquid isindependent of the quantity of liquid and vapour present, as long as both phases exist inequilibrium with each other at the specified temperature. If the temperature increases, the vapourpressure also increases up to the critical point, where the two phases become a singlehomogeneous, one-phase supercritical fluid.
If the pressure above the liquid is maintained at a fixed value, then the liquid may beheated up to a temperature at which the vapour pressure is equal to the external pressure. At thispoint, vaporization will occur by the formation of bubbles in the interior of the liquid as well asat the surface. This is the boiling point of the liquid at the specified external pressure. Clearlythe temperature of the boiling point is a function of the external pressure; in fact, the variation ofthe boiling point with external pressure is seen to be identical with the variation of the vapourpressure with temperature.
It can be shown that a definite relationship exists between the values of pressure, p, andthe temperature, T, for a pure liquid and its vapour at equilibrium:
where:# dp and dT refer to infinitesimal changes in pressure and temperature for a pure
substance with both phases present in equilibrium.# ∆S and ∆V refer to the change in entropy, S, and volume, V, when one phase
transforms to the other at constant pressure and temperature.Since the change in state is isothermal, and ∆G is zero, ∆H - T∆S = 0. ∆S may be replaced by∆H/T, giving:
which is the Clapeyron equation. It is an exact expression which may be applied to phaseequilibria of all kinds, although it is presented here in terms of a liquid-vapour phase transition ofa pure substance (i.e., one component).
Since the enthalpy of vaporization, ∆vapH, is positive, and ∆V is positive for vaporization,the vapour pressure must increase with increasing temperature.
24
dpdT
'∆vapHTVg
[3]
dlnpd(1/T)
' &∆vapH
RRTpVg
' &∆vapH
ZR [4]
Z 'pVg
RT[5]
Z ' 1 %9pTc
128pc T1 &
6T 2c
T 2[6]
ln p ' &∆vapH
R1T
% C [7]
For vapour-liquid phase transition equilibria in the range of vapour pressures less than 1atm, one may make the following assumptions:1. The molar volume of the liquid is negligible in comparison to that of the vapour, so that
∆V = Vg, where Vg is the volume of the vapour. Therefore,
Since d ln p = dp/p, and d(1/T) = – dT/T 2, [1] can be rewritten in the form
where Z is the compressibility factor. The compressibility factor takes into account real gasbehaviour, thereby yielding increasingly accurate results for determining the change intemperature with pressure. The compressibility factor for the vapour is equal to:
The compressibility factor may also be calculated using the Berthelot equation:
where:Tc = critical temperaturepc = critical pressure
2. [4] is a convenient form of the Clapeyron equation. If the vapour is a perfect gas (Z = 1)and ∆vapH is independent of the temperature, then a plot of ln p vs. 1/T yields a straightline, the slope of which is equal to ∆vapH. For many liquids, ln p is essentially a linearfunction of 1/T, which implies at that ∆vapH/Z is almost constant.
The Clausius-Clapeyron equation, which is derived from the Clapeyron equation,relates the enthalpy of vaporization, ∆vapH, of a pure liquid to its vapour pressure at varioustemperatures:
where:ln p = the natural logarithm of the vapour pressure,∆vapH = the heat of vaporization,R = the gas constant, T = temperature (in K), andC = a positive constant.
This equation resembles a linear equation of the form: y = ax + b.
25
Materials
• rubber stopper assembly• tubing with two connectors• 10 mL syringe• 2 – 100 mL dual neck round bottom flasks• 4 – 600 mL beakers• 2 – thermometers (for water baths)• 15 mm washers• 3 – 100 mL beakers (1 for waste)
• 2 – plastic caps• gas chromatography septa• Vernier Lab Pro• Vernier gas pressure sensor• Vernier temperature probe• methanol• ethanol absolute
ProcedureA. Preparing for Data CollectionPressure and temperature will be measured using a pressure sensor and a temperature probe.1. Use the 600 mL beakers to prepare four water baths, one in each of the following
temperature ranges: 0 to 5 EC, 10 to 15 EC, 20 to 25 EC (use room temperature water),and 30 to 35 EC.
2. Prepare the temperature probe and pressure sensor for data collection:– Plug the temperature probe into Channel 2 of the Lab Pro.– Plug the pressure sensor into Channel 1 of the Lab Pro.– Assemble the apparatus as per Figure 2.1. Ensure that the stopcock is open, thestopper is tightly inserted into the round bottom flask, and plastic cap and septa aretightly screwed in place. Do not “Hulk Hogan” it! (i.e., use gentle force)
temperature probe
to pressure probe
syringe
plastic cap15 mm washersseptum
100 mL dual neckround bottom flask
600 mL beaker
Figure 2.1
26
3. Prepare the computer for data collection by opening the Chemistry with Computersfolder. Then open the file: Vapour Pressure (Exp. 10. Gas Pressure-Stainles.MBL). Thevertical axis will have pressure scaled from 90 to 135 kPa. The horizontal axis will havetemperature scaled from 0 to 50 EC.
4. Close the stopcock and immerse the round bottom flask into the room temperature (20 –25 EC) water bath. N.B.: Do not apply pressure to the rubber stopper, since this will alterthe pressure inside the round bottom flask, and ruin your results!
5. After 30 seconds or so, click on the Logger Pro software. This will provide areal time plot of the temperature and pressure readings. When equilibrium has beenreached (i.e., stable pressure and temperature readings), click “KEEP” on the Logger Prosoftware. The first pressure/temperature data pair is now stored. Record the p and T datapair for the empty flask on your data sheet (round to the nearest 0.1 kPa).
B. Measurement of vapour pressure of methanol: collection of data at room temperatureStarting with a water bath at (20 – 25 EC):1. Place the temperature probe in the water bath.2. Close the stopcock and immerse the flask into the water bath, with the entire flask
covered as shown in Figure 2.1. N.B.: In order to obtain accurate results, take the samecare as you did in part A in ensuring the caps and stopper are tightly sealed.
3. Pour about 10-15 mL of methanol into a 100 mL beaker. Draw 3 mL of methanol intoyour syringe. Briskly wipe off the syringe needle with a Kimwipe. N.B.: You mustconsult your TA on the proper use of a syringe – it is very important that air bubbles beremoved and that you have the proper volume in the syringe.
4. Gently insert the syringe needle through the septum and inject the 3 mL of methanol intothe round bottom flask.
5. Return the plunger of the syringe back to the 3 mL mark, ensuring that you do not passthis mark. Be careful here!
6. Gently remove the syringe from the septum.7. Monitor the pressure and temperature data. When the p and T readings stabilize, meaning
that the equilibrium between methanol liquid and vapour has been established, click“KEEP”. Record the pressure/temperature pair on your data sheet. Click on “KEEP”multiple times to record a series of data points from which you can calculate an average.
C. Measurement of vapour pressure of methanol: collection of data at other temperatures.Obtain pressure and temperature data in a similar manner by replacing the room temperaturewater bath with the 0 to 5 EC, 10 to 15 EC and 30 to 35 EC water baths. Pressure/temperaturedata pairs for all of these trials should be recorded on your data sheet. N.B.: Be sure to wait forpressure/temperature equilibration.
D. Measurement of vapour pressure of ethanol.Dispose of the methanol as instructed by the TA. Thoroughly clean and dry all of the glasswareand the syringe. Repeat the above steps using ethanol, and water baths with temperature rangesof 0 to 5 EC, 10 to 15 EC, 20 to 25 EC and 30 to 35 EC.
27
p2
T2
'p1
T1
∆vapHo
T,m . (87 J K &1 mol &1) Tbp
Results1. Fill out data sheet on the next page.2. To obtain the vapour pressures of methanol and ethanol, air pressures must be subtracted
from each of the measured pressure values. These corrected air pressures are determinedwith the following relationship derived from the perfect gas law:
# p1 is the atmospheric pressure (in kPa) of the empty flask and T1 is the temperature (inKelvin) of the room temperature water bath (part A).# T2 is the temperature of the water bath for any other measurements.# p2 is the corrected air pressure, which is what you will solve for.
3. Obtain the vapour pressures by subtracting the corrected air pressures from the measuredpressures.
4. For both methanol and ethanol, use Excel (or other appropriate spreadsheet program) toplot graphs of vapour pressure as a function of temperature (in Kelvin) from the fourdata pairs you collected.
5. Using Excel, plot ln p as a function of l/T for both methanol and ethanol. In each case,determine the enthalpy of vaporization from the slope, – ∆Hvap/R.
Lab Questions 1. (a) An approximate relationship between the enthalpy of vaporization and the normal
boiling point of a liquid (1 atm) is given by Trouton’s rule,
Predict the boiling point of C2F3Cl given that = 21.9 kJ mol-1. Compare to the∆vapHo
T,mliterature value of this compound by calculating the % difference.(b) Calculate the Trouton’s rule constant for methanol given that = 35.3 kJ mol-1∆vapH
oT,m
at 337.9 K. Explain why this value is different from that given in the equation above.2. At what temperature will water (Tbp = 100 oC) and chloroform (Tbp = 60 oC) have the same
vapour pressure?
References1. Atkins, Peter. Physical Chemistry. 7th edition. Chapter 6, Sections 6.1 and 6.2 or 8th editionChapter 4, Sections 4.1 and 4.2.2. Shoemaker, David P. and Garland, Carl W. (1970). Experiments in Physical Chemistry.(McGraw Hill).3. Thomson, G. W. Chem. Rev., 38, 1946: 1.
Recommended ReadingCompressibility factor, Z: Lecture 4; Critical pressures and temperatures: Lecture 4, end: seecritical constants and principle of corresponding states at end of lecture; Trouton’s Rule: Lecture11; Clausius-Clapeyron equation: Lecture 14, end (Liquid-Vapour boundaries)
28
Dat
a Sh
eet
Em
pty
Flas
k:Pr
essu
re:
____
____
____
__Te
mpe
ratu
re:
____
____
____
__
Tria
l#1
(roo
m te
mp.
)#2
(0 E
C to
5 E
C)
#3 (1
0 EC
to 1
5 EC
)#4
(30 EC
to 3
5 EC
)
Subs
tanc
eC
H3O
HC
2H5O
HC
H3O
HC
2H5O
HC
H3O
HC
2H5O
HC
H3O
HC
2H5O
H
Tem
p. (E
C)
Tem
p. (K
)
Mea
sure
d pr
essu
re(k
Pa)
Cor
rect
ed a
irpr
essu
re (k
Pa)
Vap
our p
ress
ure
(kPa
)
29
dG ' γdA & ΠdV [1]
&MγMV A
'MΠMA V
[2]
EXPERIMENT 3SURFACE TENSION OF n-BUTANOL AND AMOUNT ADSORBED
IntroductionSurface Tension
A surface is an interface between two phases, and may be one or more molecular layers thick.In principle, concepts of equilibrium concentrations and thermodynamic properties can be appliedto treat surfaces in the same general way as all other phases of matter.
Within a liquid, all molecules experience very similar intermolecular interactions, beingpushed and pulled with equal force from all sides. However, at the gas-liquid interface or surfaceof a liquid, the molecules do not experience the same forces as those “buried” below the surface.These surface molecules experience only the forces from molecules within the bulk phase andessentially nothing from the other side of the interface; correspondingly, these molecules have ahigher chemical potential (µ) than those below the surface. Therefore, increasing the surface areaof a liquid requires an input of energy, and liquids have a tendency to minimize their surface areasby retaining the maximum possible number of molecules in the bulk volume. This gives rise to aunique property of liquid–gas interfaces, known as surface tension, which may be measured usinga variety of different techniques. Surface tension, γ, is commonly expressed as a force per unitdistance (e.g., N m-1) or an energy per unit area (e.g., J m-2). This corresponds to the minimum work(reversible work) needed to increase the surface by one unit of area.
Let us consider a solution with N moles of solute. The solute exists in two regions in thesolvent: (i) in the bulk “interior” of the solvent and (ii) at the surface or “interface” of the solvent.The solution has a uniform concentration right up to the surface region, with bulk concentrationNV/V = c (units of moles per unit volume). In the surface region, there is a solution with a slightlyhigher concentration (i.e., excess of solute compared to the bulk phase), with a surfaceconcentration NA/A = u (units of moles per unit area).
Any system at constant T and p seeks a state of lowest free energy, and the maximum workdone by the system is equal to the free energy decrease. In the case of solute/solvent mixtures,equilibrium conditions are reached when the free-energy decrease due to lowering surface tensionis balanced by an opposing tendency for free-energy increase due to increasing non-uniformity ofthe solute near the surface.
Imagine a solution of volume (V), surface area (A), bulk concentration (c), surfaceconcentration (u), surface tension (γ), and bulk osmotic pressure (Π), all at constant p and T. Forarbitrary changes in the area and volume of the solution (i.e., dA and dV), the free-energy change canbe written as
This is an exact differential (see Further Information 1 in Atkins, Physical Chemistry, 6th or 7th
Edition). Thus, from the reciprocity relation, we may write
Since at constant p and T, the surface tension and osmotic pressure are completely determined by
30
&MγMc
McMV A
'MΠMc
McMA V
[3]
c 'N & uA
V [4]
McMV A
' &cV
McMA V
' &uV [5]
Π 'NV
RT ' cRT [6]
dΠdc
' RT [7]
uc
' &1
RTdγdc [8]
u ' &1
RTdγ
d(lnc)or dγ
d(lnc)' & uRT ' &
NA RTA
[9]
the bulk concentration, we can rewrite [2] as
If the total number of moles of solute is N = cV + uA, then
This can be differentiated with respect to volume and area to yield:
As well, for a perfect solute, the osmotic pressure can be calculated from
which can be differentiated with respect to concentration to yield
If we combine [3], [5] and [7], we obtain the following expression:
which is known as the Gibbs isotherm. It can also be recast in the more useful forms below:
This derivation implies that the surface tension of a solution differs from that of the puresolvent because of the adsorption of solute. If there is no adsorption of solute, γ doesn’t change. Ifthere is adsorption of excess solute at the surface (solute attracted to the surface), γ decreases as theconcentration c of solute in the solution is increased. This is a well known behaviour of a soapsolution which has lower surface tension than pure water. If the solute avoids the surface region(i.e., “negative adsorption”), γ will increase with increasing c, and the solution will have a greatersurface tension than the solvent. This commonly happens with ionic solutes in water which tend todecrease foam formation (for example, it is difficult to get soap suds in salt water or “hard” watercontaining Ca(HCO3)2).
If we plot surface tension against ln c, we can observe the following:1. If positive adsorption occurs the curve should have a negative slope.2. If the plot is linear, the derivative on the left side of [9] is constant, independent of c. The
amount of solute adsorbed per unit area must be constant, and while the concentration ofsolute in the solution is changing, the concentration in the surface region is not. This likelymeans that adsorption saturation has been reached, producing a complete monolayer of
31
γ1 % γ1,2 & γ2 < 0 [10]
γ1 '12
h %r3
rρg [11]
γ1 cosθ % γ1,2 & γ2 ' 0 [12]
γ1 cosθ '12
h %r3
rρg [13]
adsorbed solute on the surface. From the slope of a plot of γ vs. ln c, we can find NA/A andhence the number of molecules of solute per unit area in a complete monolayer.
All this can be done from surface tension measurements, with the aid of the secondlaw of thermodynamics, and without any direct determination of the amount adsorbed.
Determination of Capillary DiameterThe capillary rise method is used to study the change in surface tension as a function of
concentration for aqueous solutions of n-butanol. The objective is to show that the solute forms acomplete monolayer at the surface and find the area occupied by a molecule in that monolayer, usingthe Gibbs adsorption equation.
It is known that in the absence of external forces, a body of liquid tends to assume a shapeof minimum area. When a liquid is in contact with a solid surface, a specific surface free energyexists for the interface, or interfacial tension, γ1,2. A solid surface itself has a surface tension, γ2,which is often large in comparison with the surface tensions of liquids.
Suppose a liquid with surface tension, γ1, is in contact with a solid with surface tension, γ2.Then there is an interfacial liquid-solid surface tension, γ1,2. Under what circumstances will a liquidfilm freely spread over the solid surface and “wet” it? Wetting will happen if the free energy of theentire system decreases as the result of creating a liquid-solid interface, such that
If a capillary tube of radius, r, is dipped into a liquid with a surface tension γ and density ρ,and if the liquid wets the walls of the capillary so that it adheres to the walls with contact angle θ =0, then the height, h, of liquid in the capillary tube (measured as in Figure 1) is given by balancingthe upward force of surface tension against the downward force of the weight of the column ofliquid. This will give the equation,
where r/3 is a correction for the amount of liquid below the meniscus. However, if [10] is notobeyed, then we have
For some value of θ, the liquid will not tend to spread indefinitely on the solid surface but will tendinstead to give a “contact angle, θ”. This may be the case with aqueous solutions or water on glasssurfaces that are not entirely clean. [11] can then be rewritten as:
In practice, the contact angle finally attained is somewhat variable, depending on whether the liquidis advancing over the solid surface or receding from it. If the same height is obtained regardless ofwhether the liquid was allowed to rise from below or fall from above in the capillary, it may beassumed that [12] and [13] are almost certainly valid.
32
Figure 3.1
pipette bulbgraduatedcapillary tube
large test tube
two-holedstopper
Figure 3.2
Materials• 4 – 100 mL bottles• 200 mL volumetric flask• 100 mL graduated cylinder• 100 mL beaker• large test tube• 2-holed stopper• thermometer
• graduated capillary tube• 50 mL volumetric pipette• 10 mL graduated pipette• 2 pipette bulbs• tygon tubing (attached to vacuum)• tweezers• n-butanol
ProcedureAssemble the apparatus as shown in Figure 3.2. The capillary is stored in concentrated nitric acid.The capillary should be rinsed with water and dried with a vacuum hose and Kimwipes betweenmeasurements. Pour water into the large test tube to roughly match the scale shown in Figure 3.2.Adjust the capillary upward or downward until the outside liquid level is above the lowest graduationof the capillary.1. The height, h, is the distance between the water levels inside and outside of the capillary
tube. Determine h of the capillary rise for pure water at room temperature (take a minimumof 4 readings). Attach the bulb to the pressure inlet. Gently squeezing the bulb, force theheight of the column of liquid to near the top of the capillary tube. Then, while the bulb isstill compressed, remove it from the pressure inlet. The pressure release will allow thecolumn of liquid to fall to its equilibrium position. If there is not good agreement amongthese readings, clean the capillary using concentrated HNO3 and repeat the measurements.
2. In the 200 mL volumetric flask, prepare an aqueous solution of 0.8 M n-butanol (ρ(n-butanol) = 0.810 g mL-1). This is the starting solution used for consecutive dilutions.
3. Using a 50 mL Pasteur pipette, withdraw 50 mL of solution from the volumetric flask, andempty into a 100 mL bottle. The 100 mL bottle now contains 50 mL of 0.8 M solution.
33
Measure h for the 0.8 M solution in the bottle (as described in steps 1 and 2)4. Add distilled water to the volumetric flask to bring the solution level up to the mark. This
is now a 0.6 M solution of aqueous n-butanol. Again, withdraw 50 mL of the solution, andempty into a 100 mL bottle. Measure h for this solution as described in steps 1 and 2.
5. Repeat the above procedure of dilution and extraction to produce three more solutions, andmeasure h for each. Be sure to calculate the concentrations of these new solutions and recordthis data.
Calculations1. From the data obtained for pure water, calculate the capillary radius, r, [11], then calculate
the surface tension of each solution studied. For the n-butanol solution, one may assume thatthe density is equal to that of pure water. At 25 EC for pure water the surface tension is 72dyne cm-1 and the density is 0.9970 g cm-3.
2. Plot surface tension, γ, against the natural logarithm of the bulk molar concentration of n-butanol in the solution, c, and determine the slope.
3. Use the slope of the plot, with the aid of [9], to find the amount of n-butanol adsorbed inmoles per unit area (NA/A). Convert this to molecules per square Ångstrom, then find the“effective cross-sectional area” per n-butanol molecule of absorbed butanol in Å2.
Lab Questions 1. Explain the difference between capillary rise and capillary depression. 2. For the Hg-air interface on pyrex glass, the contact angle is 140o. Find the capillary
depression of Hg in contact with air at 20 oC with and inside diameter of 0.350 mm. At20 oC, ρ(Hg) = 13.59 g ml-1, γ(Hg) = 490 mJ m-2 and ρ(air) = 0.0012 g mL-1.
3. Two capillary tubes with inner radii of 0.600 mm and 0.400 mm are inserted into a liquidwith density of 0.901 g cm-3 in contact with air with density of 0.001 g mL-1. The differencebetween capillary rises between tubes is 1.00 cm. Assuming that the contact angle is zero,calculate the γ for this liquid.
References1. Atkins, Peter. Physical Chemistry. 7th edition, Chapter 6 or 8th edition Chapter 4.2. Alberty, Silbey. (2001). Physical Chemistry. 3rd edition. Chapter 6, Section 6.4.3. Shoemaker, David P. & Garland, Carl W. (1970) Experiments in Physical Chemistry.
Recommended ReadingSurface tension and capillary action: Lecture 15See also: corresponding notes in Atkins.
34
q ' C∆T [1]
∆dissHT 'qp
n[2]
EXPERIMENT 4HEAT OF REACTION IN SOLUTION:
CONSTANT PRESSURE CALORIMETER
IntroductionIn this experiment, a constant pressure calorimeter is used to determine the enthalpies of
dissolution for several common salts. This is accomplished by monitoring changes in temperaturewhile dissolution reactions are carried out in an adiabatic vessel. The energy change, q, for areaction that takes place in a calorimeter, can be determined by multiplying the net temperaturechange, ∆T, by the heat capacity of the calorimeter and its contents, C.
The calorimeter constant, C, of a calorimeter and its contents, can be determinedexperimentally by standardization procedures, and must be known in order to calculate the energychange in the form of heat, q, for a given reaction. Three different procedures that are available forstandardizing calorimeters are:1. Chemical standardization using a “TRIS” (tris(hydroxymethyl)aminomethane) sample.
This involves the precise and reproducible exothermic reaction of TRIS with 0.1 M HCl.2. Comparison standardization which involves the use of samples whose enthalpy changes
are known and whose thermochemical behaviour is similar to that of the unknown material.3. Electrical standardization which requires an electric heating probe, a uniform power
supply, a high precision voltmeter, and a precise interval timer.The heat capacity of the constant pressure calorimeter used in this experiment (including its
contents), can be determined by running several calibration trials where the calorimeter is operatedin the usual manner, but where the reactants release a known amount of energy. For example, a verywell controlled reaction of 0.5 g of TRIS, dissolved in 100 mL of 0.1 M HCl, will evolve 245.76 Jg-1 of TRIS at 25 EC. This standard value can be used to determine the heat capacity of thecalorimeter and its contents (see Procedure, part A).
This experiment is performed at constant pressure. The heat of dissolution at constantpressure, qp, is equivalent to the enthalpy change, ∆dissHT, at the mean reaction temperature. Molarenthalpies of dissolution, ∆dissHT, can be obtained from the following relationship:
where: ∆dissHT = molar enthalpy of dissolution at mean reaction temperature, T;n = quantity of sample used (in moles);q = heat (i.e., calorimetric energy change).
35
Materials
• solution calorimeter• multimeter• 500 mL volumetric flask• 100 mL beaker• 100 mL graduated cylinder• weighing dishes• 10 mL graduated pipette• pipette bulb
• scoopula• mortar and pestle• concentrated HCl• tris(hydroxymethyl)aminomethane (TRIS)• potassium iodide• potassium nitrate• potassium chloride• ammonium nitrate
ProcedureThe experimental procedure can be divided into two major sections. The first of these
sections involves the determination of the heat capacity of the calorimeter and its contents at constantpressure by a calibration with TRIS/HCl. The second section employs the average heat capacityfound in the initial standardization to determine the enthalpies of dissolution for three common saltsin water (choose 3 of the 4 available salts).
Calibration and Use of Calorimeter (TA will demonstrate this - so read carefully!)1. The multimeter should be properly connected to the constant pressure calorimeter, and
should be set to read voltage (i.e., ).&&&V2. When calorimeter is in “zero” mode, the multimeter should read 0.000 V. In the “null” mode
it should also read 0.000 V. In the “cal” mode the calorimeter should be adjusted until themultimeter reads 1.000 V (knob on upper right hand side of calorimeter labelled “cal”).Finally, in the “read” mode, the temperature settings on the calorimeter should be adjustedto bring the voltage on the multimeter to 0.000 V. In this way, temperatures can be readdirectly from the calorimeter.
3. Once calibrated, the calorimeter will be left in “read” mode for the remainder of theexperiment. All temperature measurements will be made by zeroing voltage, and thenreading the calorimeter.
4. Before reading temperatures, always allow voltages to stabilize.5. If the multimeter shuts itself off during the experiment (power saving function), simply
switch it off, and then back on again. This will restore its function.
Part A: Determination of the Calorimeter Constant (C)A sample of TRIS is dissolved in dilute HCl in a controlled reaction for which the amount
of heat evolved is known. This standardization is performed in triplicate to obtain an average ∆T.1.1. Using an analytical balance, mass out exactly 100.00 ± 0.50 g of 0.100 M HCl (prepared by
dilution from concentrated HCl) into a graduated cylinder (approximately 100 mL). Add thisto the Dewar inside of the calorimeter.
2.2. Weigh accurately 0.50 ± 0.01 g of TRIS in the 126C Teflon dish of the calorimeter (the saltshould be ground into powder using a mortar and pestle to ensure complete reaction).
36
T ' 0.63∆T % Ti [3]
q / (J) ' mTRIS / (g) [245.76/ (J g &1) % 1.436/ (J g &1 EC &1) (25.00 EC & T) ] [4]
C 'q∆T [5]
3.3. Assemble the rotating cell, and place it in the calorimeter. (This will be demonstrated byyour TA, and additional instructions are included in the document “Calorimeter Operation”that is provided with the experimental materials.)
4.4. Allow the reactants to come to thermal equilibrium (stable voltage) in the closed calorimeterwhile stirring. Once equilibrium is established, record the initial temperature, Ti, and startthe dissolution reaction (quickly push down rod without interrupting its rotation).
5. At this point an enthalpy change will take place in the calorimeter, and a temperature changewill be observed. When the temperature stabilizes in the calorimeter, stop stirring, andrecord the final temperature, Tf.
6. The calorimeter can now be opened. All parts should be cleaned and dried to prepare for thenext trial. If all of the solid has not been dissolved, the trial must be repeated.
7. Calculate the change in temperature, ∆T, for each trial and use it to calculate T, which isequal to the temperature at which 63% of the change has taken place.
8. Calculate the energy change for each trial using:
where q = energy change in Jm = mass of TRIS in gramsT = calibrated temperature (N.B.: The term: 1.436(25.00 EC - T) adjusts
the heat of reaction to temperatures above or below the 25 ECreference temperature).
9. Calculate the calorimeter constant for each trial using the equation:
10. Calculate an average calorimeter constant. This is the value that will be employed for theremainder of the experiment. (Note that we have assumed that the heat capacity of 100 g ofa dilute aqueous solution is equal to that of 100 g of pure water. This is a valid assumption,since the specific heat capacity of 0.1 M HCl at 25 EC is 4.180 J EC-1 g-1 and the specific heatcapacity of water is 4.184 J EC-1 g-1).
Part B: Determination of the Enthalpies of Dissolution for Salt Solutions1. Determine the average change in temperature, ∆T, for the dissolution of 0.50 ± 0.01 g of
three different ground salts in 100.00 g of distilled H2O. These three salts will be assignedto you by your TA, and will be chosen from KI, KNO3, KCl, and NH4NO3. Perform twotrials for each salt you are assigned using the same techniques as were used for the TRIS/HClcalibration.
2. Using [1] and [2] determine the energy change, q, and the enthalpy of dissolution, ∆dissHT, foreach of the salts.
3. Compare the values that you calculate with the enthalpies of dissolution of these salts (in kJ
37
mol-1), with those found in the literature, and calculate a percent error for each.
Lab Questions (use data tables in the back of Atkins).1. Calculate the enthalpy of solution, ∆solnHo, for dissolving sulfuric acid at 298 K.2. Calculate the standard enthalpy of formation of CaCl2, assuming infinite dilution.3. (a) Calculate the enthalpy of neutralization, ∆neutHo, of equimolar amounts of acetic acid and
sodium hydroxide. (b) Calculate the enthalpy of neutralization for the reactionH+ (aq) + OH- (aq) 6 H2O (l)
and compare to the first calculation. Comment on the similarity of the values.
References1. Atkins, Peter. (1998). Physical Chemistry. 7th edition or 8th edition, Chapter 2.2. Parr Instrument Co. Solution Calorimeter Instruction manual. 3. Alberty, Silbey. (2001). Physical Chemistry. 3rd edition. Chapter 2, Section 2.15.
Recommended ReadingThermochemistry: Lecture 8Accompanying problems; see also: Atkins, Chapter 2.
38
pA ' xAp (
A
pB ' xB p (
B
p ' xAp (
A % xB p (
B
p ' p (
B % (p (
A & p (
B )xA
EXPERIMENT 5LIQUID-VAPOUR EQUILIBRIUM IN A BINARY SYSTEM
IntroductionIn this experiment, the compositions of the vapour and liquid phases of several boiling
mixtures of cyclohexane and acetone are determined by refractive index measurements. Thesecompositions are then plotted against temperature to produce a liquid-vapour phase diagram for thisbinary system.
Distillation is a convenient technique for determining the liquid-vapour phase diagrams ofbinary liquid systems. When a homogeneous two-component liquid is distilled, the composition ofthe vapour is generally different from that of the liquid. The vapour pressures of the components ofan ideal solution of two volatile liquids are related to the composition of the liquid mixture byRaoult’s Law:
If we substitute these expressions into Dalton’s Law of Partial Pressures, p = pA + pB, we get thefollowing expression for the total vapour pressure, p, of the mixture:
Given that xA + xB = 1, we get:
where:# p is the total vapour pressure,# pA
* and pB* are the vapour pressures of pure A and B, respectively, and
# xA and xB are the mole fractions of A and B.
Raoult’s Law is an excellent approximation for binary liquid-vapour systems when the molefraction of one component is close to unity. Major deviations from Raoult’s Law occur when neithermole fraction is close to unity, or in considering the behaviour of the dilute component of the binarymixture. At constant temperature, if the vapour pressure of solution is higher than what is predictedby Raoult’s Law, the system exhibits a positive deviation. If the vapour pressure is lower, it is saidto exhibit a negative deviation. The positive and negative deviations arise from homogeneous (i.e.,A—A, B—B) and heterogeneous (i.e., A—B) molecular attractions, respectively. For example, apositive deviation implies that the homogeneous attractions are stronger than the heterogeneous ones.These deviations may be large enough to produce minima and maxima in vapour-pressure andboiling point curves, as shown in Figure 5.1.
39
Figure 5.1. Schematic vapour pressure and boiling point diagrams forsystems showing (a) a strong positive deviation and (b) a strong negativedeviation from Raoult's Law (from Shoemaker, Garland and Nibler, 6th
Ed.).
At the maxima or minima in these curves, the vapour and liquid compositions are the same,and there is a point of tangency between the curves L and V and L* and V* at the minima ormaxima. Such systems exhibiting these minima and maxima are called azeotropes, and are of majorimportance in connection with distillation. The point of tangency in the temperature-compositiondiagrams is called the azeotropic temperature, and represents a constant pressure and temperatureat which the two components of the binary mixture cannot be separated from one another bydistillation. Binary mixtures exhibiting the so-called “positive deviation” on the pressure-composition graphs are referred to as low-boiling azeotropes, since only the liquid phase existsbelow the azeotropic temperature. Similarly, binary mixtures exhibiting the “negative deviation”are referred to as high-boiling azeotropes, since only the vapour phase exists above this temperature.
40
Figure 5.2
Materials
• Abbe refractometer and light source• 2 – dual necked boiling flasks• condenser • 20 mL syringe• Variac• heating mantle• 2 – thermometers• one-holed rubber stopper
• 400 mL beaker• rubber septa • 10 mL graduated pipette• pipette bulb• 3 100 mL beakers• 2 – condenser hoses (Tygon)• acetone• cyclohexane
ProcedureA binary liquid-vapour phase diagram is to be constructed for the acetone-cyclohexane
system by carrying out distillations of several different mixtures of the two components anddetermining their liquid (mixture remaining in the distillation flask) and vapour (distillate)compositions at their boiling points. The boiling point temperatures of the samples can be plottedagainst the compositions of the liquid and vapour phases (2 plots) in order to produce the phasediagram, and from this the azeotropic composition and temperature can be determined.
Distillation1. Set up the distillation apparatus as shown in Figure 5.2 (Be sure to include grease and boiling
chips in this step). The rubber stopper should be fit tightly into the boiling flask to preventit from being dislodged during heating.
41
2. Carry out distillations. This will involve 10 mixtures of different compositions being heatedto boiling, and then sampled for refractive index measurements. The compositions of thesesamples are summarized in Table 5.1. To prepare the first 5 mixtures, simply add to theexisting mixture each time (as per Table 5.1) without emptying the flask. When the first 5mixtures have been distilled, the flask can then be emptied and washed to prepare for thenext 5 distillations. These mixtures can also be prepared in an additive fashion (i.e., nowashing in between samples).
Table 5.1Composition
Mixtures 1 – 5 Mixtures 6 – 101 25.0 mL cyclohexane 6 25.0 mL acetone2 add 2.5 mL acetone 7 add 1.5 mL cyclohexane3 add 3.0 mL acetone 8 add 5.0 mL cyclohexane4 add 7.0 mL acetone 9 add 4.0 mL cyclohexane5 add 9.0 mL acetone 10 add 5.0 mL cyclohexane
N.B.: Read this section carefully – a TA will demonstrate this portion of the procedurein the laboratory, so be sure you are very familiar with the following. To perform distillations,ensure that the top of the thermometer bulb is well below the sidearm leading to the condenser.Also, it is critical that the distillation proceeds at a slow rate so that both liquid and vapour arenear thermal and compositional equilibrium. In order to do this, the Variac should be set between60 and 90. N.B.: For the pure cyclohexane sample, the Variac may be set near 90, but for otherdistillations, the Variac should be adjusted downwards. It is important that cool water runsthrough the condenser throughout the experiment, and that the condenser is in its reflux positionwhen heating is started for each mixture. Additionally, temperature must be monitored closelyduring each distillation. N.B.: The flask can be “tapped” or “flicked” regularly to preventsuperheating and bumping of solution. Please ask your TA to demonstrate this!
Detailed Procedure for each Distillation1. When distillation is proceeding slowly (boiling has just begun, and the condenser is
dripping), the condenser should be twisted into its collecting position.2. When the condenser has collected a sufficient volume of distillate, the temperature should
be recorded, and the heating mantle should be removed from below the flask (safety first!).3. A cold water bath should then be used to replace the heating mantle. This will quickly cool
the mixture and stop the distillation. This should be done by bringing the cold water bath tothe boiling flask, and not vice versa, so that the distillate in the condenser is not spilled backinto the mixture below.
4. Sample the liquid mixture in the boiling flask first. This is accomplished by inserting asyringe through the septum of the apparatus, and drawing up a small volume of the mixture.
5. The refractive index of this portion can be immediately determined using the Abbe
42
refractometer (see below). This should be recorded as the “liquid” refractive index at thedetermined temperature.
6. Be sure to return the unused portion from the syringe back into the boiling flask (piercing theseptum again). N.B.: Ensure that the syringe is cleaned with acetone between samples.
7. The “vapour” (distillate) can then be sampled by inserting the syringe down into thecondenser.
8. Measure the refractive index of the distillate. These refractive indices can be used, alongwith Table 5.2, to determine the vapour and liquid compositions in mole % for all tenmixtures.
9. Finally, return the unused distillate to the boiling flask, twist the condenser into its refluxingposition, and proceed to the distillation of the next mixture. Discard all residues anddistillates into the waste bottle when you are finished with them.
Refractometer Operation1. Open the viewing chamber and clean it with a Kimwipe and acetone.2. Spread a thin film of the solution on the glass plate with the syringe. Do not touch the plate
with the syringe. Close the viewing chamber.3. Rotate the large knob on the right until the dark/light separation is close to the diagonal
crosshairs in the eyepiece.4. Rotate the smaller knob on the right to fine tune the position of the light/dark separation. 5. Read the refractive index on the upper scale using the central vertical line as a reference
point.6. Clean the glass plate with a Kimwipe and acetone immediately after taking a reading.
Results1. Determine the mole fraction for the liquid and vapour portions of each of the 10 mixtures by
referring to Table 5.2.2. On a single graph, make 2 plots of temperature as a function of the mole fraction of acetone.
One of these plots will be for the “vapour” and the other will be for the “liquid”.3. Determine the composition and boiling point of the azeotrope. As well, determine the
boiling points of each of the pure liquids. Compare these values to those given in theliterature.
4. Label the phases and components present in each area of the diagram, as well as the boilingtemperatures of the pure compounds.
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Lab Questions 1. From the data table below (Table Q5), prepare a liquid-vapour temperature-composition
phase diagram of the ethanol-ethylacetate system at 1 atm, using an Excel spreadsheet. Isit possible to distill pure ethyl acetate from a mixture containing x(CH3COOCH2CH3) =0.65? Explain.
Table Q5 - Data for Question in Experiment #5T (EC) x(CH3COOCH2CH3)l x(CH3COOCH2CH3)vap
78.3 0.000 0.000
76.6 0.050 0.102
75.5 0.100 0.187
73.9 0.200 0.305
72.8 0.300 0.389
72.1 0.400 0.457
71.8 0.500 0.516
71.8 0.540 0.540
71.9 0.600 0.576
72.2 0.700 0.644
73.0 0.800 0.726
74.7 0.900 0.837
76.0 0.950 0.914
77.1 1.000 1.000
References1. Atkins, Peter. Physical Chemistry. 7th edition. Chapter 8 or 8th edition Chapter 6.2. Shoemaker, David P. and Garland, Carl W. (1970). Experiments in Physical Chemistry.
(McGraw-Hill).3. Alberty, Silbey. (2001). Physical Chemistry. 3rd edition. Chapter 6, Section 6.5.
Recommended ReadingPartial pressures: Lecture 2; Raoult’s Law: Lecture 16Lever rule: Lecture 18; Liquid-liquid phase diagrams and azeotropes: Lecture 19
44
Table 5.2Mole%Acetone
nd25 Mole%
Acetonend
25 Mole%Acetone
nd25 Mole%
Acetonend
25
0.00 1.4238 25.00 1.4091 50.00 1.3919 75.00 1.3744
1.00 1.4233 26.00 1.4085 51.00 1.3912 76.00 1.3737
2.00 1.4228 27.00 1.4079 52.00 1.3905 77.00 1.3730
3.00 1.4222 28.00 1.4072 53.00 1.3898 78.00 1.3723
4.00 1.4217 29.00 1.4066 54.00 1.3891 79.00 1.3715
5.00 1.4211 30.00 1.4059 55.00 1.3883 80.00 1.3708
6.00 1.4206 31.00 1.4053 56.00 1.3877 81.00 1.3700
7.00 1.4200 32.00 1.4047 57.00 1.3873 82.00 1.3693
8.00 1.4195 33.00 1.4042 58.00 1.3866 83.00 1.3685
9.00 1.4189 34.00 1.4035 59.00 1.3859 84.00 1.3678
10.00 1.4183 35.00 1.4029 60.00 1.3852 85.00 1.3671
11.00 1.4177 36.00 1.4021 61.00 1.3845 86.00 1.3664
12.00 1.4171 37.00 1.4015 62.00 1.3838 87.00 1.3657
13.00 1.4165 38.00 1.4008 63.00 1.3831 88.00 1.3649
14.00 1.4159 39.00 1.4001 64.00 1.3824 89.00 1.3642
15.00 1.4153 40.00 1.3994 65.00 1.3815 90.00 1.3635
16.00 1.4147 41.00 1.3989 66.00 1.3808 91.00 1.3628
17.00 1.4140 42.00 1.3981 67.00 1.3801 92.00 1.3621
18.00 1.4134 43.00 1.3974 68.00 1.3794 93.00 1.3614
19.00 1.4128 44.00 1.3966 69.00 1.3786 94.00 1.3607
20.00 1.4122 45.00 1.3959 70.00 1.3779 95.00 1.3600
21.00 1.4116 46.00 1.3951 71.00 1.3772 96.00 1.3593
22.00 1.4110 47.00 1.3943 72.00 1.3764 97.00 1.3587
23.00 1.4104 48.00 1.3936 73.00 1.3759 98.00 1.3579
24.00 1.4098 49.00 1.3926 74.00 1.3751 99.00 1.3572
100.00 1.3563
