General ChemistryGeneral ChemistryReview for the MCATReview for the MCAT

Dr. Paul A. JellissDr. Paul A. JellissMonsanto Hall 114Monsanto Hall 114

(314) 977(314) 977--28342834jellissp@slu.edujellissp@slu.edu

MCATMCATMCAT

22

The MCAT: Basic StructureThe MCAT: Basic Structure

Verbal Reasoning:Verbal Reasoning:•• 85 minutes, 65 questions.85 minutes, 65 questions.

Physical Sciences Physical Sciences Physics & Physics & Gen. Chem.Gen. Chem.: : •• 100 minutes, 77 questions.100 minutes, 77 questions.

Writing Sample:Writing Sample:•• 30 minutes, 2 essays.30 minutes, 2 essays.

Biological Sciences Biological Sciences Organic & Biology:Organic & Biology:•• 100 minutes, 77 questions.100 minutes, 77 questions.

MCATMCATMCAT

33

The Essentials for ClassThe Essentials for ClassA functional brain:A functional brain:

Eye(s) & Ear(s):Eye(s) & Ear(s):

•• not yet turned to mush?not yet turned to mush?•• it might after this.it might after this.

•• preferably attached to aforementioned brain.preferably attached to aforementioned brain.

MCATMCATMCAT

Pen/pencil & notepaper:Pen/pencil & notepaper:•• to write stuff down when I suggest, to write stuff down when I suggest, e.ge.g. examples.. examples.•• we’ll try to make this at least a bit interactive to we’ll try to make this at least a bit interactive to

keep you awake.keep you awake.•• where else would you rather be early on a cold where else would you rather be early on a cold

February Saturday morning?February Saturday morning?

44

What can we do in 6 hours?What can we do in 6 hours?

MCATMCATMCAT

No way can we cover absolutely everything from No way can we cover absolutely everything from two semesters of general chemistry.two semesters of general chemistry.•• would you really want to relive that entire nightmare would you really want to relive that entire nightmare

anyway?anyway?We can look at key concepts from gen. chem. and We can look at key concepts from gen. chem. and try some examples which are MCATtry some examples which are MCAT--relevant.relevant.Most importantly, RELAX!Most importantly, RELAX!•• but don’t overbut don’t over--do it.do it.•• you will learn and test better under moderate anxiety.you will learn and test better under moderate anxiety.•• Freaking out won’t help!Freaking out won’t help!

55

General Chemistry on the General Chemistry on the MCATMCAT

Intermingled with physics in a Physical Intermingled with physics in a Physical Sciences section (total 77 questions in 100 Sciences section (total 77 questions in 100 minutes).minutes).•• ~75 seconds per question.~75 seconds per question.

Some passages, some free standing Some passages, some free standing questions: consider doing the latter first.questions: consider doing the latter first.Immediately following the verbal section Immediately following the verbal section before lunch.before lunch.

MCATMCATMCAT

66

Back to the Basics:Back to the Basics:Atomic StructureAtomic Structure

Atom: smallest unit of any element.Atom: smallest unit of any element.Subunits: Subunits: protonsprotons, , neutronsneutrons, , electronselectrons::•• protons and neutrons are protons and neutrons are neucleonsneucleons..

Atomic numberAtomic number ((ZZ): proton number:): proton number:•• identifies element, X.identifies element, X.•• charge of charge of +1+1..•• mass of ~1 mass of ~1 amuamu (1.66 (1.66 × × 1010––2727 kg).kg).

77

Back to the Basics:Back to the Basics:Atomic StructureAtomic Structure

Mass numberMass number ((AA): mass of the atom.): mass of the atom.AA = = ZZ protonsprotons + + NN neutronsneutrons = = ΣΣ nucleonsnucleons..NeutronsNeutrons: same mass as protons, no charge.: same mass as protons, no charge.Written as superscript before the element Written as superscript before the element symbol:symbol:

AAZZ XX

##electronselectrons = = ZZ in a in a neutralneutral atom!atom!

88

Isotopes, Atomic Weight, and Isotopes, Atomic Weight, and IonsIons

Atomic weight (not atomic mass) Atomic weight (not atomic mass) –– what’s the what’s the difference?difference?Weighted average of masses of naturally Weighted average of masses of naturally occurring isotopes.occurring isotopes.Ions: Ions: gaingain or or lossloss of electrons of electrons –– anionanion or or cationcation..

77 99

What is an What is an isotopeisotope??Two atoms of the same element that differ in Two atoms of the same element that differ in their number of neutrons:their number of neutrons:•• 44Be and Be and 44Be.Be.

99

Average Atomic WeightAverage Atomic Weight

Element X has two isotopes of atomic mass Element X has two isotopes of atomic mass 38.6 and 42.6 in 1:3 relative abundance.38.6 and 42.6 in 1:3 relative abundance.What is the atomic weight of X?What is the atomic weight of X?

•• 42.642.6•• 41.741.7•• 40.640.6•• 39.7 39.7

1010

Isotopes, Atomic Weight, and Isotopes, Atomic Weight, and Ions Ions –– ExampleExample

An atom contains 16 protons, 17 neutrons, An atom contains 16 protons, 17 neutrons, and 18 electrons. Which of the following and 18 electrons. Which of the following best indicates this atom?best indicates this atom?

•• 3333ClCl––

•• 3434ClCl––

•• 3333SS22––

•• 3434SS22––

1111

Quantum Numbers:Quantum Numbers:Electron Zip CodeElectron Zip Code

What is the purpose of quantum numbers?What is the purpose of quantum numbers?Quantum numbers designate a unique “zip Quantum numbers designate a unique “zip code” for each electron in an energy level.code” for each electron in an energy level.No two can have same zip code.No two can have same zip code.How many quantum numbers in a zip code?How many quantum numbers in a zip code?One zip code One zip code four quantum numbers.four quantum numbers.•• shellshell, , subshellsubshell, , orbitalorbital, , spinspin..

1212

The First Quantum NumberThe First Quantum Number

What does it designate? What is its symbol?What does it designate? What is its symbol?Principal quantum number designates the Principal quantum number designates the shellshell(symbol is (symbol is nn).).Related to the size and energy of an orbital (a Related to the size and energy of an orbital (a three dimensional region around the nucleus in three dimensional region around the nucleus in which the electron is likely to be found).which the electron is likely to be found).What are the possible values?What are the possible values?nn = 1, 2, 3, 4, 5...∞ (higher values are higher in = 1, 2, 3, 4, 5...∞ (higher values are higher in energy and farther from nucleus).energy and farther from nucleus).

1313

The Second Quantum NumberThe Second Quantum Number

What does it designate? Symbol?What does it designate? Symbol?SubshellSubshell number (symbol is number (symbol is ll) describes shape ) describes shape of electron’s orbital.of electron’s orbital.Values?Values?ll = 0, 1, 2,…= 0, 1, 2,…n n –– 1 (If 1 (If n n = 3, then = 3, then ll = 0, 1, or 2).= 0, 1, or 2).ss, , pp, , dd, and , and ff subshellssubshells correspond to correspond to l l values of values of 0, 1, 2, and 3 respectively.0, 1, 2, and 3 respectively.SubshellsSubshells have shape have shape –– what are they?what are they?

1414

The Second Quantum NumberThe Second Quantum NumberShapes mnemonic easy to remember:Shapes mnemonic easy to remember:ss is for is for ssphericalpherical dd is for is for ddaisyaisypp is for is for ppeanuteanut ff is for is for ff------ed up! ed up!

1515

The Third Quantum NumberThe Third Quantum Number

What does it designate? Symbol?What does it designate? Symbol?OrbitalOrbital number (symbol is number (symbol is mmll ) describes the ) describes the three dimensional orientation of an orbital.three dimensional orientation of an orbital.Values?Values?Value of Value of mmll = = ––l...0...l...0...++l l inclusive.inclusive.•• If If l l = 0, then = 0, then mmll = 0= 0•• If If l l = 1, then = 1, then mmll = = ––1, 0, 11, 0, 1•• If If l l = 2, then = 2, then mmll = = ––2, 2, ––1, 0, 1, 21, 0, 1, 2

1616

The Fourth Quantum NumberThe Fourth Quantum Number

What does it designate? Symbol?What does it designate? Symbol?SpinSpin number (symbol is number (symbol is mmss ) designates ) designates electron’s intrinsic magnetism.electron’s intrinsic magnetism.Values?Values?Value of Value of mmss = = ++ or or –– only.only.11

221122

Every orbital can accommodate 2 electrons.Every orbital can accommodate 2 electrons.If an orbital is full, the electrons it holds are If an orbital is full, the electrons it holds are “spin“spin--paired”.paired”.

1717

Assigning Quantum Numbers: RulesAssigning Quantum Numbers: RulesAufbauAufbau principle: What is it?principle: What is it?Electrons occupy the lowest energy Electrons occupy the lowest energy orbitalsorbitalsavailable:available:

Hund’sHund’s Rule: Basic point?Rule: Basic point?Electrons in same Electrons in same subshellsubshell occupy available occupy available orbitalsorbitals singly before pairing up.singly before pairing up.PauliPauli Exclusion Principle: Think exclusion?Exclusion Principle: Think exclusion?No two electrons can have same set of four No two electrons can have same set of four quantum numbers.quantum numbers.

•• 11ss--22ss--22pp--33ss--33pp--44ss--33dd--44pp--55ss--44dd--55pp--66ss--44ff--55dd--66pp--77ss--55ff--66dd--77pp--

1818

1s

2s 2p

3s 3p 3d

4s 4p 4d 4 f

5s 5p 5d 5 f6s 6p 6d

7s 7p

Assigning Quantum Numbers: RulesAssigning Quantum Numbers: Rules

Fill

in o

rder

of i

ncre

asin

g Fi

ll in

ord

er o

f inc

reas

ing

nn+ +

ll

1919

Ground State Electron Ground State Electron ConfigurationsConfigurations

Use previous three rules to write.Use previous three rules to write.How would oxygen look?How would oxygen look?11ss2222ss2222pp44

Frequently, shortcut designations are used Frequently, shortcut designations are used instead of writing out the entire configuration instead of writing out the entire configuration –– P for example:P for example:•• [Ne]3[Ne]3ss2233pp33

2020

Electron Configurations: Electron Configurations: AnomaliesAnomalies

Sometimes the anticipated electron Sometimes the anticipated electron configuration is not the actual one: stability configuration is not the actual one: stability through through filledfilled or or halfhalf--filledfilled subshellssubshells..What are some exceptions?What are some exceptions?The exceptions: Cr, Cu, Mo, Ag, Au.The exceptions: Cr, Cu, Mo, Ag, Au.What is Cr expected?What is Cr expected?[Ar]4[Ar]4ss2233dd44

But what is it really?But what is it really?Cr actual: [Ar]4Cr actual: [Ar]4ss1133dd55

2121

Electron Configurations: IonsElectron Configurations: Ions

Anions accommodate the gained electrons in Anions accommodate the gained electrons in the first available orbital with the lowest the first available orbital with the lowest available energy.available energy.F (F (ZZ=9) has =9) has configconfig. 1. 1ss2222ss2222pp55 while Fwhile F–– has has configconfig. 1. 1ss2222ss2222pp66

•• configuration exactly like configuration exactly like NeNe (F(F–– and and NeNe are called are called isoelectronicisoelectronic).).

•• isoiso-- = same, = same, --electronic = configuration.electronic = configuration.

2222

Electron Configurations: IonsElectron Configurations: Ions

CationsCations lose electrons from the most unstable lose electrons from the most unstable orbital: How would Liorbital: How would Li++ look?look?Li (Z = 3) has Li (Z = 3) has configconfig. 1. 1ss2222ss11 and Liand Li++ has has configconfig. 1. 1ss22

How about TiHow about Ti++??For transition metals, the valence For transition metals, the valence ss electrons electrons are always lost first, before any are always lost first, before any dd electrons.electrons.TiTi++ ((ZZ = 22) expected [Ar]3= 22) expected [Ar]3dd1144ss22 but Tibut Ti++

actually: [Ar]3actually: [Ar]3dd2244ss11

2323

Electron Configurations: Electron Configurations: ExamplesExamples

Which of the following gives the electron Which of the following gives the electron configuration of an aluminum atom?configuration of an aluminum atom?•• 11ss2222ss2222pp11

•• 11ss2222ss2222pp22

•• 11ss2222ss2222pp6633ss2233pp11

•• 11ss2222ss2222pp6633ss2233pp22

2424

Electron Configurations: Electron Configurations: ExamplesExamples

What is the electron configuration of an atom What is the electron configuration of an atom of copper?of copper?Remember, Cu is an exception!Remember, Cu is an exception!Expected: [Ar]3Expected: [Ar]3dd9944ss22

Actual: [Ar]3Actual: [Ar]3dd101044ss11

MoralMoral: beware of stability in transition metals!: beware of stability in transition metals!

2525

Diamagnetic and Paramagnetic Diamagnetic and Paramagnetic AtomsAtoms

DiamagneticDiamagnetic: all electrons are spin paired : all electrons are spin paired (even number of electrons):(even number of electrons):•• atom repelled by a magnetic field.atom repelled by a magnetic field.

ParamagneticParamagnetic: not all electrons are spin: not all electrons are spin--paired:paired:•• atom attracted by a magnetic field.atom attracted by a magnetic field.

Know the difference Know the difference –– these are easy points!these are easy points!

2626

Electron Energy Levels and Electron Energy Levels and SpectraSpectra

Ground stateGround state: define?: define?•• Lowest possible energy.Lowest possible energy.

Excited stateExcited state??•• At least 1eAt least 1e–– in higher energy level.in higher energy level.

Absorption: + or Absorption: + or –– energy change?energy change?•• Incoming photon absorbed by electron, jumping to Incoming photon absorbed by electron, jumping to

higher energy level.higher energy level.Emission: + or Emission: + or –– energy change?energy change?•• Electron dropping to lower energy level emits Electron dropping to lower energy level emits

photon.photon.

2727

Electron Energy Levels and Electron Energy Levels and SpectraSpectra

Formula for the energy of a photon?Formula for the energy of a photon?•• EE = = hhνν = = hchc//λλ…define the terms!…define the terms!•• Planck’s constant, Planck’s constant, hh = 6.63 = 6.63 ××1010––3434 JJ..ss

Emission Emission vsvs. absorption spectra: What’s the . absorption spectra: What’s the difference?difference?•• EmissionEmission: electrons dropping to lower energy : electrons dropping to lower energy

levels emit light of specific frequencies which are levels emit light of specific frequencies which are separated into bright lines by a prism.separated into bright lines by a prism.

•• AbsorptionAbsorption: specific frequencies of white light are : specific frequencies of white light are absorbed by gaseous element based on differences absorbed by gaseous element based on differences between quantized energy levels between quantized energy levels –– dark bands.dark bands.

2828

Electromagnetic SpectrumElectromagnetic Spectrum

From lowest to highest energy level?From lowest to highest energy level?RadiowavesRadiowaves microwaves microwaves infrared infrared visible light visible light ultraviolet ultraviolet XX--rays rays gamma gamma rays.rays.Visible light, from lowest to highest frequency?Visible light, from lowest to highest frequency?Red Red orangeorange yellowyellow greengreen

blueblue indigoindigo violetviolet•• RROOYYGGBBIIVV

Trends are important, not values.Trends are important, not values.

2929

Nuclear Structure and DecayNuclear Structure and Decay

Protons and neutrons held together by strong Protons and neutrons held together by strong nuclear force which overcomes the electrical nuclear force which overcomes the electrical repulsion between the protons.repulsion between the protons.What is radioactive decay?What is radioactive decay?Unstable nuclei undergo a transformation by Unstable nuclei undergo a transformation by altering the number and ratio of protons and altering the number and ratio of protons and neutrons or lowering their energy.neutrons or lowering their energy.What are parent and daughter nuclei?What are parent and daughter nuclei?Anyone done the different types in class?Anyone done the different types in class?

3030

Alpha Decay: Alpha Decay: αα

An alpha particle, denoted by An alpha particle, denoted by αα, consists of , consists of 2 2 protonsprotons and and 2 neutrons2 neutrons, equivalent to a He , equivalent to a He nucleus, which is ejected.nucleus, which is ejected.Alpha decay reduces the parent’s atomic Alpha decay reduces the parent’s atomic number by 2 and mass number by 4.number by 2 and mass number by 4.210210

8484Po Po + + 4422HeHe

∆∆ZZ = = ––2, 2, ∆∆AA = = ––44

2062068282PbPb

3131

Beta Decay: Beta Decay: ββ––

When unstable nucleus contains too many When unstable nucleus contains too many neutrons, it may convert a neutron into a neutrons, it may convert a neutron into a proton and an electron (proton and an electron (ββ–– particle) which is particle) which is ejected: ejected: 11

00n n 1111pp + + 00

––11ee––

Atomic number of daughter nucleus is 1 Atomic number of daughter nucleus is 1 greater than parent, but mass number same.greater than parent, but mass number same.1414

66C C + + 00––11ee––

∆∆ZZ = +1, = +1, ∆∆AA = 0= 0

141477NN

3232

Positron Decay: Positron Decay: ββ++

When unstable nucleus contains too few When unstable nucleus contains too few neutrons, it may convert a proton into a neutron neutrons, it may convert a proton into a neutron and positron (and positron (ββ++ particle) which is ejected: particle) which is ejected: 11

11p p 1100n n + + 00

+1+1ee++

Positron is electron’s antiparticle Positron is electron’s antiparticle –– identical to identical to electron, but charge is positive.electron, but charge is positive.Atomic number of daughter nucleus is 1 less Atomic number of daughter nucleus is 1 less than parent, but mass number same.than parent, but mass number same.1818

99F F + + 00+1+1ee++1818

88OO

∆∆ZZ = = ––1, 1, ∆∆AA = 0= 0

3333

Electron CaptureElectron Capture

Conversion of a proton into a neutron by an Conversion of a proton into a neutron by an unstable nucleus by capturing an electron (unstable nucleus by capturing an electron (ee––) ) from the closest shell: from the closest shell: 11

11p p + + 00––11ee–– 11

00nnAtomic number of daughter nucleus is 1 less Atomic number of daughter nucleus is 1 less than parent, but mass number same than parent, but mass number same –– just like just like positron emission.positron emission.5151

2424Cr + Cr + 00––11ee–– 5151

2323VV

∆∆ZZ = = ––1, 1, ∆∆AA = 0= 0

3434

Gamma Decay: Gamma Decay: γγ

Nucleus in excited state (often after alpha or Nucleus in excited state (often after alpha or beta decay) emits energy in form of photons of beta decay) emits energy in form of photons of electromagnetic radiation.electromagnetic radiation.Gamma photons (Gamma photons (γγ rays) have neither mass nor rays) have neither mass nor charge, and their ejection changes neither charge, and their ejection changes neither atomic mass or number.atomic mass or number.3131

1414Si Si 31311515P + P + ββ–– ++ γγ

∆∆ZZ = 0, = 0, ∆∆AA = 0= 0

31311515PP

3535

Radioactive Decay: ExampleRadioactive Decay: Example

Radioactive calciumRadioactive calcium--47, a known 47, a known ββ–– emitter, is emitter, is administered in form of administered in form of 4747CaClCaCl22 by I.V. as a by I.V. as a diagnostic tool to study calcium metabolism. diagnostic tool to study calcium metabolism. What is the daughter nucleus of What is the daughter nucleus of 4747CaCa2+2+??•• 4646KK++

•• 4747KK++

•• 4747CaCa2+2+

•• 4747ScSc2+2+

3636

Radioactive Decay: ExampleRadioactive Decay: Example

Memory device:Memory device:•• ββ++ decay starts with decay starts with protonproton and makes it a and makes it a neutronneutron..•• ββ–– decay starts with decay starts with neutronneutron and makes it a and makes it a protonproton..

3737

Radioactive Decay: Half LifeRadioactive Decay: Half Life

What is a halfWhat is a half--life?life?The time it takes for oneThe time it takes for one--half of some sample half of some sample of radioactive substance to decay.of radioactive substance to decay.Shorter half lives mean faster decay.Shorter half lives mean faster decay.Half life denoted by Half life denoted by tt1/2.1/2.

Make a chart to solve these problems Make a chart to solve these problems –– forget forget the formula unless you do ethe formula unless you do e--functions in your functions in your head!head!

3838

Radioactive Decay: Half LifeRadioactive Decay: Half Life

TimeTime Amount of Sample Amount of Sample RemainingRemaining

00 100 %100 %

1 half1 half--life life tt1/21/2 1/2 = 50 %1/2 = 50 %

22 halfhalf--lives lives 22tt1/21/2 (1/2)(1/2)22 = 1/4 = 25 %= 1/4 = 25 %

33 halfhalf--lives lives 33tt1/21/2 (1/2)(1/2)33 = 1/8 = 12.5 %= 1/8 = 12.5 %

44 halfhalf--lives lives 44tt1/21/2 (1/2)(1/2)44 = 1/16 = 6.25 %= 1/16 = 6.25 %

3939

Half Life: ExampleHalf Life: ExampleRadiolabeledRadiolabeled vitamin Bvitamin B--12 containing 12 containing radioactive cobaltradioactive cobalt--58 is administered to diagnose 58 is administered to diagnose a defect in a patient’s vitamin Ba defect in a patient’s vitamin B--12 absorption. 12 absorption. If the halfIf the half--life is 72 days, approximately what life is 72 days, approximately what percentage of the radioisotope will remain in the percentage of the radioisotope will remain in the patient a year later?patient a year later?•• 3 %3 %•• 5 %5 %•• 8 %8 %•• 10 %10 %

4040

The MoleThe MoleMole:Mole: amount of substance amount of substance contains same # contains same # of elementary entities as carbonof elementary entities as carbon--12 atoms in 12 atoms in exactlyexactly 12 g carbon12 g carbon--12.12.AvogadroAvogadro’’s constants constant, , NNAA = 6.022 = 6.022 ×× 10102323 molmol––11..Molar massMolar mass: mass (g) of 1 mole of substance.: mass (g) of 1 mole of substance.

# moles = mass (g)

molar mass (gmol–1)

4141

Chemical CompoundsChemical Compounds

Chemical compoundChemical compound pure substance, pure substance, can be broken into 2/more elements.can be broken into 2/more elements.MoleculeMolecule smallest unit of a compound, smallest unit of a compound, still retains properties (formula unit for still retains properties (formula unit for ionic compounds).ionic compounds).AtomAtom smallest unit of an element.smallest unit of an element.Any compound always contains same % Any compound always contains same % composition by mass, composition by mass, e.g.e.g. iron (III) oxide:iron (III) oxide:Fe = 69.9 %Fe = 69.9 % O = 30.1 %O = 30.1 %

4242

Empirical FormulaEmpirical FormulaFind lowest multiple(s) of whole atoms Find lowest multiple(s) of whole atoms 22--step process:step process:•• assume 100 g compound:assume 100 g compound:

•• convert numbers to lowest whole multiple(s):convert numbers to lowest whole multiple(s):

1 mol 55.9 g

= 1.25 molFe = 69.9 g ×

= 1.88 molO = 30.1 g ×

1.5 mol O1.0 mol Fe

3 mol O2 mol Fe

= =

1 mol 16.0 g

Fe2O31.88 mol O1.25 mol Fe

4343

Molecular FormulaMolecular Formula

For many (usually organic) compounds, For many (usually organic) compounds, actual molecular formula usually not actual molecular formula usually not empirical (simplest ratio), empirical (simplest ratio), e.ge.g. glucose:. glucose:Empirical: CHEmpirical: CH22OO molecular: Cmolecular: C66HH1212OO66

molecular mass= integer n CCnnxxHHnnyyOOnnzzempirical mass

For glucose For glucose nn = 6= 6..

4444

Balanced Chemical EquationsBalanced Chemical Equations

Inorganic chemistry Inorganic chemistry conservation of matterconservation of matter::22HH22 + O+ O22 →→ 22HH22OO

Organic chemistry:Organic chemistry:CC33HH88 + O+ O22 →→ COCO22 + H+ H22OO

CC33HH88 + O+ O22 →→ 33COCO22 + H+ H22OOCC33HH88 + O+ O22 →→ 33COCO22 + + 44HH22OOCC33HH88 + + 55OO22 →→ 33COCO22 + + 44HH22OO

Balance O last Balance O last –– whywhy??

StoichiometricStoichiometriccoefficientscoefficients

4545

Chemical ReactionsChemical ReactionsStoichiometricStoichiometric factors:factors:

44Fe(s) + Fe(s) + 33OO22(g) (g) →→ 22FeFe22OO33(s)(s)How many moles OHow many moles O22 required to react required to react completely with completely with 55 mol Fe?mol Fe?

5 mol Fe ×3 mol O2

4 mol Fe= 3.75 mol O2

How many moles FeHow many moles Fe22OO33 are produced are produced when when 55 mol Fe react completely?mol Fe react completely?

5 mol Fe ×2 mol FeFe22OO33

4 mol Fe= 2.50 mol FeFe22OO33

4646

Limiting ReagentLimiting Reagent

279 g Fe & 128 g O279 g Fe & 128 g O22 are allowed to react. are allowed to react. Which is the limiting reagent? Which is the limiting reagent?

2 mol FeFe22OO3 160 g Fe2O31 mol Fe 55.9 g Fe

× 3279 g Fe × ×4 mol Fe 1 mol Fe2O3

= 400. g Fe2O3 Fe is limitingFe is limiting..2 mol FeFe22OO3 160 g Fe2O3128 g O2 ×

= 427 g Fe2O3 OO22 is in excessis in excess.

1 mol O232.0 g O2

× 3 ×

.3 mol O2 1 mol Fe2O3

4747

YieldYield

Theoretical yieldTheoretical yield maximum yield maximum yield allowed by limiting reagent (in grams).allowed by limiting reagent (in grams).Percentage yieldPercentage yield::

actual yield× 100 % = percentage yield

theoretical yield

Measure of how successfully reaction Measure of how successfully reaction proceeds in forward direction.proceeds in forward direction.

4848

YieldYield

When 279 g Fe & 128 g OWhen 279 g Fe & 128 g O22 are allowed to are allowed to react, only 300. g of Fereact, only 300. g of Fe22OO33 are recovered. are recovered. What is the percentage yield?What is the percentage yield?

300. g× 100 % = 75.0 %

400. g

4949

Types of Chemical ReactionTypes of Chemical Reaction

1.1. Precipitation reactions.Precipitation reactions.2.2. Neutralization reactions.Neutralization reactions.3.3. GasGas--forming reactions.forming reactions.4.4. RedoxRedox reactionreaction

5050

Precipitation ReactionsPrecipitation Reactions

Formation of insoluble product:Formation of insoluble product:Pb(NOPb(NO33))22((aqaq) + 2KI() + 2KI(aqaq) ) →→ PbIPbI22((ss) + 2KNO) + 2KNO33((aqaq))

PbPb2+2+((aqaq) + 2NO) + 2NO33––((aqaq) + 2K) + 2K++((aqaq) + 2I) + 2I––((aqaq) ) →→

PbIPbI22((ss) ) + 2K+ 2K++((aqaq)) + + 2NO2NO33––((aqaq))

Spectator ions

Net ionic reactionNet ionic reaction: Pb: Pb2+2+((aqaq) 2I) 2I––((aqaq) ) →→ PbIPbI22((ss))

5151

Neutralization ReactionsNeutralization Reactions

Strong acid + strong base Strong acid + strong base →→ salt + watersalt + waterHCl(HCl(aqaq) + ) + NaOH(NaOH(aqaq) ) →→ NaCl(NaCl(aqaq) + H) + H22O(O(ll))

HH++(aq(aq) + ) + ClCl––((aqaq) + ) + NaNa++(aq(aq) + OH) + OH––((aqaq) ) →→NaNa++(aq(aq) + ) + ClCl––((aqaq) + H) + H22O(O(ll))

Net ionic reactionNet ionic reaction: : HH++(aq(aq) + OH) + OH––((aqaq) ) →→ HH22O(O(ll))

Spectator ions

5252

GasGas--forming Reactionsforming ReactionsReaction where one of the products is a gas:Reaction where one of the products is a gas:

NaNa22COCO33((aqaq) + 2HCl() + 2HCl(aqaq) ) →→COCO22((gg) + H) + H22O(O(ll) + 2NaCl() + 2NaCl(aqaq))

2Na2Na++((aqaq) + CO) + CO3322––((aqaq) + 2H) + 2H++((aqaq) + 2Cl) + 2Cl––((aqaq) ) →→

COCO22((gg) + H) + H22O(O(ll) + 2Na) + 2Na++((aqaq) + 2Cl) + 2Cl––((aqaq))

Net ionic reactionNet ionic reaction: CO: CO3322–– ((aqaq) + 2H) + 2H+ + ((aqaq) ) →→

COCO22((gg) + H) + H22O(O(ll))

Spectator ions

5353

RedoxRedox ReactionsReactionsReactions involving transfer of electrons Reactions involving transfer of electrons and changes in oxidation state.and changes in oxidation state.

FeFe2+2+(aq)(aq) →→ FeFe3+3+(aq) + e(aq) + e––

MnOMnO44––((aqaq)) + 5e+ 5e–– →→ MnMn2+2+(aq)(aq)

MnOMnO44––((aqaq) + 5e) + 5e–– →→ MnMn2+2+(aq) (aq) + 4H+ 4H22O(l)O(l)

MnOMnO44––((aqaq) + ) + 8H8H++(aq)(aq) + + 55ee–– →→ MnMn2+2+(aq) + 4H(aq) + 4H22O(l)O(l)

55FeFe2+2+(aq) (aq) →→ 55FeFe3+3+(aq) + (aq) + 55ee––

5Fe5Fe2+2+(aq) + MnO(aq) + MnO44––((aqaq) + 8H) + 8H++(aq) (aq) →→5Fe5Fe3+3+(aq)(aq) + Mn+ Mn2+2+(aq) + 4H(aq) + 4H22O(l)O(l)

reductantreductantoxidantoxidant

Net ionic reactionNet ionic reaction

5454

The Periodic TableThe Periodic Table

5555

Groups of the Periodic TableGroups of the Periodic Table

PeriodsPeriods are horizontal rows.are horizontal rows.GroupsGroups (families) are vertical columns.(families) are vertical columns.MetalsMetals, , nonmetalsnonmetals and and metalloidsmetalloids: which : which are which?are which?What are the electrons in an atom’s What are the electrons in an atom’s outermost shell called?outermost shell called?Valence electrons: primarily responsible for Valence electrons: primarily responsible for chemical behavior.chemical behavior.

5656

5757

Groups of the Periodic TableGroups of the Periodic TableGroupGroup NameName Valence Valence ConfigConfig

Group IGroup I Alkali MetalsAlkali Metals nsns11

Group IIGroup II Alkaline Earth MetalsAlkaline Earth Metals nsns22

Group VIIGroup VII HalogensHalogens nsns22npnp55

Group VIIIGroup VIII Noble GasesNoble Gases nsns22npnp66

The The ss blockblock Representative ElementsRepresentative Elements nsns11––22

The The dd blockblock Transition MetalsTransition Metals ((nn––1)1)ddxxnsnsyy

The The pp blockblock Representative ElementsRepresentative Elements nsns22npnp11––66

The The ff blockblock Rare Earth MetalsRare Earth Metals ((nn––2)2)ffxx((nn––1)1)ddyynsnszz

5858

5959

Groups of the Periodic TableGroups of the Periodic Table

The Octet RuleThe Octet Rule: What is an octet?: What is an octet?Great stability in Great stability in nsns22npnp66 electron electron configuration.configuration.All noble gases have a complete octet:All noble gases have a complete octet:•• 8 valence electrons.8 valence electrons.•• One exception: what is it?One exception: what is it?

6060

Periodic Trends: Nuclear ShieldingPeriodic Trends: Nuclear ShieldingWhat is nuclear shielding?What is nuclear shielding?Each filled shell between the Each filled shell between the nucleus and valence shell nucleus and valence shell “shields” the valence “shields” the valence electrons from full effect of electrons from full effect of protons.protons.Effective nuclear charge, Effective nuclear charge, ZZeffeff•• Valence electrons feel a Valence electrons feel a

reduction in the positive reduction in the positive elementary charge (elementary charge (ZZ) in the ) in the nucleus.

e.g. Mg

nucleus.

6161

Periodic Trends:Periodic Trends:Atomic and Ionic RadiusAtomic and Ionic Radius

What properties of an atom determine radius?What properties of an atom determine radius?Radius is a function of total pull of protons on Radius is a function of total pull of protons on valence electrons: what does the trend look like?valence electrons: what does the trend look like?More protons to the right within a period means More protons to the right within a period means stronger pull stronger pull smaller radiussmaller radius::•• Number of shells doesn’t change in a period.Number of shells doesn’t change in a period.

More shells downward within a group means More shells downward within a group means more shielding more shielding larger radiuslarger radius..

6262

Periodic Trends:Periodic Trends:Ionization EnergyIonization Energy

What is an ionization energy?What is an ionization energy?Amount of energy necessary to remove the Amount of energy necessary to remove the leastleast--tightly bound electron: tightly bound electron: IEIEnn ((nn = 1,2,3..)= 1,2,3..)What is IE related to?What is IE related to?Smaller radii means leastSmaller radii means least--tightly bound tightly bound electron is closer to nucleus, held tighter, and electron is closer to nucleus, held tighter, and requires more energy to ionize.requires more energy to ionize.Filled valence shells have high IE: reluctant to Filled valence shells have high IE: reluctant to relinquish stability relinquish stability –– IEIE22 vsvs. IE. IE11

6363

Periodic Trends:Periodic Trends:Electron AffinityElectron Affinity

Anyone want to define it?Anyone want to define it?The energy associated with the addition of an The energy associated with the addition of an electron electron –– negative and positive values.negative and positive values.How is electron affinity related to octet stability?How is electron affinity related to octet stability?Becomes more negative the closer the atom is to Becomes more negative the closer the atom is to an octet configuration: what does this mean?an octet configuration: what does this mean?Positive values: energy Positive values: energy requiredrequired for atoms to for atoms to accept an electron accept an electron –– anions of these are unstable.anions of these are unstable.

6464

Periodic Trends: Periodic Trends: ElectronegativityElectronegativity

Definition or description?Definition or description?An atom’s ability to pull electrons to itself when An atom’s ability to pull electrons to itself when forming a covalent bond.forming a covalent bond.Greater attraction means higher Greater attraction means higher electronegativityelectronegativity..Notice a pattern?Notice a pattern?Trend follows same pattern as IE.Trend follows same pattern as IE.A Hobbit mnemonic A Hobbit mnemonic FONClFONCl BrISCHBrISCH::•• F > O > N ~ F > O > N ~ ClCl > Br > I > S > C > H> Br > I > S > C > H

6565

Periodic Trends: ExamplePeriodic Trends: Example

Which of the following will have a greater Which of the following will have a greater value for phosphorus than for magnesium?value for phosphorus than for magnesium?

II Atomic radiusAtomic radiusIIII Ionization energyIonization energyIIIIII ElectronegativityElectronegativity

••I onlyI only••I and II onlyI and II only••II and III onlyII and III only••I, II, and IIII, II, and III

6666

Lewis Dot StructuresLewis Dot StructuresAnyone remember the rules?Anyone remember the rules?Pay attention to valence electrons.Pay attention to valence electrons.1.1. skeleton structure skeleton structure central atom (lowest central atom (lowest χχ).).2.2. total valence etotal valence e–– count (group #s).count (group #s).3.3. # valence e# valence e–– pairspairs = valence e= valence e––/2./2.4.4. make single covalent bonds.make single covalent bonds.5.5. remaining pairs remaining pairs terminal atoms terminal atoms lone pairslone pairs (octet (octet

rule!).rule!).6.6. left over eleft over e–– central atom.central atom.7.7. if still < 8 eif still < 8 e–– then turn lone pair then turn lone pair bond pair bond pair

multiple bondsmultiple bonds (C, N, O, P, S).(C, N, O, P, S).

6767

Lewis Dot Structures:Lewis Dot Structures:Formal ChargeFormal Charge

Anyone know what it is?Anyone know what it is?Are atoms sharing valence electrons in the Are atoms sharing valence electrons in the bestbest way possible (formal charge = 0)?way possible (formal charge = 0)?HCN or HNC? Only one is right even HCN or HNC? Only one is right even though both satisfy the octet rule.though both satisfy the octet rule.FC = FC = VV –– BB –– LL11

22•• VV = # valence electrons (free atom)= # valence electrons (free atom)•• BB = # bonding electrons= # bonding electrons•• LL = # lone pair electrons= # lone pair electrons

6868

Lewis Dot Structure: ExamplesLewis Dot Structure: Examples

Which is the best Lewis structure for Which is the best Lewis structure for CHCH22O?O?A common question!A common question! Count valence Count valence electrons first and rule out any with the electrons first and rule out any with the wrong number. If more than one accounts wrong number. If more than one accounts for the right number, use formal charge.for the right number, use formal charge.

6969

Lewis Dot Structure: ExamplesLewis Dot Structure: Examples

Which is the best Lewis structure for the Which is the best Lewis structure for the nitroniumnitronium ion, NOion, NO22

++??

7070

Polar Covalent BondsPolar Covalent Bonds

Covalent bonding: shared electrons.Covalent bonding: shared electrons.Polar covalent: unequal sharing.Polar covalent: unequal sharing.A bond is polar if electron density between A bond is polar if electron density between the atoms is uneven the atoms is uneven –– a function of what?a function of what?Dipole moment, Dipole moment, µ µ = = δδerer..Polar or not? Polar or not?

•• CClCCl44…HF…OCS…NO…HF…OCS…NO33–

X Yδ+ δ–r–

7171

Coordinate Covalent BondsCoordinate Covalent Bonds

Still covalent bonding: shared electrons.Still covalent bonding: shared electrons.How different from covalent bond?How different from covalent bond?Here one atom will donate Here one atom will donate bothboth of the of the shared electrons in the bond.shared electrons in the bond.Complex contains a Complex contains a Lewis baseLewis base (ligand) (ligand) and and Lewis acidLewis acid –– which is which?which is which?Good example: BFGood example: BF33 and NHand NH3 A B3

7272

Ionic BondsIonic Bonds

What are they?What are they?One atom gives a valence electron to the One atom gives a valence electron to the other and electrostatic interaction holds other and electrostatic interaction holds atoms together.atoms together.Usually between a Usually between a metalmetal and and nonmetalnonmetal, but , but always between two atoms with large always between two atoms with large electronegativityelectronegativity difference, difference, ∆∆χχ..NaClNaCl……KClKCl……etcetc..

7373

VSEPR TheoryVSEPR TheoryBasic premise: electron pairs on a central Basic premise: electron pairs on a central atom try to move apart as far as possible.atom try to move apart as far as possible.Electron group geometry Electron group geometry vsvs. molecular . molecular geometry?geometry?

•• Electron group geometryElectron group geometry : electron groups : electron groups ((bondingbonding and and nonbondingnonbonding) on center atom ) on center atom determine geometric family.determine geometric family.

•• Molecular geometryMolecular geometry: : bondingbonding pairs around pairs around center atom determine shape, more specific than center atom determine shape, more specific than electron groups.electron groups.

MoralMoral: determine family, then shape.: determine family, then shape.

7474

VSEPR Theory: The FamiliesVSEPR Theory: The Families

Electron GroupsElectron Groups Geometric FamilyGeometric Family

22 LinearLinear

33 TrigonalTrigonal PlanarPlanar

44 TetrahedralTetrahedral

55 TrigonalTrigonal BipyramidalBipyramidal

66 OctahedralOctahedral

7575

VSEPR Theory:VSEPR Theory:Shape & Lone PairsShape & Lone Pairs

7676

7777

7878

7979

VSEPR Theory: ExamplesVSEPR Theory: Examples

Determine the geometric family and predict Determine the geometric family and predict the shape of each of the following molecules:the shape of each of the following molecules:•• HH22OO•• BrFBrF33

•• XeOFXeOF44

•• NHNH33

•• NHNH44++

•• BFBF33

8080

VSEPR Theory: ExamplesVSEPR Theory: Examples

Draw/think about Lewis structures!Draw/think about Lewis structures!Count electron groups around center atom Count electron groups around center atom for for familyfamily..Count Count bondingbonding groups around center atom to groups around center atom to narrow down family into molecular narrow down family into molecular shapeshape..•• multiple bond counts as one group.multiple bond counts as one group.

Don’t memorize all of this Don’t memorize all of this –– visualize!visualize!•• except geometry names (familiar?).except geometry names (familiar?).

8181

HybridizationHybridizationHow do you determine hybridization around a How do you determine hybridization around a central atom?central atom?Determine number of electron pairs surrounding Determine number of electron pairs surrounding central atom.central atom.Each pair needs an orbital:Each pair needs an orbital:•• ss fills first (fills first (×× 1), then 1), then p p ((×× 3), then 3), then d d ((×× 5).5).•• 22 electron groups electron groups spsp hybridized,hybridized,•• 33 electron groups electron groups spsp22 hybridized,hybridized,•• 44 electron groups electron groups spsp33 hybridized,hybridized,•• 55 electron groups electron groups spsp33dd hybridized,hybridized,•• 66 electron groups electron groups spsp33dd22 hybridized.hybridized.

8282

Hybridization: ExampleHybridization: Example

Determine the hybridization of the central Determine the hybridization of the central atom in each of the following molecules:atom in each of the following molecules:•• HH22OO•• BrFBrF33

•• XeOFXeOF44

•• NHNH33

•• NHNH44++

•• BFBF33

8383

Polar Molecules?Polar Molecules?

CClCCl44…HF…OCS…NO…HF…OCS…NO33–– Polar or not? Polar or not?

8484

Solids and Intermolecular Solids and Intermolecular ForcesForces

Differentiate between ionic, network, and Differentiate between ionic, network, and metallic solids.metallic solids.Ionic: electrostatic attractions (Ionic: electrostatic attractions (NaClNaCl, CaF, CaF22).).Network: lattice of covalent bonds (diamond, Network: lattice of covalent bonds (diamond, quartz).quartz).Metallic: covalent lattice of nuclei and inner Metallic: covalent lattice of nuclei and inner electrons surrounded by cloud of electrons.electrons surrounded by cloud of electrons.•• What are conduction electrons?What are conduction electrons?

8585

Solids and Intermolecular Solids and Intermolecular ForcesForces

Intermolecular forces are relatively weak Intermolecular forces are relatively weak interactions between neutral/charged molecules.interactions between neutral/charged molecules.Four major types: what are they?Four major types: what are they?•• IonIon--dipoledipole: polar molecules attracted to ions.: polar molecules attracted to ions.•• DipoleDipole--dipoledipole: between positive and negative end of : between positive and negative end of

two polar molecules.two polar molecules.•• DipoleDipole--induced dipoleinduced dipole: permanent dipole induces : permanent dipole induces

dipole in nondipole in non--polar molecule.polar molecule.•• London dispersion forcesLondon dispersion forces: instantaneous dipole : instantaneous dipole

induces a dipole in neighboring noninduces a dipole in neighboring non--polar molecule polar molecule (also (also Van Van derder WaalsWaals forces).forces).

8686

Solids and Intermolecular Solids and Intermolecular Forces: Hydrogen BondingForces: Hydrogen Bonding

When does it occur?When does it occur?Only between H attached to an N, O, F and the Only between H attached to an N, O, F and the lone pair of another N, O, or F atom.lone pair of another N, O, or F atom.This is major! N, O, and F only This is major! N, O, and F only –– not C or any not C or any other atom!!other atom!!Why does it occur?Why does it occur?VeryVery small hydrogen (low small hydrogen (low χχ) next to ) next to fairlyfairly small small atom (very high atom (very high χχ) ) intense partial positive intense partial positive charge, charge, δδ++ latches onto lone pair of electrons with latches onto lone pair of electrons with high high δδ––..

8787

Phase TransitionsPhase TransitionsClosely related to what property of molecules?Closely related to what property of molecules?Temperature Temperature –– measure of internal kinetic measure of internal kinetic energy.energy.States or phases: name them!States or phases: name them!Solids, liquids, gases all differ in kinetic Solids, liquids, gases all differ in kinetic energy and intermolecular forces.energy and intermolecular forces.Phase change caused by overcoming or Phase change caused by overcoming or strengthening intermolecular forces strengthening intermolecular forces –– boiling boiling point, vapor pressure, point, vapor pressure, etcetc..

8888

Phase Transitions: SummaryPhase Transitions: Summary

Evaporation, condensation, fusion, Evaporation, condensation, fusion, crystallization, sublimation, deposition: crystallization, sublimation, deposition: define!define!Evaporation: liquid to gas.Evaporation: liquid to gas.Condensation: gas to liquid.Condensation: gas to liquid.Fusion (melting): solid to liquid.Fusion (melting): solid to liquid.Crystallization (freezing): liquid to solid.Crystallization (freezing): liquid to solid.Sublimation: solid to gas.Sublimation: solid to gas.Deposition: gas to solid.Deposition: gas to solid.

8989

Phase Transitions: SummaryPhase Transitions: Summary

Gas Gas liquid liquid solid: what happens to heat, solid: what happens to heat, KE, and entropy?KE, and entropy?Heat released, internal KE decreases, Heat released, internal KE decreases, entropy decreases.entropy decreases.Solid Solid liquid liquid gas: what happens to heat, gas: what happens to heat, KE, and entropy?KE, and entropy?Heat absorbed, internal KE increases, Heat absorbed, internal KE increases, entropy increases.entropy increases.Know the conceptual trends!Know the conceptual trends!

9090

Heats of Phase ChangesHeats of Phase Changes

A change of phase depends on what two things?A change of phase depends on what two things?TypeType of substance and of substance and amountamount of substance.of substance.Heat of transition: Heat of transition: ∆∆HH –– what does it represent?what does it represent?∆∆HH is amount of energy required to complete a is amount of energy required to complete a phase transition @ const. pressure.phase transition @ const. pressure.Equation: Equation: qq = = nn∆∆HH …what is …what is nn? signs on terms?? signs on terms?Positive Positive ∆∆HH and and qq heat absorbed heat absorbed endothermicendothermicNegative Negative ∆∆HH and and qq heat released heat released exothermicexothermic..

9191

CalorimetryCalorimetryAbsorption or release of heat: what are two Absorption or release of heat: what are two possible consequences?possible consequences?Temperature change or phase change, but not Temperature change or phase change, but not both at same time!both at same time!Equation for amount of heat absorbed/released?Equation for amount of heat absorbed/released?qq = = mcmc∆∆TT … define the terms!… define the terms!What is specific heat?What is specific heat?Intrinsic property…resistance to temperature Intrinsic property…resistance to temperature change:change:•• High High cc means small temperature change, holds means small temperature change, holds

absorbed heat better.absorbed heat better.

9292

CalorimetryCalorimetry: Example: Example

Equal amounts of heat are absorbed by 10Equal amounts of heat are absorbed by 10--g g solid samples of four different metals: solid samples of four different metals: aluminum, lead, tin, and iron. Of the four, aluminum, lead, tin, and iron. Of the four, which will exhibit the smallest temp change?which will exhibit the smallest temp change?•• Aluminum (Aluminum (cc = 0.90 = 0.90 JgJg––11KK––11))•• Lead (Lead (cc = 0.13 = 0.13 JgJg––11KK––11))•• Tin (Tin (cc = 0.23 = 0.23 JgJg––11KK––11))•• Iron (Iron (cc = 0.45 = 0.45 JgJg––11KK––11))

9393

Phase Transition DiagramsPhase Transition DiagramsWhat is plotted on one? What does it show?What is plotted on one? What does it show?Note: during a phase transition, temperature of Note: during a phase transition, temperature of substance does not change substance does not change –– sound familiar?sound familiar?Pressure Pressure vsvs. temperature…shows how phases are . temperature…shows how phases are determined by these properties.determined by these properties.Some terms: Some terms: triple pointtriple point, , critical pointcritical point..Triple pointTriple point: temp. and pressure at which all : temp. and pressure at which all phases exist simultaneously in equilibrium.phases exist simultaneously in equilibrium.Critical pointCritical point: beyond this point, substance has : beyond this point, substance has properties of gas and liquid (high density, low properties of gas and liquid (high density, low viscosity)…supercritical fluid.viscosity)…supercritical fluid.

9494

Phase Transition DiagramsPhase Transition Diagrams

9595

Phase Diagrams: Water & COPhase Diagrams: Water & CO22

One difference between water and other One difference between water and other substances substances –– what?what?Let’s draw and label water and carbon Let’s draw and label water and carbon dioxide phase diagrams.dioxide phase diagrams.For water, an increase in pressure at constant For water, an increase in pressure at constant temperature can favor liquid phase not the temperature can favor liquid phase not the solid as usual…ice skating!solid as usual…ice skating!

9696

Phase Diagrams: Water & COPhase Diagrams: Water & CO22

9797

Gases and KineticGases and Kinetic--Molecular Molecular TheoryTheory

What is the purpose of the theory?What is the purpose of the theory?Sets the conditions for an ideal gas.Sets the conditions for an ideal gas.Normally, real gases operate like ideal gases, Normally, real gases operate like ideal gases, so these conditions can be applied to so these conditions can be applied to understand gas behavior.understand gas behavior.A good example of this application: the ideal A good example of this application: the ideal gas law.gas law.

9898

Assumptions of the TheoryAssumptions of the Theory

First assumption?First assumption?Gas molecules take up essentially no volume, Gas molecules take up essentially no volume, compared to the average spacing between them.compared to the average spacing between them.Second assumption?Second assumption?Constant motion, constant speeds, and random Constant motion, constant speeds, and random collisions:collisions:•• Pressure Pressure average force exerted per unit area,average force exerted per unit area,•• Elasticity Elasticity KEKEii = = KEKEff•• No intermolecular forces.No intermolecular forces.

9999

Assumptions of the TheoryAssumptions of the Theory

Third assumption?Third assumption?Direct proportionality between average Direct proportionality between average kinetic energy of gas molecules and kinetic energy of gas molecules and temperature in Kelvin degrees: KE temperature in Kelvin degrees: KE ∝∝ TTNote that this is Note that this is averageaverage kinetic energy, not kinetic energy, not average speed average speed –– speed involves additional speed involves additional factors, as we will see.factors, as we will see.

100100

Ideal Gas Law: UnitsIdeal Gas Law: Units

What are the units of volume, temperature, What are the units of volume, temperature, and pressure that are used?and pressure that are used?1 cm1 cm33 = 1 = 1 mLmL…1 m…1 m33 = 1000 L.= 1000 L.Kelvin = Celsius + 273.Kelvin = Celsius + 273.1atm = 760 1atm = 760 torrtorr = 760 mmHg.= 760 mmHg.Standard temp. and pressure…?Standard temp. and pressure…?273 K and 1 273 K and 1 atmatm..

101101

Ideal Gas LawIdeal Gas Law

Describes behavior of gases following Describes behavior of gases following kinetickinetic--molecular theory.molecular theory.What is the equation?What is the equation?PVPV = = nRTnRT…define the terms.…define the terms.Gas constantGas constant: : RR = 0.0821 = 0.0821 LatmLatm molmol––11KK––11

Derivations of other laws from the idealDerivations of other laws from the ideal--gas gas law law –– three proportionalities, two have names.three proportionalities, two have names.

102102

Other POther P--VV--T Gas LawsT Gas Laws

Volume proportional to temperature at Volume proportional to temperature at constant pressure constant pressure –– what law?what law?Charles’ LawCharles’ Law VV11//TT11 = = VV22//TT22

Pressure inversely proportional to volume at Pressure inversely proportional to volume at constant temperature constant temperature –– what law?what law?Boyle’s LawBoyle’s Law PP11VV11 = = PP22VV22

Pressure proportional to temperature at Pressure proportional to temperature at constant volume constant volume PP11//TT11 = = PP22//TT22

103103

Other POther P--VV--T Gas LawsT Gas Laws

Suppose you hold Suppose you hold nn constant?constant?Combined gas lawCombined gas law PP11VV11//TT11 = = PP22VV22//TT22

Avogadro’s LawAvogadro’s Law –– what did he propose?what did he propose?If two equalIf two equal--volume containers hold gas at the volume containers hold gas at the same pressure and temp., then they contain the same pressure and temp., then they contain the same number of particles (regardless of identity).same number of particles (regardless of identity).What is the consequence of this law?What is the consequence of this law?Standard molar volumeStandard molar volume::

22.4 L22.4 L @ 273 K and 1 @ 273 K and 1 atmatm

104104

IdealIdeal--Gas Law: ExampleGas Law: Example

How many atoms of helium are present in 11.2 How many atoms of helium are present in 11.2 liters of the gas at a pressure of 1 liters of the gas at a pressure of 1 atmatm and and temperature of 273 K?temperature of 273 K?•• 3.01 3.01 × × 10102323

•• 6.02 6.02 ×× 10102323

•• 1.20 1.20 ×× 10102323

•• Cannot be determined from information Cannot be determined from information given.given.

105105

Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

Total pressure of sample of 3 different gases Total pressure of sample of 3 different gases is due to collisions of all types with container is due to collisions of all types with container wall. What does this say for the pressure of wall. What does this say for the pressure of each type of gas?each type of gas?Dalton’s Law of Partial Pressures;Dalton’s Law of Partial Pressures;•• PP = = PPaa + + PPbb + + PPcc

Corollary: Corollary: PPaa = = XXaaPP, where , where XXaa is mole fraction is mole fraction of gas “a”. of gas “a”.

106106

Dalton’s Law: ExampleDalton’s Law: Example

A mixture of neon and nitrogen contains 0.5 A mixture of neon and nitrogen contains 0.5 mol of mol of NeNe and 2 mol of Nand 2 mol of N22(g). If total (g). If total pressure is 20 pressure is 20 atmatm, what is partial pressure of , what is partial pressure of neon?neon?

107107

Graham’s Law of EffusionGraham’s Law of Effusion

What is effusion?What is effusion?Escape of a gas molecule through a tiny hole Escape of a gas molecule through a tiny hole (comparable in size to the molecule) into an (comparable in size to the molecule) into an evacuated region.evacuated region.Our concerns with Graham’s Law:Our concerns with Graham’s Law:•• What factors determine speed of effusion?What factors determine speed of effusion?•• What equations will help determine relative rates What equations will help determine relative rates

of effusion for two gases?of effusion for two gases?

108108

Graham’s Law Graham’s Law –– The ConditionsThe Conditions

Temperature in container of gas molecules is Temperature in container of gas molecules is a constant.a constant.Average kinetic energies are equal.Average kinetic energies are equal.Molar masses of gases may be different.Molar masses of gases may be different.Given what we know about kinetic energy, Given what we know about kinetic energy, mass must play a role in average speedmass must play a role in average speed•• KE = KE = mvmv221

2

109109

Graham’s Law Graham’s Law –– FormulasFormulas

The usable formula:The usable formula:Rate of Gas ARate of Gas A √√ Molar Mass Gas BMolar Mass Gas BRate of Gas BRate of Gas B √√ Molar Mass Gas AMolar Mass Gas A=

Notice the relationships…Notice the relationships…The rate of effusion and molar mass are The rate of effusion and molar mass are inverses, so the faster a gas effuses, the smaller inverses, so the faster a gas effuses, the smaller its molar mass must be.its molar mass must be.

110110

Graham’s Law Graham’s Law –– Remember…Remember…

Molecules of different gases at same temp. Molecules of different gases at same temp. have same average kinetic energy.have same average kinetic energy.Average speed takes into account molar mass.Average speed takes into account molar mass.As temp. of sample is increased, the average As temp. of sample is increased, the average speed will increase:speed will increase:•• Cannot account for wide range of speeds in Cannot account for wide range of speeds in

individual molecules.individual molecules.

111111

Graham’s Law Graham’s Law –– Some Some ExamplesExamples

A container holds methane and sulfur dioxide A container holds methane and sulfur dioxide at temp. of 227 at temp. of 227 °°C. Which of following best C. Which of following best describes the relationship between their describes the relationship between their speeds, where speeds, where vvmm represents methane and represents methane and vvsssulfur dioxide?sulfur dioxide?•• vvss = 16= 16vvmm

•• vvss = 2= 2vvmm

•• vvmm = 2= 2vvss

•• vvmm = 16= 16vvss

112112

Graham’s Law Graham’s Law –– Some Some ExamplesExamples

Chamber A holds a mix of four gases, 1 mol of Chamber A holds a mix of four gases, 1 mol of each. A tiny hole is made in the side and the each. A tiny hole is made in the side and the gases are allowed to effuse into an empty gases are allowed to effuse into an empty chamber. When 2 mol of gas have escaped, chamber. When 2 mol of gas have escaped, which gas will have the greatest mole fraction which gas will have the greatest mole fraction in Chamber A?in Chamber A?•• ClCl22

•• FF22

•• NN22

•• COCO22

113113

Approaching Ideal Gas Approaching Ideal Gas BehaviorBehavior

Under normal conditions, real gases behave Under normal conditions, real gases behave like ideal gases, so the assumptions of kineticlike ideal gases, so the assumptions of kinetic--molecular theory apply:molecular theory apply:•• molecules are so small compared with surrounding molecules are so small compared with surrounding

space that they essentially occupy no volume.space that they essentially occupy no volume.•• molecules experience no intermolecular forces.molecules experience no intermolecular forces.

114114

Approaching Ideal Gas Approaching Ideal Gas BehaviorBehavior

But these assumptions fail under certain But these assumptions fail under certain conditions, making the real gasconditions, making the real gas notnot ideal ideal ––name them!name them!High pressures.High pressures.Low temperatures.Low temperatures.Strong intermolecular forces (esp. HStrong intermolecular forces (esp. H--bonds).bonds).High MW and diatomic gases behave less High MW and diatomic gases behave less ideally than low MW and monatomic gases.ideally than low MW and monatomic gases.

115115

Ideal Gas Behavior Ideal Gas Behavior –– ExampleExample

Of the following, which gas would likely Of the following, which gas would likely deviate the most from ideal behavior at high deviate the most from ideal behavior at high pressure and low temperature?pressure and low temperature?•• He (g)He (g)•• HH22 (g)(g)•• OO22 (g)(g)•• HH22O (g)O (g)