Unit 2: Measurement Measurements are

Measurements include a number and a unit

Examples:Measuremen

tQuantity

teaspoon volumemeter lengthCelsius temperatur

emm Hg pressureg/mL densitykilograms mass

In science, we use the SI measurement system (Le Systeme International d’Unites). Why?

Seven SI base units: (all others considered “derived” units)Quantity Quantity Symbol Unit name Unit Abbreviation

length ℓ meter mmass m kilogram kgtime t second stemperature T Kelvin Kamount of substance

n mole mol

electric current I ampere Aluminous intensity Iv candela cd

Metric Prefixes:prefix abbreviation amount of base unit

Tera- T 1012

Giga- G 109

Mega- M 106

kilo- k 103

base unit: meter, gram, second, liter, etc.deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

MEMORIZE!Metric Prefixes and Conversion Factors:

relationship to base

prefix abbr

amount of base unit conversion factor

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unitlarger than base unit

Tera- T 1012 = 1 000 000 000 000 (trillion)

1 Tm = 1012 m

Giga- G 109 = 1 000 000 0000 (billion)

1 Gm = 109 m

Mega- M 106 = 1 000 000 (million)

1 Mm = 106 m

kilo- k 103 = 1000 (thousand)

1 km = 1000 m

hecto- h 102 = 100 (hundred)

1 hm = 100 m

deca- da 101 = 10 (ten)

1 dam = 10 m

base unit: meter, gram, second, liter, etc.

smaller than base

unit

deci- d 10-1 = 0.1 (tenth)

1 m = 10 dm

centi- c 10-2 = 0.01 (hundredth)

1 m = 100 cm

milli- m 10-3 = 0.001 (thousandth)

1 m = 1000 mm

micro- μ 10-6 = 0.000 001 (millionth)

1 m = 106 μm

nano- n 10-9 = 0.000 000 001 (billionth)

1 m = 109 nm

pico- p 10-12 = 0.000 000 000 001 (trillionth)

1 m = 1012 pm

Temperature Scales

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There are three temperature scales in use today, Fahrenheit, Celsius and Kelvin.

Fahrenheit temperature scale is a scale based on 32 for the freezing point of water and 212 for the boiling point of water, the interval between the two being divided into 180 parts. The 18th-century German physicist Daniel Gabriel Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30 and 90 for the freezing point of water and normal body temperature, respectively; these later were revised to 32 and 96, but the final scale required an adjustment to 98.6 for the latter value.

Until the 1970s the Fahrenheit temperature scale was in general common use in English-speaking countries; the Celsius, or centigrade, scale was employed in most other countries and for scientific purposes worldwide. Since that time, however, most English-speaking countries have officially adopted the Celsius scale. The conversion formula for a temperature that is expressed on the Celsius (C) scale to its Fahrenheit (F) representation is: F = 9/5C + 32.

Celsius temperature scale also called centigrade temperature scale, is the scale based on 0 for the freezing point of water and 100 for the boiling point of water. Invented in 1742 by the Swedish astronomer Anders Celsius, it is sometimes called the centigrade scale because of the 100-degree interval between the defined points. The following formula can be used to convert a temperature from its representation on the Fahrenheit (F) scale to the Celsius (C) value: C = 5/9(F - 32). The Celsius scale is in general use wherever metric units have become accepted, and it is used in scientific work everywhere.

Kelvin temperature scale is the base unit of thermodynamic temperature measurement in the International System (SI) of measurement. It is defined as 1/ 273.16 of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water. The kelvin (symbol K without the degree sign ⁰) is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson, Baron Kelvin. Such a scale has as its zero point absolute zero, the theoretical temperature at which the molecules

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of a substance have the lowest energy. Many physical laws and formulas can be expressed more simply when an absolute temperature scale is used; accordingly, the Kelvin scale has been adopted as the international standard for scientific temperature measurement. The Kelvin scale is related to the Celsius scale. The difference between the freezing and boiling points of water is 100 degrees in each, so that the Kelvin has the same magnitude as the degree Celsius.

Significant Figures What are significant figures, why are they used?To express uncertainty in measurement, cannot be more sure of the answer than your original measurements

Rules: Example:1. digits 1 through 9: always significant 123 has 3 sig figs

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2. zero between 2 sig figs: always significant 5004 has 4 sig figs

3. leading zeros (come before non-zero digits): never significant0.000367 has 3 sig figs

4. trailing zeros (at the right end of the number)a. are NOT significant when: no decimal point in the number

1160 has 3 sig figs

b. are significant only when: decimal point in the number1160. has 4 sig figs

5. exact/counting numbers: sig figs do not make sense because these are not measurements: “infinite” number of significant figures

Rules for Rounding: 1. In a series of calculations, let your calculator hold all the digits, and round ONCE at

the end.

2. The digit that determines rounding, once place PAST the last sig fig will be removed.a. If it is less than 5, the preceding digit remains the sameb. If it is greater than or equal to 5, the preceding digit is rounded up by 1

Calculations With Sig Figs: Example:

Multiplication or Division: Round answer to fewest number of sig figs in original 56.01 x 8.2 = 460

Measurements 3 sig figs 2 sig figs 2 sig figs

Addition and Subtraction: Round answer to fewest sig figs to the right of the 56.01 + 8.2 = 64.2

decimal point in original measurements 2 after dec 1 after dec 1 after dec

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Chemistry Name:________________________Determining and Rounding Significant Figures Date Due: _______________

Determine the number of significant figures in the following numbers. Place your answer in the space provided.

1. _____ 5090 32. _____ 0.1010 43. _____ 260 001 64. _____ 89.000 55. _____ 87 000 26. _____ 0.9 17. _____ 10 000.01 78. _____ 1 001 000 79. _____ 0.000001 110. _____ 809.000 611. _____ 10 112. _____ 0.09650 413. _____ 0.808050 614. _____ 7000 1

15. _____ 43.000 516. _____ 2.160 417. _____ 23 000 000 000 000 000

001 2018. _____ 5000 119. _____ 0.000000000000040000500

6 920. _____ 9.090 421. _____ 63 000 222. _____ 1694.0 523. _____ 0.45980 524. _____ 12 000 000 225. _____ 911 3

Round the following numbers to 4 significant figures26. _______ 333 999 3.340 x

105

27. _______ 3.09005 3.09028. _______ 47.833 47.83

29. _______ 0.0038965 0.003897

30. _______ 88.889 88.8931. _______ 13 475 13 48032. _______ 1.0004 1.000

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33. _______ 0.0357849 0.03578 34. _______ 99 999 1.000 x 10

Round the following numbers to 2 significant figures

35. _______ 3.93 3.936. _______ 708 71037. _______ 0.00604 0.006038. _______ 34 999 35 00039. _______ 76.09 7640. _______ 5.95 6.041. _______ 100.0 1.0 x 102

42. _______ 4750 480043. _______ 0.000206 0.00021

44. _______ 119 12045. _______ 6.948 6.946. _______ 900 9.0 x 102

47. _______ 690.9 69048. _______ 8.100 8.149. _______ 1 890 000 1 900

00050. _______ 8.0995 8.1

How should the number be written if when rounding, not enough significance is shown?scientific notation

Which numbers on this page fall into this category?26, 34, 41, 46

Chemistry Name:________________________Significant Figure Practice Date Due: _______________

Determine the number of significant figures in the following numbers. Place your answer in the space provided.

1. _____ 340 010 52. _____ 0.0009010

43. _____ 400.00 54. _____ 1.90001 6

5. _____ 900 16. _____ 0.7 17. _____ 19.00 48. _____ 2 010 000

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9. _____ 560.000010

10. _____ 8.3070 511. _____ 1000 112. _____ 600.900 6

Round the following numbers to 3 significant figures

13. ________ 25.99 26.014. ________ 22 999 2.30 x 104

15. ________ 0.0038249 0.0038216. ________ 1.099 1.1017. ________ 84.94 84.918. ________ 7448 7450

19. ________ 0.09995 0.10020. ________ 9996 1.00 x 104

21. ________ 4.0005 4.0022. ________ 6008 601023. ________ 81 850 81 90024. ________ 30.04489 30.0

Calculate the answers for the following problems. All answers must be expressed with the proper number of significant figures!

Rule for multiplication and division: _______________________________

Rule for addition and subtraction: ________________________________

25. 23.73 + 76.27 = 100.00

26. 345.0 x 1.80 = 621

27. .004890 ÷ .035 = 0.14

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28. 3000.90 - 2.975 = 2997.93

29. 27 - 9.5 = 18

30. 23.000 x 13.8900 = 319.47

31. 186.654 + 8.65291 = 195.307

32. 7.9025 ÷ 83.0 = 0.0952

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Scientific Notation10

Scientific Notation

Why is scientific notation used?1) Express extremely large and really tiny numbers

2) Express the correct number of sig figs

Form: Examples:one digit to * keep same # sig figsthe left of the decimal pointlarge numbers: 460 000 000 = 4.6 x 108

positive exponent tells how many places the decimal point is movedtiny numbers: 0.000 000 000 046 = 4.6 x 10-11

negative exponent tells how many places the decimal point is moved

How do you use scientific notation on your calculator?EE or EXP

More Uncertainty in Measurement:

Accuracy vs. Precision:Accuracy: closeness to accepted or actual value (literature value)

Precision: closeness of trials to one another “reproducibility”

Percent error: |measured−actual|actual

x 100%

Practice: Students were asked to find the density of an unknown white powder. Each student measured the volume and mass of three separate samples. They reported calculated densities for each trial and an average of the three calculations. The powder was sucrose, also called table sugar, which has a density of 1.59 g/cm3.Density Data Collected by Three Different Students

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Student A Student B Student CTrial 1 1.54 g/cm3 1.40 g/cm3 1.70 g/cm3

Trial 2 1.60 g/cm3 1.68 g/cm3 1.69 g/cm3

Trial 3 1.57 g/cm3 1.45 g/cm3 1.71 g/cm3

Average 1.57 g/cm3 1.51 g/cm3 1.70 g/cm3

1. Who collected the most accurate data? Why? A

2. Which students collected the most precise data? Why? C

3. Use the table to explain why averages could be misleading. B has data that is neither accurate nor precise, but the average makes it seem like it is good data

Percent Error:4. Below, calculate the percent error from each student’s average calculated

densities in the table above. SHOW ALL WORK!Student A:|1.57−1.59|

1.59 x 100% = 1.26 % error

Student B:|1.51−1.59|

1.59 x 100% = 5.03 % error

Student C:|1.70−1.59|

1.59 x 100% = 6.92 % error

Chemistry Name:__________________2.2 Numerical Problem Solving Date: ____________

SI units/Metric2. Complete the table:

Quantity Unit Unit Symbolelectric current ampere A

length meter mtime second smass kilogram kg

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Temperature Kelvin Kamount of substance mole mol

luminous intensity candela cd

3. List the units from largest to smallest: meter, millimeter, kilometer, centimeter, picometer.

kilo, meter, centi, milli, pico

Match each quantity to be measured with the most appropriate SI unit.a. centimeterb. gramc. Kelvind. kilograme. meterf. Newtong. second

e 4. length of swimming poola 5. length of a pencilb 6. mass of a pencil d 7. mass of a bag of applesg 8. time between two heartbeatsc 9. temperature of boiling waterf 10. weight of a textbook

SIGNIFICANT FIGURES11. For each group of digits indicated in the three numbers below, state whether the digits are significant. State the rule that applies.

4500.60 0.000799 220

a. yes, digits 1-9 significantb. yes, captive zeroes significantc. yes, digits 1-9 significant, trailing zero with decimal in number significantd. no, leading zeros never significant e. yes, digits 1-9 significantf. no, trailing zero without decimal in number not significant

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12. A stack of books contains 10 books, each of which is determined, by a ruler graduated in centimeters, to be 25.0 cm long. How do these two quantities differ in terms of significant digits?

10 is a count. They can only be whole numbers. 25.0 is a measurement so we can describe it as having 3 significant figures. The certainty is set by the measuring tool.

Percent Error13. What is the percent error in a determination that yields a value of 8.38 g/cm3 as the density of copper? The literature value for this quantity is 8.92 g/cm3.|8.38−8.92|

8.92 x 100% = 6.05 % error

14. Yusuf measures the melting point of ammonium acetate, NH4C2H3O2, as 117 ˚C, but the literature value is 114 ˚C. What is the percent error in the measurement? |117−114|

114 x 100% = 2.63 % error

GRAPHING: Graph the data in the following data table and answer the questions. Use the graph paper provided.Graph Requirements: ** Use a Straight Edge!

1) Descriptive Title2) Indent axes so you have room to label them3) Label x-axis with measurement and units (independent variable)4) Label y-axis with measurement and units (dependent variable)5) Choose a convenient scale - your graph should take up at least ¾ of the graph

area6) Plot points as an X or a dot with a circle around it7) Use a line of “best fit” or connect with a smooth curve when applicable

Volume and Mass of Aluminum at 20.0 CVolume (cm3) (independent = x) Mass (g) (dependent = y)

11.7 27.019.7 54.730.9 79.442.0 108.349.3 134.6

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59.8 150.01. Is it valid to begin the graph at the origin (0, 0) ? Explain.

2. What is the mass, in grams, of the aluminum at:a. 17.0 cm3

b. 35.0 cm3

c. 0.0 cm3

3. What is the volume, in cubic centimeters, of aluminum at:a. 189.0 g

b. 50.0 g

c. 1.0 g

4. Which of the determinations in questions #3 and #4 are a. interpolations

b. extrapolations

5. Find the slope of the line and units.

6. What value does the slope of this data represent?

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DensityWhat is density?

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How closed packed the particles are

How is it different from weight?Weight is a force, gravity’s pull on mass

possible SI mass units?g, kg, mg

possible SI volume units? cm3, mL, L

**Remember: 1 mL = 1 cm3

1 L = 1 dm3

SI Density units?Solids: g/cm3 (water displacement: g/mL)

Liquids: g/mL

Gases: g/L

Equation for calculating Density: D=mV

Reminder: 4 steps for full credit:1. write the equation2. list variables3. plug in the numbers4. answer (needs rounded to proper sig figs and correct units)

Density practice:

1. The largest meteorite discovered on earth is the Hoba West stone in Namibia, Africa. The volume of the stone is about 7 500 000 cm3. If the meteorite has a density of 8.0 g/cm3, what is its mass? answer: 6.0 x 107 g

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2. One of the largest emeralds ever discovered had a mass of 17 230 g. Assuming its density to be 4.02 g/cm3, what was the emerald's volume? answer: 4290 cm3

3. Lithium is the lightest of metals and the least dense of all nongaseous elements. A pure lithium sample with a volume of 13.0 cm3 has a mass of 6.94 g. What is the density of lithium? 0.534 g/cm3

D = m/V

Chemistry Name:__________________Density Worksheet Date:_____________

SHOW ALL WORK!1. What is the density of a sample of ore that has a mass of 74.0 g and occupies

20.3 cm3?

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2. What is the density of an 84.7 g sample of an unknown substance if the sample occupies 49.6 cm3?

3. What is the density of an object that has a mass of 3.05 g and a volume of 8.47 mL?

4. What is the density of an object that has a mass of 6.00 g and is 6.10 cm long, 0.25 cm wide and 4.90 cm high?

5. Find the volume of a sample of wood that has a mass of 95.10 g and a density of 0.857 g/cm3.

6. What is the mass of a sample of material that has a volume of 55.1 cm3 and a density of 6.72 g/cm3?

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7. A student calculates the density of iron as 6.80 g/cm3 using lab data for mass and volume. A handbook reveals that the correct value is 7.86 g/cm3. What is the percent error.

Answer Bank: (I did not include units below, be sure that your answers have units!)

0.80 3.64 111 13.5 0.360 370. 1.71

Chemistry Name:__________________Specific Heat Date:_____________

Using your knowledge of specific heat, why might the fish love it?

The specific heat is the amount of heat required to raise one gram of a substance one degree.

swater = 1.00 cal/g deg C

swater = 4.184 J/g deg C’

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Chemistry Name:___________________Calorimetry Date:_______________

Where: q = total heat flowm = massT = change in temp. s = specific heat

Example 1:Calculate the number of joules (and kilojoules) required to warm 1.00 x 102grams of water from 25.0 oC to 80.0 oC. answer: 2.30 x 104 J = 23.0 kJ

Heat energy = mass x change in temperature x specific heat

Specific Heat:Many times Calorimetry problems involve solving for one of the other

quantities such as specific heat or temperature change. This is done by simply using algebra to rearrange the formula q = mTs.

Example 2:Calculate the specific heat of gold if it required 48.0 joules of heat to warm 25.0 grams of gold from 40.0 oC to 55.0 oC. answer: 0.128 J/g °C

Problems: Show all work for full credit!

1. How many joules are needed to warm 25.5 grams of water from 14 oC to 22.5 oC?

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q = m T s

2. Calculate the number of joules released when 75.0 grams of water are cooled from 100.0oC to 27.5 oC.

3. How much heat is absorbed by 60.0 g of copper when it is heated from 20.0 oC to 80.0 oC? The specific heat of copper is 0.385 J/gCo.

4. A 38-kg block of lead is heated from -26.0oC to 180oC. How much heat does it absorb during the heating? The specific heat of lead is .138 J/g Co.

5. How many joules are needed to warm 45.0 grams of water from 30.0oC to 75.0oC?

6. What would be the final temperature if 3.31 x 103 joules were added to 18.5 grams of water at 22.0oC

7. A sample of lead, specific heat 0.138J/goC, released 1.20 x 103J when it cooled from 93.0oC to 29.5oC. What was the mass of this sample of lead?

Energy Transfer

One of the major uses of Calorimetry is to measure the specific heats of metals and various metallic alloys. Chemists use specific heats in their study of the

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structure and attractive forces in the materials. Specific heats are useful for engineers in planning structures or processes.

This use of Calorimetry is based upon the law of conservation of energy--energy is neither created nor destroyed but can be transformed from one form to another.

In this application, hot metal is added to cold water in an insulated container called a calorimeter. The cold water gains the heat lost by the hot metal as they come to the same final temperature. If you measure the temperature changes you can calculate the heat gained by the water and thus the heat lost by the metal, and finally can calculate the specific heat of the metal.

Example 3:A 175 gram sample of a metal at 93.5oC was added to 105 grams of water at 23.5oC in a perfectly insulated calorimeter. The final temperature of the water and metal was 33.8oC. Calculate the specific heat of the metal in joules/gram oC.

heat lost by the metal = - heat gained by the watermmTmsm = - mwTwsw

Problems: Show all work for full credit.

8. A 185 gram sample of copper at 98.0 oC was added to 102 grams of water at 20.0 oC in a perfectly insulated calorimeter. The final temperature of the copper-water mixture was 31.2 oC. Calculate the specific heat of copper using this data.

9. A chemistry student added 225 grams of aluminum at 85.0 oC to 115 grams of water at 23.0 oC in a perfect calorimeter. The final temperature of the aluminum- water mixture was 41.4 oC. Use this student's data to calculate the specific heat of aluminum in joules/gram Co.

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10. A student was given a sample of a silvery gray metal and told that it was bismuth, specific heat 0.122 J/goC, or cadmium, specific heat 0.232 J/g oC. The student measured out a 250 gram sample of the metal, heated it to 96.0oC and then added it to 98.5 grams of water at 21.0oC in a perfect calorimeter. The final temperature in the calorimeter was 30.3oC. Use the student's data to calculate the specific heat of the metal sample and then identify the metal.

Unit 2 Studyguide:Vocabulary/To know:

quantitative/qualitative accuracy/precision SI base units (see table in notes) Metric prefixes and conversions (see “memorize” table) Determining, rounding with significant figures and scientific notation % error calculations Why do sig figs not apply to counting and exact numbers? Solving density problems for mass, volume, or density

SHOW ALL STEPS FOR FULL CREDIT! Solving calorimetry problems for heat, mass, temperature difference,

or specific heat SHOW ALL STEPS FOR FULL CREDIT!

Measurements are taken to ONE PLACE after the “minor scale”25

Beverage Density Lab

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