Unit 2: Measurement Measurements are

Measurements include a _________ and a _________

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?

Rules: Example:1. digits 1 through 9:

2. zero between 2 sig figs:

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3. leading zeros (come before non-zero digits):

4. trailing zeros (at the right end of the number)a. are NOT significant when: b. are significant only when:

5. exact/counting numbers:

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:

Addition and Subtraction:

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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 2. _____ 0.1010 3. _____ 260 001 4. _____ 89.000 5. _____ 87 000 6. _____ 0.9 7. _____ 10 000.01 8. _____ 1 001 000 9. _____ 0.000001 10. _____ 809.000 11. _____ 10 12. _____ 0.09650 13. _____ 0.808050 14. _____ 7000

15. _____ 43.000 16. _____ 2.160 17. _____ 23 000 000 000 000 000

001 18. _____ 5000 19. _____ 0.000000000000040000500

6 20. _____ 9.090 21. _____ 63 000 22. _____ 1694.0 23. _____ 0.45980 24. _____ 12 000 000 25. _____ 911

Round the following numbers to 4 significant figures26. _______ 333 999 27. _______ 3.09005 28. _______ 47.833 29. _______ 0.0038965 30. _______ 88.889

31. _______ 13 475 32. _______ 1.0004 33. _______ 0.0357849 34. _______ 99 999

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Round the following numbers to 2 significant figures

35. _______ 3.93 36. _______ 708 37. _______ 0.00604 38. _______ 34 999 39. _______ 76.09 40. _______ 5.95 41. _______ 100.0 42. _______ 4750

43. _______ 0.000206 44. _______ 119 45. _______ 6.948 46. _______ 900 47. _______ 690.9 48. _______ 8.100 49. _______ 1 890 000 50. _______ 8.0995

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

Which numbers on this page fall into this category?

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 2. _____ 0.0009010 3. _____ 400.00 4. _____ 1.90001 5. _____ 900

6. _____ 0.7 7. _____ 19.00 8. _____ 2 010 000 9. _____ 560.00001

0

10. _____ 8.3070 11. _____ 1000 12. _____ 600.900

Round the following numbers to 3 significant figures

13. ________ 25.99 14. ________ 22 999 15. ________ 0.0038249 16. ________ 1.099 17. ________ 84.94 18. ________ 7448

19. ________ 0.09995 20. ________ 9996 21. ________ 4.0005 22. ________ 6008 23. ________ 81 850 24. ________ 30.04489

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 =

26. 345.0 x 1.80 =

27. .004890 ÷ .035 =

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28. 3000.90 - 2.975 =

29. 27 - 9.5 =

30. 23.000 x 13.8900 =

31. 186.654 + 8.65291 =

32. 7.9025 ÷ 83.0 =

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Scientific Notation10

Scientific Notation

Why is scientific notation used?

Form: Examples:

How do you use scientific notation on your calculator?

More Uncertainty in Measurement:

Accuracy vs. Precision:Accuracy:

Precision:

Percent error:

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?

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

3. Use the table to explain why averages could be misleading.

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

densities in the table above. SHOW ALL WORK!Student A:

Student B:

Student C:

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

SI units/Metric2. Complete the table:

Quantity Unit Unit SymbolElectric current

meters

MassKelvin

Amount of substanceLuminous Intensity cd

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3. List the units from largest to smallest:

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

4. length of swimming pool5. length of a pencil6. mass of a pencil7. mass of a bag of apples8. time between two heartbeats9. temperature of boiling water10. 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

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?

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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.

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?

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 79.442.0 108.349.3 134.659.8 150.0

1. 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

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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?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 variables

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3. 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?

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?

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

Chemistry Name:__________________17

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?

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.

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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?

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.

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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.

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.

Problems: 21

q = m T s

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?

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?

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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 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

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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” Beverage Density Lab

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