1. CHEM 10 SPRING 2008 CHP 2 MEASUREMENT & PROBLEM SOLVING
CHEM 10: CHAPTER TWO
MEASUREMENT & PROBLEM SOLVING

2. Scientific Notation
Very large and very small numbers are often encountered in science.
Large:
And small:
Very large and very small numbers like these are awkward and difficult to work with.
A method for representing these numbers in a simpler form is called scientific notation.
Large: x And small: x 10-21

3. Scientific Notation To write a number as a power of 10
- Move the decimal point in the original number so that it is located after the first nonzero digit.
- Follow the new number by a multiplication sign and 10 with an exponent (power).
- The exponent is equal to the number of places that the decimal point was shifted.

4. Write 6419 in scientific notation.
decimal after first nonzero digit
power of 10
64.19x102
6.419 x 103
641.9x101
6419.
6419

5. Write 0.000654 in scientific notation.
decimal after first nonzero digit
power of 10
x 10-1
x 10-2
0.654 x 10-3
6.54 x 10-4

6. Scientific Notation
Adding and subtracting in exponential or scientific notation:
- must be in same power of ten
Try adding: 3.47x x105
x x105 = x105

7. Scientific Notation Multiplying and dividing:
10a * 10b = 10a+b 10a/10b = 10a-b
Your calculator will do all this for you, if you enter the numbers correctly!
Group practice:
A x 102 * 1.20 x 10-3 =
B x 10-2 =
C x 102 / 1.20 x 10-3 =
A x 10-1
B x 10-2
C x 105

8. Measurements Experiments are performed.
Numerical values or data are obtained from these measurements.
The values are recorded to the most significant digits provided by the measuring device.
The units (labels) are recorded with the values.

9. Form of a Measurement
numerical value
70.0 kilograms =
154 pounds
unit

10. 5.16143 Significant Figures known estimated
The number of digits that are known plus one estimated digit are considered significant in a measured quantity
known
estimated

11. 6.06320 Significant Figures known estimated
The number of digits that are known plus one estimated digit are considered significant in a measured quantity
known
estimated

12. The temperature 21.2oC is expressed to 3 significant figures.
Temperature is estimated to be 21.2oC. The last 2 is uncertain.

13. The temperature 22.0oC is expressed to 3 significant figures.
Temperature is estimated to be 22.0oC. The last 0 is uncertain.

14. The temperature 22.11oC is expressed to 4 significant figures.
Temperature is estimated to be 22.11oC. The last 1 is uncertain.

15. 2 1 3 5 4 Exact Numbers Defined numbers are exact.
Exact numbers have an infinite number of significant figures.
Exact numbers occur in simple counting operations 2 1 3 5 4
Defined numbers are exact.
100 centimeters = 1 meter
12 inches = 1 foot

16. Significant Figures
All nonzero numbers are significant.
461

17. Significant Figures
All nonzero numbers are significant.
461

18. Significant Figures
All nonzero numbers are significant.
461

19. 461 Significant Figures All nonzero numbers are significant.

20. Significant Figures
A zero is significant when it is between nonzero digits.
3 Significant Figures
401

21. Significant Figures
A zero is significant when it is between nonzero digits.
5 Significant Figures 9 3 . 6

22. Significant Figures
A zero is significant when it is between nonzero digits.
3 Significant Figures 9 . 3

23. Significant Figures
A zero is significant at the end of a number that includes a decimal point.
5 Significant Figures 5 5 .

24. Significant Figures
A zero is significant at the end of a number that includes a decimal point.
5 Significant Figures 2 . 1 9 3

25. Significant Figures
A zero is not significant when it is before the first nonzero digit.
1 Significant Figure . 6

26. Significant Figures
A zero is not significant when it is before the first nonzero digit.
3 Significant Figures . 7 9

27. Significant Figures
A zero is not significant when it is at the end of a number without a decimal point.
1 Significant Figure 5

28. Significant Figures
A zero is not significant when it is at the end of a number without a decimal point.
4 Significant Figures 6 8 7 1

29. Rounding Off Numbers
Often when calculations are performed extra digits are present in the results.
It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures.
When digits are dropped the value of the last digit retained is determined by a process known as rounding off numbers.

30. 80.873 Rounding Off Numbers 4 or less
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
4 or less
80.873

31. 1.875377 Rounding Off Numbers 4 or less
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
4 or less

32. Rounding Off Numbers
Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1.
5 or greater
drop these figures
increase by 1 6

33. CALCULATIONS AND SIGNIFICANT FIGURES
The results of a calculation cannot be more precise than the least precise measurement.
Learn how to determine number of sig figs in answers after performing calculations, including multiply/divide and add/subtract.
In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.
The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.
- The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

34. The correct answer is 440 or 4.4 x 102
2.3 has two significant figures.
(190.6)(2.3) =
190.6 has four significant figures.
Answer given by calculator.
The answer should have two significant figures because 2.3 is the number with the fewest significant figures.
Drop these three digits.
Round off this digit to four.
438.38
The correct answer is 440 or 4.4 x 102

35. Round off to the nearest unit.
Add , 129 and 52.2
Least precise number.
125.17
129.
52.2
Answer given by calculator.
306.37
Correct answer.
Round off to the nearest unit.
306.37

36. 0.018286814 Answer given by calculator. Two significant figures.
Drop these 6 digits.
Correct answer.
The answer should have two significant figures because is the number with the fewest significant figures.

37. The Metric System
The metric or International System (SI, Systeme International) is a decimal system of units.
It is built around standard units.
It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.

38. International System’s Standard Units of Measurement
Quantity Name of Unit Abbreviation
Length meter m
Mass kilogram kg
Temperature Kelvin K
Time second s
Amount of substance mole mol

39. Prefixes and Numerical Values for SI Units
Power of 10
Prefix Symbol Numerical Value Equivalent
exa E 1,000,000,000,000,000,
peta P 1,000,000,000,000,
tera T 1,000,000,000,
giga G 1,000,000,
mega M 1,000,
kilo k 1,
hecto h
deca da
— — 1 100

40. Prefixes and Numerical Values for SI Units
Power of 10
Prefix Symbol Numerical Value Equivalent
deci d
centi c
milli m
micro 
nano n
pico p
femto f
atto a

41. GROUP RACE FOR ANSWERS IN METRIC WIN A PRIZE!
a. one millionth of a scope = ____scope
b mental = ____mental
c. 1,000,000 phones = ___phones
d mockingbird =___bird
e. 1/1000 tary =___tary

42. MEMORIZE THESE ENGLISH/METRIC CONVERSIONS: (table 2.3 plus others)
1 lb = grams 1 inch = 2.54 cm
(exactly)
1 mile = km qt = 1 L
1000 mL = 1 L
1 mL = 1 cm3
1 cal = Joule 1 atm = torr
oF = 1.8oC K = oC

43. Dimensional Analysis
Dimensional analysis converts one unit to another by using conversion factors.
unit1 x conversion factor = unit2
Basic Steps
1. Read the problem carefully. Determine what is to be solved for and write it down.
2. Tabulate the data given in the problem.
Label all factors and measurements with the proper units.

44. Dimensional Analysis Basic steps – continued:
3. Determine which principles are involved and which unit relationships are needed to solve the problem.
You may need to refer to tables for needed data.
4. Set up the problem in a neat, organized and logical fashion.
Make sure unwanted units cancel.
Use sample problems in the text as guides for setting up the problem.

45. Dimensional Analysis Basic steps continued:
5. Proceed with the necessary mathematical operations.
Make certain that your answer contains the proper number of significant figures.
6. Check the answer to make sure it is reasonable.

46. Unit Abbreviation Metric Equivalent Equivalent
Metric Units of Length
Exponential
Unit Abbreviation Metric Equivalent Equivalent
kilometer km 1,000 m 103 m
meter m 1 m 100 m
decimeter dm 0.1 m 10-1 m
centimeter cm 0.01 m 10-2 m
millimeter mm m 10-3 m
micrometer m m 10-6 m
nanometer nm m 10-9 m

47. How many millimeters are there in 2.5 meters?
Use the conversion factor with millimeters in the numerator and meters in the denominator.

48. Convert 3.7 x 103 cm to micrometers.
Centimeters can be converted to micrometers by writing down conversion factors in succession.
cm  m  meters

49. Convert 3.7 x 103 cm to micrometers.
Centimeters can be converted to micrometers by two stepwise conversions.
cm  m  meters

50. Convert 16.0 inches to centimeters.
Use this conversion factor

51. Unit Abbreviation Gram Equivalent Equivalent
Metric Units of mass
Exponential
Unit Abbreviation Gram Equivalent Equivalent
kilogram kg 1,000 g 103 g
gram g 1 g 100 g
decigram dg 0.1 g 10-1 g
centigram cg 0.01 g 10-2 g
milligram mg g 10-3 g
microgram g g 10-6 g

52. Convert 45 decigrams to grams.
1 g = 10 dg

53. Grams can be converted to ounces by a series of stepwise conversions.
An atom of hydrogen weighs x g. How many ounces does the atom weigh?
Grams can be converted to ounces by a series of stepwise conversions.
1 lb = 454 g
16 oz = 1 lb

54. An atom of hydrogen weighs 1. 674 x 10-24 g
An atom of hydrogen weighs x g. How many ounces does the atom weigh?
Grams can be converted to ounces using a linear expression by writing down conversion factors in succession.

55. Derived Units: Area & Volume
Area: Measure of the amount of two-dimensional space occupied. It is a derived unit from the two dimensions of area: length x width.
Volume: Measure of the amount of three-dimensional space occupied. It is a derived unit from the three dimensions of volume: length x width x height.
SI unit = cubic meter (m3)
Usually measure liquid or gas volume in milliliters (mL)
1 L is slightly larger than 1 quart (1 L = qt)
1 L = mL = 103 mL
1 mL = L = 10-3 L
1 mL = 1 cm3

57. Convert 4.61 x 102 microliters to milliliters.
Microliters can be converted to milliliters by a series of stepwise conversions.
L  L  mL

58. Convert 4.61 x 102 microliters to milliliters.
Microliters can be converted to milliliters using a linear expression by writing down conversion factors in succession.
L  L  mL

59. Heat
A form of energy that is associated with the motion of small particles of matter.
Heat refers to the quantity of this energy associated with the system.
The system is the entity that is being heated or cooled.

60. Temperature A measure of the intensity of heat.
It does not depend on the size of the system.
Heat always flows from a region of higher temperature to a region of lower temperature.

61. Temperature Measurement
The SI unit of temperature is the Kelvin.
There are three temperature scales: Kelvin, Celsius and Fahrenheit.
In the laboratory temperature is commonly measured with a thermometer.

63. It is not uncommon for temperatures in the Canadian plains to reach –60.oF and below during the winter. What is this temperature in oC and K?

64. It is not uncommon for temperatures in the Canadian planes to reach –60.oF and below during the winter. What is this temperature in oC and K?

65. Density is the ratio of the mass of a substance to the volume occupied by that substance.

66. Density varies with temperature

69. Density examples Try to rank: air, lead, feathers, water, gasoline
Air < feathers < gasoline < water < lead
1.28 g/L <0.5 g/mL <0.7 g/mL< 1.0 g/mL < 11.3 g/mL
gas (solid) liquid liquid solid

70. (b) Substitute the data and calculate.
The density of ether is g/mL. What is the mass of 25.0 milliliters of ether?
Method 1
(a) Solve the density equation for mass.
(b) Substitute the data and calculate.

71. The conversion of units is
The density of ether is g/mL. What is the mass of 25.0 milliliters of ether?
Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:
mL → g
The conversion of units is

72. (b) Substitute the data and calculate.
The density of oxygen at 0oC is g/L. What is the volume of grams of oxygen at this temperature?
Method 1
(a) Solve the density equation for volume.
(b) Substitute the data and calculate.

73. The conversion of units is
The density of oxygen at 0oC is g/L. What is the volume of grams of oxygen at this temperature?
Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:
g → L
The conversion of units is

74. SPECIFIC GRAVITY An older concept still used in many places.
Specific gravity of a liquid or solid is always its density referenced to water at the same temperature.
Specific gravity of a gas is always referenced to air at the same temperature and pressure.