1. The Numerical Side of Chemistry
Chapter 2

2. Types of measurement Quantitative- use numbers to describe
4 feet
100 ْF
Qualitative- use description without numbers
extra large
Hot

3. Scientists prefer Quantitative- easy check
Easy to agree upon, no personal bias
The measuring instrument limits how good the measurement is

4. How good are the measurements?
Scientists use two word to describe how good the measurements are
Accuracy- how close the measurement is to the actual value
Precision- how well can the measurement be repeated

5. Differences
Accuracy can be true of an individual measurement or the average of several
Precision requires several measurements before anything can be said about it
examples

6. Let’s use a golf analogy

7. Accurate?
Precise?

8. Accurate?
Precise?

9. Accurate?
Precise?

10. In terms of measurement
Three students measure the room to be m, 10.3 m and 10.4 m across.
Were they precise?
Were they accurate?

11. Summary of Precision Vs. Accuracy
How close to true value
Can use one measurement or many
Can have accuracy without precision
Precision
Grouping of measurements
Need to have several measurements
Repeatability
Can have precision without accuracy

12. Significant Figures

13. Significant figures (sig figs)
How many numbers mean anything
When we measure something, we can (and do) always estimate between the smallest marks. 2 1 3 4 5

14. Significant figures (sig figs)
The better marks, the better we can estimate.
Scientist always understand that the last number measured is actually an estimate 1 2 3 4 5

15. Sig Figs
What is the smallest mark on the ruler that measures cm?
142 cm?
140 cm?
Here there’s a problem does the zero count or not?
They needed a set of rules to decide which zeroes count.
All other numbers count

16. Which zeros count?
Those at the end of a number before the decimal point don’t count
1000
12400
If the number is smaller than one, zeroes before the first number don’t count
0.045
0.123

17. Which zeros count? Zeros between other sig figs COUNT.
1002
zeroes at the end of a number after the decimal point COUNT
If they are holding places, they don’t.
If they are measured (or estimated) they do

18. Sig Figs Only measurements have sig figs. Counted numbers are exact
A dozen is exactly 12
A a piece of paper is measured 11 inches tall.
Being able to locate, and count significant figures is an important skill.
YOU MUST KNOW ALL THE SIG FIG RULES !!!!

19. Summary of Significant Figures
A number is not significant if it is:
• A zero at the beginning of a decimal number
ex lb, 0.075m
• A zero used as a placeholder in a number without a decimal point
ex. 992,000,or 450,000,000
A number is a S.F. if it is:
• Any real number ( 1 thru 9)
• A zero between nonzero digits
ex. 2002g or 1.809g
• A zero at the end of a number or decimal point
ex ml or g

20. Learning Check 2 How many sig figs in the following measurements?

21. Learning Check 2 Con’t 405.0 g______ 4050 g_______ 0.450 g_______

22. Scientific Notation

23. Problems 50 is only 1 significant figure
if it really has two, how can I write it?
A zero at the end only counts after the decimal place
Scientific notation
5.0 x 101
now the zero counts.

24. Purposes of Scientific Notation
Express very small and very large numbers in a compact notation.
2.0 x 108 instead of 200,000,000
3.5 x 10-7 instead of
Express numbers in a notation that also indicates the precision of the number.
What is meant if two cities are said to be separated by a “distance of 3,000 miles”?

25. What Do We Mean by 3,000 miles?
A distance between 2,999 and 3,001 miles?
A distance between 2,990 and 3,010 miles?
A distance between 2,900 and 3,100 miles?
A distance between 2,000 and 4,000 miles?

26. What Do We Mean by 3,000 miles?
Without a context, we don’t know what is meant. In each case above, the colored digit is the largest one that is uncertain. As you ascend from bottom to top, the uncertainty decreases and the numbers become increasingly precise.
Scientific notation will allow us to express these quantities (all are “three thousand”) with the precision or uncertainty being explicit.

27. First Things First…
Power-of-ten exponential notation is central to scientific notation.
To start, you should review powers of ten and make sure that you understand the exponential notation and can covert it to standard notation.

31. How to Handle Significant Figs and Scientific Notation When Doing Math

32. Adding and subtracting with sig figs
The last sig fig in a measurement is an estimate.
Your answer when you add or subtract can not be better than your worst estimate.
You have to round it to the least place of the measurement in the problem

33. For example
27.93
6.4 +
First line up the decimal places
27.93
6.4 +
27.93
6.4
Then do the adding
Find the estimated numbers in the problem.
34.33
This answer must be rounded to the tenths place

34. What About Rounding?
look at the number behind the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
round to four sig figs
to three sig figs
to two sig figs
to one sig fig

35. Practice
6.0 x x 103
6.0 x x 10-3

36. Multiplication and Division
Rule is simpler
Same number of sig figs in the answer as the least in the question
3.6 x 653
2350.8
3.6 has 2 s.f. 653 has 3 s.f.
answer can only have 2 s.f.
2400

37. Multiplication and Division
Same rules for division
practice
4.5 / 6.245
4.5 x 6.245
x .043
3.876 / 1983
16547 / 714

38. The Metric System
An easy way to measure

39. Measuring The numbers are only half of a measurement
It is 10 long
10 what.
Numbers without units are meaningless.

40. The Metric System Easier to use because it is a decimal system
Every conversion is by some power of 10.
A metric unit has two parts
A prefix and a base unit.
prefix tells you how many times to divide or multiply by 10.

41. The SI System
• The SI system has seven base units from which all others are derived. Five of them are showed here
Physical Quantities
Name of Unit
Abbreviation
Mass
Kilogram kg
Length
Meter m
Time
Second s
Temperature
Kelvin K
Amount of Substance
Mole
mol
When a number represents a measured quantity, the units of that quantity must be specified
In 1960 an international agreement was reached specifying a particular choice of metric units for use in scientific measurements

42. SI Units (Con’t)
Prefix
Abbreviation
Meaning
Mega- M
106
Kilo- k
103
Deci- d
10-1
Centi- c
10-2
Milli- m
10-3
Micro- 
10-6
Nano- n
10-9
Pico- p
10-12
Femto- f
10-15
These prefixes indicate decimal fractions or multiples of various units

43. Derived Units

44. Derived Units
SI units are used to derive the units of other quantities.
Some of these units express speed, velocity, area and volume….
They are either base units squared or cubed, or they define different base units

45. Volume calculated by multiplying
L x W x H (for a square)
π x r2 x H (for a cylinder)
(for a sphere)
Basic SI unit of volume is the cubic meter (m3 ).
Smaller units are sometimes employed ex. cm3, dm3 ….
Volume is more commonly defined by liter (L).

46. Mass weight is a force, is the amount of matter.
1gram is defined as the mass of 1 cm3 of water at 4 ºC.
1000 g = 1000 cm3 of water
1 kg = 1 L of water

47. Converting k h D d c m
how far you have to move on this chart, tells you how far, and which direction to move the decimal place.
The box is the base unit, meters, Liters, grams, etc.

48. k h D d c m Conversions 5 6 Change 5.6 m to millimeters
starts at the base unit and move three to the right.
move the decimal point three to the right 5 6

49. k h D d c m Conversions convert 25 mg to grams convert 0.45 km to mm
convert 35 mL to liters
It works because the math works, we are dividing or multiplying by 10 the correct number of times

50. Temperature Scales

51. Measuring Temperature
0ºC
Celsius scale.
water freezes at 0ºC
water boils at 100ºC
body temperature 37ºC
room temperature ºC

52. Measuring Temperature
273 K
Measuring Temperature
Kelvin starts at absolute zero (-273 º C)
degrees are the same size
C = K
K = C
Kelvin is always bigger.
Kelvin can never be negative.

53. Temperature Conversions
At home you like to keep
the thermostat at 72 F. While
traveling in Canada, you find
the room thermostat calibrated
in degrees Celsius. To what
Celsius temperature would you
need to set the thermostat to
get the same temperature you
enjoy at home ?
• °C = 5/9 ( °F-32)
°F = 9/5 (°C ) +32
K = °C

54. Which is heavier?
it depends

55. Density how heavy something is for its size
the ratio of mass to volume for a substance
D = M / V
Independent of how much of it you have
gold - high density
air low density.

56. Calculating The formula tells you how units will be g/mL or g/cm3
A piece of wood has a mass of 11.2 g and a volume of 23 mL what is the density?
A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?

57. Calculating
A piece of wood has a density of 0.93 g/mL and a mass of 23 g what is the volume?
The units must always work out.
Algebra 1
Get the thing you want by itself, on the top.
What ever you do to onside, do to the other

58. Floating Lower density floats on higher density.
Ice is less dense than water.
Most wood is less dense than water
Helium is less dense than air.
A ship is less dense than water

59. Density of water 1 g of water is 1 mL of water.
density of water is 1 g/mL
at 4ºC
otherwise it is less

60. Problem Solving

61. Word Problems
The laboratory does not give you numbers already plugged into a formula.
You have to decide how to get the answer.
Like word problems in math.
The chemistry book gives you word problems.

62. Problem solving Identify the unknown. Identify what is given
Both in words and what units it will be measured in.
May need to read the question several times.
Identify what is given
Write it down if necessary.
Unnecessary information may also be given

63. Problem solving Plan a solution The “heart” of problem solving
Break it down into steps.
Look up needed information.
Tables
Formulas
Constants
Equations

64. Problem solving Do the calculations – algebra Finish up Sig Figs Units
Check your work
Reread the question, did you answer it
Is it reasonable?
Estimate

65. Conversion factors “A ratio of equivalent measurements.”
Start with two things that are the same.
One meter is one hundred centimeters
Write it as an equation.
1 m = 100 cm
Can divide by each side to come up with two ways of writing the number 1.

66. Conversion factors A unique way of writing the number 1.
In the same system they are defined quantities so they have unlimited significant figures.
Equivalence statements always have this relationship.
1000 mm = 1 m

67. Write the conversion factors for the following
kilograms to grams
feet to inches
1.096 qt. = 1.00 L

68. What are they good for?
We can multiply by one creatively to change the units .
13 inches is how many yards?
36 inches = 1 yard.
1 yard = inches
13 inches x yard = inches

69. What are they good for?
We can multiply by one creatively to change the units .
13 inches is how many yards?
36 inches = 1 yard.
1 yard = inches
13 inches x yard = inches

70. Dimensional Analysis Dimension = unit Analyze = solve
Using the units to solve the problems.
If the units of your answer are right, chances are you did the math right.

71. Dimensional Analysis
A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm)
in meters?
A race is 10.0 km long. How far is this in miles?
1 mile = 1760 yds
1 meter = yds
Pikes peak is 14,110 ft above sea level. What is this in meters?

72. Multiple units The speed limit is 65 mi/hr. What is this in m/s? 65 mi
1 mile = 1760 yds
1 meter = yds
65 mi hr
1760 yd
1 mi
1.094 yd
1 m
1 hr
60 min
1 min
60 s

73. Units to a Power 3 How many m3 is 1500 cm3? 1 m 100 cm 1 m 100 cm 1 m

74. Dimensional Analysis
Another measuring system has different units of measure ft = 1 fathom fathoms = 1 cable length 10 cable lengths = 1 nautical mile 3 nautical miles = 1 league
Jules Verne wrote a book 20,000 leagues under the sea. How far is this in feet?

75. Quantifying Energy

76. Recall Energy Capacity to do work
Work causes an object to move (F x d)
Potential Energy: Energy due to position
Kinetic Energy: Energy due to the motion of the object

77. Energy KE = ½ m v 2 Kinetic Energy – energy of motionA C B
Kinetic Energy – energy of motion
KE = ½ m v 2
mass
velocity (speed)
Potential Energy – stored energy
Batteries (chemical potential energy)
Spring in a watch (mechanical potential energy)
Water trapped above a dam (gravitational potential energy)

78. The Joule The unit of heat used in modern thermochemistry is the Joule
Non SI unit calorie
1Cal=1000cal
4.184J =1cal or 4.184kJ=Cal

79. Calorimetry
The amount of heat absorbed or released during a physical or chemical change can be measured…
…usually by the change in temperature of a known quantity of water
1 calorie is the heat required to raise the temperature of 1 gram of water by 1 C

80. Coffee Cup Calorimeter
Bomb Calorimeter

81. Specific heat
Amount of heat energy needed to warm 1 g of that substance by 1oC
Units are J/goC or cal/goC

82. Specific heats of some common substances
(cal/g° C) (J/g ° C)
Substance
Water
Iron
Aluminum
Ethanol

83. Calculations Involving Specific Heat
s = Specific Heat Capacity
q = Heat lost or gained
T = Temperature change (Tfinal-Tinital)

84. Example Example Calculate the energy required to raise the temperature
of a 387.0g bar of iron metal from 25oC to 40oC. The
specific heat of iron is J/goC