CHEM 1405

1
CHEM 1405

• Class Meeting 2

2
Assignments and Reminders

• Reading Assignment
• Chapter 2 by Tuesday
• Homework Problems due Tuesday
• Chapter 1 problems 6, 8, 14, 16, 24, 26, 28, 30,
  34, 36, 44, 46, 52, 56, 58
• For those in my laboratory section
• Reminder to have Safety goggles and appropriate
  clothing for lab class on Tuesday
• Also dont forget to do prelab questions due at
  beginning of lab class

3
Metric System, Calculations, Conversions, Density

• 7. What is the metric system of measurement? How
  does one convert between metric units and the
  units commonly used in the United States?
• 8. What is the difference between precision and
  accuracy in measurements?
• 9. Why is an understanding of significant
  figures important in chemistry? How do we
  determine the number of significant figures to
  report?
• 10. What is density?
• 11. What is the difference between temperature
  and heat?
• 12. How are the different temperature scales
  related to one another?

4
When you can measure what you are speaking
about, and express it in numbers, you know
something about it but when you cannot express
it in numbers, your knowledge is of a meager and
unsatisfactory kind. It may be the beginning of
knowledge, but you have scarcely Advanced to the
state of Science.
Lord Kelvin (1824 - 1907)
5
Measurement

• Consists of two parts
• a number AND a unit
• HAVE to have both
• E.g. I have a cat that is 3

years old?
days old?
months old?
6
Review of Scientific Notation

• Used to deal with very small or very large
  numbers as powers of 10
• Examples
• 0.00002 is written as 2 x 10-5
• 4,000,000 is written as 4 x 106
• Note a negative exponent just means its a
  number less than 1

7
Scientific Notation Review (Continued)
Appendix 1 in text reviews in detail

• 100 1
• 101 10
• 102 100 ( 10 x 10)
• 103 1000 ( 10 x 10 x 10)
• 104 10000
• 105 100000
• 106 1000000

• 100 1
• 10-1 0.1 ( 1/10)
• 10-2 0.01 ( 1/(10 x 10))
• 10-3 0.001
• 10-4 0.0001
• 10-5 0.00001
• 10-6 0.000001

- To add or subtract numbers in exponential
notation, it is necessary to express each
quantity as the same power of ten - To multiply
numbers expressed in exponential form, multiply
all coefficients to obtain the coefficient of the
result, and add all exponents to obtain the power
of ten in the result.
8
Modern Metric System

• International System of Units (SI)
• SI comes from French Systeme International
• Based on decimal system
• All units related by factors of 10
• Prefixes denote magnitude
• All measured quantities based on 7 base units

Makes is easier to use!
Only the United States, Liberia and Mynamar
(Burma) have not officially adopted the metric
system
9
The Seven SI Base Units
Name of Unit
Symbol of Unit
Physical Quantity
meter
Length
m
Mass
kilogram
kg
Time
second
s
Temperature
kelvin
K
Amount of substance
mole
mol
Electric Current
ampere
A
Luminous Intensity
candela
cd
10
Length

• Originally the meter was intended to equal 10-7
  or one ten-millionth of the length of the
  meridian through Paris from pole to the equator.
• They were about 0.2 millimeter short. oops!

The meter now defined as the length of the path
traveled by light in vacuum during a time
interval of 1/299 792 458 of a second.
11
Metric Prefixes
Prefix Symbol Value giga G 109 mega M 106
kilo k 103 deci d 10-1 centi c 10-2
milli m 10-3 micro m 10-6 nano n 10-9
12
Metric Lengths

• Distance from Campus to Scotty Ps Hamburgers
  2560 meters
• 2.56 x 103 meters
• Basketball Diameter 0.146 meters
• 1.46 x 10-1 meter
• Dime Diameter 0.0179 meter
• 1.79 x 10-2 meter
• Dime Thickness 0.00135 meter
• 1.35 x 10-3 meter

2.56 kilometers
1.46 decimeters
14. 6 centimeters
1.79 centimeters
1.35 millimeters
13
Volume

• Derived from length

Liter 1 dm x 1 dm x 1 dm 10 cm x 10
cm x 10 cm 1000 cm3
Since 1 liter 1000 cm3 liter/1000 cm3
10-3 liter cm3 milliliter cm3
mL cm3
Volume Length x Width x Height
Sometimes you will see mL or cm3 referred to as
cc which stands for cubic centimeter
14
Measurements

• Numbers obtained from measurements are not exact
• Measurements are subject to error
• Calibration of the equipment may be off
• May not be able to read value accurately

15
Precision and Accuracy

• Precision is how closely members of a set of
  measurements agree with one another. It reflects
  the degree of reproducibility of the
  measurements.
• Accuracy the closeness of the average of the set
  to the "correct" or most probable value

16
Accuracy vs. Precision
17
Ability To Read a Scale
Significant figures - all digits in a number
representing data or results that are known with
certainty plus one uncertain digit.
18
Significant Figures

• Not every number your calculator gives you can be
  believed
• The measuring device determines the number of
  significant figures a measurement has.

19

• For example, if you measured the length, width,
  and height of a block you could calculate the
  volume of a block
• Length 0.11 cm
• Width 3.47 cm
• Height 22.70 cm
• Volume 0.11cm x 3.47cm x 22.70cm
• 8.66459 cm3
• Where do you round off?
• 8.66? 8.6? 8.7? 8.66459?

20
Rules for Significant Figures

• All nonzero digits are significant.
• 3.51 has 3 sig figs
• The number of significant digits is independent
  of the position of the decimal point
• 0.00000000034 and 56. Both have 2 sig
  figs
• Zeros located between nonzero digits are
  significant
• 4055 has 4 sig figs

21
Rules for Significant Figures (cont.)

• Zeros at the end of a number (trailing zeros) are
  significant if the number contains a decimal
  point.
• 5.7000 has 5 sig figs
• Trailing zeros are ambiguous if the number does
  not contain a decimal point
• 2000. versus 2000
• Zeros to the left of the first nonzero integer
  are not significant.
• 0.00045 (note 4.5 x 10-4)

22
Examples of Significant Figures

• How many significant figures are in the
  following?
• 7.500
• 2009
• 600.
• 0.003050
• 80.0330

23
Examples of Significant Figures cont
2.30900 0.00040 30.07 300 0.033
24
Scientific Notation and Significant Figures

• Often used to clarify the number of significant
  figures in a number.
• Example
• 4,300 4.3 x 1,000 4.3 x 103
• 0.070 7.0 x 0.01 7.0 x 10-2

25
Sig Figs in CalculationsRules for Addition and
Subtraction

• The answer in a calculation cannot have greater
  significance than any of the quantities that
  produced the answer.
• example 54.4 cm 2.02 cm
• 54.4 cm
• 2.02 cm
• 56.42 cm

correct answer 56.4 cm
26
Sig Figs in CalculationRules for Multiplication
and Division

• The answer can be no more precise than the least
  precise number from which the answer is derived.
• The least precise number is the one with the
  fewest significant figures.

Which number has the fewest sig figs?
The answer is therefore, 3.0 x 10-8
27
Return to our example

• For example, if you measured the length, width,
  and height of a block you could calculate the
  volume of a block
• Length 0.11 cm
• Width 3.47 cm
• Height 22.70 cm
• Volume 0.11cm x 3.47cm x 22.70cm
• 8.66459 cm3
• Where do you round off?
• 8.66? 8.6? 8.7? 8.66459?

2 Significant Figures
3 Significant Figures
4 Significant Figures
Need 2 significant figures
But How do we round off?
One of these
28
Rules for Rounding Off Numbers

• If the leftmost digit to be dropped is less than
  5, leave the final digit unchanged.
• If the leftmost digit to be dropped is greater
  than 5, increase the final digit by one.
• If the leftmost to be dropped is exactly 5, we
  round up if the preceding digit is odd and down
  if the preceding digit is even.

5
5
29
Examples of Rounding Rules

• Round following numbers to 3 significant figures

Left most digit is less than 5, final digit
unchanged
3.14159
3.14
3 Digits
Left most digit is greater than 5, final digit
increased by 1
0.000338 or 3.38 x 10-4
0.0003377112
3 Digits
30
Examples of Rounding Rules

• Round following numbers to 3 significant figures

Leftmost digit is exactly 5, round up if the
preceding digit is odd
2.235159
2.24
3 Digits
Leftmost digit is exactly 5, round down if the
preceding digit is even
5.525558 x 10-7
5.52 x 10-7
3 Digits
31
Return to our example again

• For example, if you measured the length, width,
  and height of a block you could calculate the
  volume of a block
• Length 0.11 cm
• Width 3.47 cm
• Height 22.70 cm
• Volume 0.11cm x 3.47cm x 22.70cm
• 8.66459 cm3
• Where do you round off?
• 8.66? 8.6? 8.7? 8.66459?

Need 2 significant figures
8.7
Applying rounding rules
32
Unit Conversion

• You dont always have the units you want or need
• The method used for conversion is called the
  Dimensional Analysis

33
Unit Conversion

• Need to be able to convert between units
• We use these two mathematical facts to do the
  dimensional analysis
• a number divided by itself 1
• any number times one gives that number back

N x 1 N
34
Dimensional Analysis

• Example I have 3 dozen doughnuts how many
  doughnuts do I have
• We know 1 dozen 12

This ratio is a conversion factor
3 dozen doughnuts x 1 same
number of doughnuts
3 doughnuts x 12 same number of doughnuts
36 doughnuts
35
Dimensional Analysis

• Example convert 1.47 miles to inches

5280 feet
7761.6 feet
1.47 miles x
1 mile
93100 in. or 9.31 x 104 in.
Sig Figs
12 inches
7761.6 feet x
93139.2 feet
1 foot
1.47 x 5280 x 12 inches
93100 in. or 9.31 x 104 in.
Sig Figs
93139.2 in.
36
Dimensional Analysis

• Example convert 67.34 kilometers to millimeters

67,340,000 mm or 6.734 x 107 mm
Keep track of all the units it will help you
find your errors
37
Conversion FactorsSome Conversions Between
Common (U.S) and Metric Units
Table 1.7 in text

• Metric Common
• Mass
• 1 kg 2.205 lb
• 453.6 g 1 lb
• 28.35 g 1 ounce (oz)
• Length
• 1 m 39.37 in.
• 1 km 0.6214 mile
• 2.54 cm 1 in. a
• aThe U.S. inch is defined as exactly 2.54 cm.
  The other equivalencies are rounded off.

• Metric Common
• Volume
• 1 L 1.057 qt
• 3.785 L 1 gal
• 29.57 mL 1 fluid ounce (fl oz)

Need to know these But there is a way to
without memorizing the whole table...
38
How to remember length conversion
Length 1 m 39.37 in. 1 km 0.6214
mile 2.54 cm 1 in.

• Remember at least one of length conversions
• Use dimensional analysis to find others

1 m
100 cm
1 in
39.37 in
1 m
2.54 cm
1 mile
1 ft
1000 m
1 km
1 in
100 cm
0.6214 miles
5280 ft
1 km
2.54 cm
12 in
1 m
39
Volume Example

• Convert 4832 cm3 to liters

Remember 1 liter 1 dm3
cm x cm x cm
1 dm
4832 cm3
1 dm
1 L
1 dm
4.832 L
10 cm
10 cm
1 dm3
10 cm
Alternatively
Remember 1 mL 1 cm3
1 L
4832 cm3
1 mL
4.832 L
1 cm3
1000 mL
40
Density

• Density the ratio of mass to volume
• Most commonly used units are
• g/mL for liquids and solids
• g/L for gases

41
How is density useful?

• Allows us to relate how much stuff is in a volume
• Determines what materials will float

cork
water
brass nut
liquid mercury
42
Density Example

• If 73.2 mL of a liquid has a mass of 61.5 g, what
  is its density in g/mL?

43
Density Example

• How much volume does 130.4 g of gold (density
  19.30 g/mL) occupy?

Solving equation for V
Sig Figs
6.756 mL or 6.756 cm3
44
Specific Gravity

• Specific gravity the density of a substance
  compared to water as a standard
• Often the health industry uses specific gravity
  to test urine and blood samples
• Also used by brewers to measure alcohol content
  of beer

45
Specific Gravity

• Specific gravity - the ratio of the density of
  the object in question to the density of pure
  water at 4oC.
• 1.00 g/mL

Units cancel
Specific gravity is a unit-less term.
46
Example of Specific Gravity

• The density of copper at 20C is 8.92 g/mL.
  The density of water at the reference temperature
  4oC is 1.00 g/mL. What is the specific gravity of
  copper?

47
Hint for Specific Gravity

• Specific gravity is really just the density (in
  g/mL) but without the units
• If the density of an object is 2.3 g/mL, what is
  the specific gravity of the object?
• 2.3

48
Energy Heat and Temperature

• Heat flows from warmer objects to cooler objects
• Temperature is a property that tells us in what
  direction heat will flow
• Temperature is the degree of hotness or coldness
  of a body or environment (corresponding to its
  molecular kinetic energy)

Heat is an energy transfer into or out of a
system caused by a difference in temperature
between a system and its surroundings.
49
Temperature Scales

• Fahrenheit (F) defined by setting 0ºF at the
  coldest temperature he could achieve (ice/salt
  bath) and 100ºF at his body temperature
• This led to freezing point of water at 32F and
  the boiling point of water at 212F

Not very convenient
50
Temperature Scales

• Celsius (C) defined by setting freezing point of
  water at 0C and boiling point of water at 100C

A bit more convenient
51
Temperature Scales

• Kelvin (K) defined by setting absolute zero as 0
  Kelvin and and using the Celsius degree interval
• 0 K is the temperature where all molecular motion
  stops
• Temperature in Kelvin is proportional to average
  kinetic energy

Note no degree mark (º) with Kelvin
Very useful
52
Comparing Temperature ScalesFahrenheit and
Celsius
53
Comparing Temperature ScalesCelsius and Kelvin
K ºC 273.15
ºC K - 273.15
54
Comparing Temperature Scales
55
Heat Energy

• SI unit of heat is the joule(J)
• calorie(cal) is another unit of heat energy
• A calorie is defined as the is the amount of heat
  required to raise the temperature of 1 g of water
  1 C

1 cal 4.184 J
56
Little c calories and Big C Calories

• 1000 cal 1 kilocalorie
• The Calories on a food label are kilocalories

1 Calorie
Little c calorie
Big C calorie
That Hersheys bar actually has 230,000 calories!
Make sure to keep the units straight
57
Specific Heat

• The specific heat of a substance is the quantity
  of heat required to raise the temperature of one
  gram of substance by 1 C (or 1 K).
• From definition of the calorie the specific heat
  of water is 1.00 cal/(gºC)

58
Specific Heat

• Substance cal/(gC) J/(gC)
• Aluminum 0.216 0.902
• Copper (Cu) 0.0921 0.385
• Ethyl alcohol 0.588 2.46
• Iron (Fe) 0.106 0.443
• Ethylene glycol 0.561 2.35
• Magnesium (Mg) 0.245 1.025
• Mercury (Hg) 0.0332 0.139
• Sulfur 0.169 0.706
• Water (H2O) 1.000 4.182

59
Using Specific Heat
Heat absorbed or released mass x specific heat
x DT
DT T2 - T1
D is the Greek letter delta and is used to
represent change or difference
60
Using Specific Heat
Example How much heat does it take to raise
500.0 g of iron (Fe) from 40.0ºC
to 90.0ºC
First calculate DT T2 - T1 (90.0ºC- 40.0ºC)
50.0ºC
Heat absorbed or released mass x specific heat
x DT
Heat absorbed or released 500.0g x 0.106
cal/(gC) x 50.0ºC
Heat absorbed 2650 cal or 2.65 kcal