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CHEMISTRYCHEMISTRY

Observations

Hypothesis

Experiment

Theory

The Scientific Method

Data (quantitative); “natural law”

Measurement• Metric system (National Assembly of France, 1790)• International System of Units (SI, 1960)

3

What do we measure?Length

VolumeMass

Time

Temperature

Metric Unitsm

L

g

s

˚C

SI Units

m

m3

kg

s

K

Derived units: combinations of fundamental units

Ex. Speed (m/s)

Equipment for Measurement

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Length

Volume

Mass

Time

Temp

Scientific Notation

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Coefficient

Power of Ten: 10x

Width of a human hair = 0.000008 m

Coefficient?

8 Power? 10-6

8 x 10-6 m

Seconds to drive from Seattle to NYC = 90,000 s

Coefficient?

9 Power? 104

9 x 104 s

Scientific Notation on Calculators

Your calculator should work with scientific notation! Look for:

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EE EXP

Note:9.64 x 105 = 9.65 E5

Coefficient Power of Ten

2. x 10-8 = 2.E-8

Scientific Notation

Conversion to a standard number

3.252 x 106

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If power of ten is positive, move decimal point to the

RIGHT(add zeros if necessary)

If power of ten is negative, move decimal point to the

LEFT(add zeros if necessary)

4.56 x 10-3

0.00456

3252000

Measured Numbers – Numbers obtained when you measure a quantity– Estimate the final digit

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1 2 6543

Read greater than 4 and less than 5; estimate last digit

1 2 6543

Read greater than 4.8 and less than 4.9; estimate last digit

4.84 in

4.8 in

Significant Figures

• All measured digits, including the estimated digit

4.84 cm

2045 g2.333 x 10-5 L50. s

• Zeros not significant in 2 situations:– At the beginning of a decimal number– At the end of a number without decimal point

4500 cm

0.0063 kg

0.05202 L 9

Exact Numbers

• A counted number (not measured!)– Ex. # of students in this classroom

• A definition comparing two units in same measurement system– Ex. 1 ft = 12 in– Ex. 1 kg = 1000 g

NOT considered as significant figures!

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Significant Figures in Calculations

• In lab, at work, we measure things. Then what?

• The number of sig figs in measured numbers limits the number of sig figs in a calculated answer.

You can’t have more detail in your answer than

you have in your measurements

Number of sig figs in answer depends on what type of calculations you performed

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Sig Figs in Calculations• Multiplication and Division:

– Final answer has the same number of sig figs as the measurement with the fewest significant figures

• Addition and Subtraction:– Final answer has the same number of decimal places

as the measurement with the fewest decimal places

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24.64 x 3.2 = 78.848

79.

3.525 - 5.2 = -1.675

-1.7

3.525 + 6.475 = 10

10.000

Rounding Rules

How do we limit the number of sig figs? Rounding!

Look at first non-significant number (to be dropped)

Is this number 4 or less?Is this number 5 or more?

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Round “down”Round “up”

2390.321 to 4 sig figs

2390.

0.0056194 to 1 sig fig

0.006

688511 to 3 sig figs

689000

Prefixes

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Is it easier to write:• 590000 g or 590 kg?• 0.0004 g or 0.4 mg?

Prefixes can be attached to units to increase or decrease size by a factor of 10 (multiply by 10 or divide by 10)

Multiply by 10x

Multiply by 10-

x

Common Prefixes with SI Units

Prefix Prefix Symbol

Word Exponential Notation

Mega M Million 1,000,000 1 x 10 6

Kilo k Thousand 1,000 1 x 10 3

Deci d Tenth 0.10 1 x 10 -1

Centi c Hundredth 0.01 1 x 10 -2

Milli m Thousandth

0.001 1 x 10 -3

Micro μ Millionth 0.000001 1 x 10 -6

Nano n Billionth 0.000000001 1 x 10 -9

Pico p Trillionth 0.000000000001 1 x 10 -12

Femto f Quadrillionth

0.000000000000001

1 x 10 -15

Equalities used in MeasurementsEquality:

A relationship between two units that measure the same quantity

• Length: 1 m = 100 cm = 1000 mm

• Volume:1 L = 10 dL = 1000 mL

1 dL = 100 mL

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Cubic centimeter: cc

1 cm x 1 cm x 1 cm = 1 cm3

Thinking about volume conversions…

If 1 cubic centimeter equals 1 mL,how many milliliters does 1 cubic meter

equal?

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100 cm x 100 cm x 100 cm = 1000000 cm3

1 m = 100 cm

1000000 cm3 = 1000000 mL

1 x 106 mL

1 x 103 L

• Mass:1 kg = 1000 g1 g = 1000 mg1 mg = 1000 μg

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Equalities used in Measurements

Conversion Factors: Changing Between Units

1 hr = 60 min

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Conversion Factor:

hr 1

hr 11

min 60

min601

Metric Conversion Factor:

min 60

hr 1

hr 1

min60

cm 100

m 1

m 1

cm 100

More Conversion Factors

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Metric Conversion Factors:

3cm 1

mL 1

mL 1

cm 1 3

Metric- U.S. System Conversion Factors:

lb 2.20

kg 1

kg 1

lb 20.2

L 1

mL 1000

mL 1000

L 1

1 kg = 2.20 lb

mi 0.621

km 1

km 1

mi 621.01 km = 0.621 mi

More Conversion Factors

• Standard equalities can be looked up in a table (Table 1.9 in your book, for example)

• Other equalities may be stated in a problem

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Examples: • The average speed of cars driving on I-5 during

rush hour is 11 mph.

Equality: 11 miles = 1 hour

h 1

mi 11

mi 11

h 1

• One five pound bag of sugar costs $4.00. Equality: 1 bag = 5 lb =

$4.00

Percents as Conversion Factors

• Percent means 1 per 100

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Example: • If a person is 20% body fat by mass, then:

body kg 100

fat kg 20

20 kg fat = 100 kg body total

fat kg 20

body kg 100

End of class Practice Questions• How many sig figs are in each the following?

0.00500 L 53,069 s 0.00004715 m 0.509 kg

• Write the numbers above in scientific notation.– How many sig figs does each have now?

• Write a conversion factor relating micrograms to grams

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Practice Questions

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Is each of the following an exact or measured number?• The number of chair legs in this room• The length of your benchtop in inches• The length of your benchtop in cm• The area of the projector screen

What is the temperature on each (˚C) thermometer shown? (sig figs!)

4.9 ˚C 61.5 ˚C

Exact

Measured

Measured

Measured

Using Conversion Factors

1. What’s given? What do we want to know?

2. What conversion factors do I need?

3. Set up problem

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weight lost (kg)= 15 kg

Your patient tells you that she recently lost 15 kg.

How many pounds has she lost?

weight lost (lb)= ? lb

kg lb

2.20 lb = 1 kg lb 2.20

kg 1

kg 1

lb 20.2

factor(s) conversion Given

Using Conversion Factors

3. Set up problem

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lb 2.20

kg 1

kg 1

lb 20.2factor(s) conversion Given

15 kg x ?

kg lb

lb 2.20

kg 1 kg 15

kg 1

lb 2.20 kg 15

81818.6lb

kgkg

33kg

kglblb 33

Check sig figs!

Using Conversion Factors

1. What’s given? What do we want to know?

2. What conversion factors do I need?

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1 week

The recommended daily value of vitamin C is 60 mg. If an average orange contains 45 mg of vitamin C, how many oranges should you eat in a week?

# of oranges

week # oranges

days 7

week1

day 1

mg 60

orange 1

C vitamin mg 45

week 1 week1

days 7

day 1

mg 60 mg 45

orange 1oranges 33333.9

oranges 9

days mg vitamin C

Physical Properties of Materials

• Physical Property:– can be measured or perceived without

changing the material’s identity– Intensive

• Independent of amount of substance

• Ex. Boiling point

– Extensive• Depends on amount of substance

• Ex. Mass, volume

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Density

• Relationship between mass and volume

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volume

massdensity

V

m

• Density is a physical property

• Density is an intensive property 4 times more mass

4 times more volume

V4

m4

V

m

Density

• Units: – SI: kg/m3

– often use: g/L

g/mL

g/cm3

g/cc

• Density of water (at 20˚C and typical room pressure)

1 g/cc 1 g/mL

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Density of Solids

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• How can we determine the density of a solid?

– Need to know mass– Need to know volume volume

massdensity

Measure displacement

of water

Does this method work for all solid materials?

Density Table

Density can be used as a conversion factor!

(relates mass to volume) 32

Specific Gravity (sp gr)

Ratio between density of substance & density of water

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waterofdensity

sample ofdensity gravity specific

Measure sp gr with a hydrometer

Units for sp gr?

waterofdensity

sample ofdensity gr sp

mlg 1.1

mlg 1.2

Unitless!

Temperature

• Measure of how hot or cold a substance is relative to another substance

• Scales and Units

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Scale Boiling Point H2O

Freezing Point H2O

Celsius ˚C

Fahrenheit ˚F

Kelvin K

100˚C 0˚C

212˚F 32˚F

373.15 K

273.15 K

Note: the unit is not ˚K

Temperature Conversions

How many units are between boiling point and freezing point of water?

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Scale

Celsius ˚C

Fahrenheit ˚F

Kelvin K

100˚C – 0˚C212˚F –

32˚F

= 100 units= 180 units

373 K –273 K

= 100 units

the unit 1 Kelvin equals the unit 1 degree Celsius 273TT CK

Converting Units Fahrenheit to Units Celsius

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180 Fahrenheit degrees = 100 Celsius degrees

degrees Celsius 100

degrees Fahrenheit 180C 1

F 8.1o

o

C 1

TF 8.1T

oC

o

F

o32

oCF 32 )T(8.1T

Things to Remember about the Temperature Scales

1. 0 K is absolute zero2. You can never (ever ever ever) have a

temperature of negative K3. The unit for the Celsius scale is the degree C (˚C)4. The unit for the Fahrenheit scale is the degree F

(˚F)5. The units for the Kelvin scale is the Kelvin (K)

6. A change of x Kelvin = a change of x ˚C

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K 300 -K 350 C300 -C350 oo

Start value and end values are different; Both changed the same amount (50 K units = 50 ˚C

units)

Precision and Accuracy• Precision: reproducibility• Accuracy: how close to actual value

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Temp (˚C)