chapter 1

CHEM 205CHEM 205

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Units of measurement

MeasurementMeasurement

You are making a measurement when you

Check you weight

Read your watch

Take your temperature

Weigh an apple

What kinds of measurements did you make today?

Some Tools for MeasurementSome Tools for Measurement

How do you measure….

Temperature?

Time?

Volume?

Weight?

Measurement in ScienceMeasurement in Science

In Science we

do experiments

measure quantities

use numbers to report measurements

Units in the Metric System (S.I.)Units in the Metric System (S.I.)

length meter m

volume liter L

mass gram g

temperatureCelsius °C

Stating a MeasurementStating a Measurement

In every measurement there is aNUMBER followed by a UNIT from measuring device

The patient’s temperature is 102°F.

The sack holds 5 lbs of potatoes.

It is 8 miles from your house to school.

The bottle holds 2 L of orange soda

Significant Figures

Reading a measureReading a measure

First digit (known) = 2 2.?? cm

Second digit (known) = 0.7 2.7? cm

Third digit (estimated) between 0.05- 0.07

Length reported = 2.74 cm

or 2.75 cm

or 2.73 cm

Known, significant, estimated digitsKnown, significant, estimated digits

2.74 cm

Known

(100% certain)Estimated

(uncertain)

Significant!

l5. . . . I . . . . I6. . . .I . . . . I7. . cm

1) 6.0 cm

2) 6.06 cm

3) 6.60 cm

What is the length of the line?

Exact NumbersExact Numbers

Obtained when you count objects

2 soccer balls

1 watch

3 pizzas

Obtained from a defined relationship1 foot = 12 inches

1 meters = 100 cm

Not obtained with measuring tools

A._M_Gold melts at 1064°C

B._E_1 yard = 3 feet

C._M_A red blood cell with diameter 6 x 10-4 cm

D._E_There were 6 hats on the shelf

E._M_A can of soda contains 355 mL of soda

Classify each of the following as an exact (E) or a measured (M) number.

A.___Gold melts at 1064°C

B.___1 yard = 3 feet

C.___A red blood cell with diameter 6 x 10-4 cm

D.___There were 6 hats on the shelf

E.___A can of soda contains 355 mL of soda

Significant Figures in Calculations

Number of Significant Figures

38.15 cm

0.008 ft

25000 in

0.48600 gal

4

1

2

5

Counting Significant FiguresCounting Significant Figures

Significant Numbers in CalculationsSignificant Numbers in Calculations

A calculated answer cannot be more precise than the measuring tool.

Significant figures are needed for final answers from

1) adding or subtracting

2) multiplying or dividing

Adding and SubtractingAdding and Subtracting

The answer has the same number of decimal places as the measurement with the fewest decimal places.

25.2 ONE decimal place

+ 1.34 TWO decimal places

26.54

answer 26.5 ONE decimal place

In each calculation, round the answer to the correct number of significant

figures.

A. 235.05 + 19.6 + 2.1 =

1) 256.75 2) 256.8 3) 257

B. 58.925 - 18.2 =

1) 40.725 2) 40.73 3) 40.7

Multiplying and DividingMultiplying and Dividing

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60

C. 2.54 X 0.0028 =

0.0105 X 0.060

1) 11.3 2) 11 3) 0.041

In each calculation, round the answer to the correct number of significant figures.

Prefixes and

Equalities

Metric PrefixesMetric Prefixes

Increase or decrease basic unit by 10

Form new units larger or smaller than the

basic units

0.00356 = 3.56 x 10-3

123 000 000 000 000 = 123 x 1012

Prefix Symbol Value Exponential

giga G 1,000,000,000 109

mega M 1,000,000 106

kilo k 1,000 103

hecto h 100 102

deca da 10 101

no prefix means: 1 100

deci d 0.1 10-1

centi c 0.01 10-2

milli m 0.001 10-3

micro m 0.000001 10-6

nano n 0.000000001 10-9

A. 1 kg = ____ g

1) 10 g 2) 100 g 3) 1000 g

B. 1 mm = ____ m

1) 0.001 m 2) 0.01 m 3) 0.1 m

Give the value of the following units:

Equalities Equalities

State the same measurement in two

different units

length

10.0 in.

25.4 cm

Conversion FactorsConversion Factors

Express an equality between two different units

Example: 1 in = 2.54 cm

Factors: 1 in and 2.54 cm

2.54 cm 1 in

3 in → ? cm 3 in x1in

2.54cm= 7.62 cm8

Initial unit = pints Final unit =

Blood has a density of 0.05 g/mL. If a

person lost 0.30 pints of blood at

18°C, how many ounces of blood

would that be?

oz

1 US pint = 16 US fluid ounces

oz 4.8 pint 1

oz 16 pints 0.30

How many seconds are in 14 days?

14 day x 1 day x 60 min x 60 s 24 h 1 h 1 min

14 day x 24 h x 60 min x 60 s 1 day 1 h 1 min

= 1.2 x 105 s

READ problem

IDENTIFY data

Write down a unit plan

from the INITIAL UNIT to the DESIRED UNIT

Select CONVERSION factors

Change initial unit to desired unit

CANCEL units and check

Do math on CALCULATOR (is the result logical?)

Give an answer using SIGNIFICANT FIGURES

Steps to solve a problemSteps to solve a problem

Measuring Temperature

Kelvin ScaleKelvin Scale

0 K is the lowest temperature

0 K = - 273°C

K °C

K = °C + 273

37°C to K?

K = °C + 273 == 37°C + 273 = = 310 K

°C = K - 273

298K to °C ?

°C = K - 273 == 298 - 273 = = 25 °C

Density

DensityDensity

Density compares the mass of an object to its volume

3cm

g

mL

g

volume

mass d

Note: 1 mL = 1 cm3

1) 0.2 g/ cm3 2) 6 g/cm3 3) 252 g/cm3

25 mL

33 mL

What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?

Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL

Volume of metal (cm3) = 8 mL x 1 cm3 = 8 cm3

1 mL

Density of metal =

mass = 48 g = 6 g/cm3

volume 8 cm3

Solution: 6 g/cm3 (#2)

What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?

W

V

K

Which diagram represents the liquid layers in the cylinder?(K) Karo syrup (1.4 g/mL)(V) vegetable oil (0.91 g/mL)(W) water (1.0 g/mL)

W

V

K

W

V

K

1 2 3

Density as Conversion FactorDensity as Conversion Factor

A substance has a density of 3.8 g/mL.

Density = 3.8 g/mL

Equality 3.8 g = 1 mL = 1 cm3

Conversion factors:

g 3.8

mL 1 or

mL 1

g 3.8

1) 0.614 kg

2) 614 kg

3) 1.25 kg

The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?

Unit plan: mL g kg

Equalities: 1 mL = 0.702 g and 1 kg = 1000 g

Calculation:

875 mL x 0.702 g x 1 kg = 0.614 kg

1 mL 1000 g

Solution: 0.614 kg (#1)

The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?