Math and Measurement Review

Chemistry is the science of substances ― their structure,

their properties, and the reactions that change them into

other substances.

Linus Pauling, “General Chemistry”

Scientific/Exponential Notation

a x 10n

1 ≤ |a| < 10, n is an integer

Negative exponent:

33

110 0.001

10 5

5

110 0.00001

10

Express the following numbers in scientific notation

25

2500

−270000

0.25

−0.0000250

Read Appendix I: A

Units are involved in calculations just as numbers.

Your calculator does not deal with units.You must work on it!

Examples that involve unit calculations

Never drop units!

A physical quantity can be considered asa product of a number and its unit.

a x

number unit

5 m

A B

AB = 15 m

C

AC = 10 m

CB = ?

CB = AB − AC = 15 m − 10 m = (15 − 10) m = 5 m

a x − b x = (a − b) x

H = 3 cm

W = 6 cm

Area = W x H = 6 cm x 3 cm = 18 cm2

a x • b x = ab x2

What is the volume of a cube with edgelength 5 cm?

V = L3 = (5 cm)3 = 53 (cm)3 = 125 cm3

(a x)3 = a3 x3

How many times is AB compared to CD in length?

5.1m10

m15

AC

AB

a a=

b

x

x b

A B15 m

C10 m

D

A B15 m

Time consumed to move from A to B is 5 s.What is the average speed?

m/s3s5

m15

Time

DistanceSpeed

meters per second

a a=

b b

xx/y

y

Chem 1211 and 1212

Mass is a measure of the amount of material in anobject.

Weight is the force that gravity exerts on an object.

F = ma

G = mg

Unit: kg

Unit: N

Mass ≠ Weight

Chemistry is a discipline of science that stronglydepends on experiments.

Experiments Measurements

Some basic concepts related to measurements

Reliability of Measurements

Accuracy refers to the agreement of a particularmeasurement with the true value.

absolute error = experimental value − true value

To quantify accuracy, define:

experimental value (m) absolute error (m)

52 2

50 0

51 1

48 −2

True value = 50 m

sign of error: direction|error|: size

experimental value theoretical value% error = x 100%

theoretical value

relative error = absolute error / true value

= absolute error / theoretical

relative error is often given in percentage:

| |: to make % error a positive number

unknown

experimental value (m) absolute error (m)

52 2

50 0

51 1

48 −2

True value = 50 m

experimental value theoretical value% error = x 100%

theoretical value

What are the percent errors for the measurementslisted in the table?

Error

Random Error: random, cannot avoid. But can take average of multiple measurements to reduce to certain degree.

Systematic Error: same direction, could fix

Based on source

true value

Random error only

true value

Random error and systematic error.

Reliability of Measurements

Accuracy refers to the agreement of a particularmeasurement with the true value.

Precision is the degree of agreement among severalmeasurements.

Accuracy ≠ Precision

The Results of Several Dart Throws Show the Difference Between Precise and Accurate

How to report a measurement?

mL

We report a measurement by recording

ALL the certain digits + ONE uncertain digit

Significant Figures

(except leading zeros)

Or conversions involving prefixes:

Note: Scientific expression does not change the number of sig figs.

a x 10n

1 ≤ |a| < 10, n is an integer

Only need to count sig figs in “a”

Conversion factor # desired unit

# given unit

#: copy from the relation between two units.

= 1

Physical quantity with given unit x Conversion factor

= Physical quantity with desired unit

5.0 in = ? cm

5.000 in = ? cm

19.21 cm = ? in

6.81 cm2 = ? in2

66 km/h = ? m/s

5.000 in = ? m

3.2 m = ? mm

3.2 cm = ? mm

7.8 g/cm3 = ? kg/m3

Three Basic Physical Quantities

Volume

Density

Temperature

1 m = 10 dm = 100 cm

(1 m)3 = (10 dm)3 = (100 cm)3

1 m3 = 103 dm3 = 106 cm3

For liquid, define: 1 L = 1 dm3

Then: 1 mL = ? cm3

= 1 cm3

Volume and its units

How much room an object occupiesin space.

Density: mass of a substance per unit volume of the substance.

V

md ,

Volume

MassDensity

Unit: kg/m3, g/cm3, g/mL

Density is a property of substances. It is determined by thesubstance’s identity and external conditions, not by thesubstance’s mass or volume.

V

md ,

Volume

MassDensity

How to find density?

How to find mass?

How to find volume?

balance

• Liquid: graduated cylinder, beaker, buret, pipet…

• Solid

Regular shape: Measure dimensions, then calculate

Irregular shape: water displacement

Temperature scales

TC, Celsius scale, °C

TF, Fahrenheit scale, °F

TK, Kelvin scale, K (not °K)

Temperature: a measure of hotness or coldness of an object.

Temperature conversions

K C o

KT T 273 K

C

F23C5

F9TT o

o

o

CF

Normal body temperature is 98.6 °F. Convert this temperature tothe Celsius and Kelvin scales.