Measurement

International System of Units (SI)

• revised metric system proposed in 1960

• widely used in science

• 7 base units

SI Base Units

Length Meter mMass Kilogram kgTime Second sElectrical current Ampere ATemperature Kelvin KAmount of Substance Mole molLuminous intensity Candela cd

SI Prefixes

Tera- T 1012 Deci- d 10–1

Giga- G 109 Centi- c 10–2

Mega- M 106 Milli- m 10–3

Kilo- k 103 Micro- µ 10–6

Nano- n 10–9

Pico- p 10–12

Derived units in SI

measured in terms of one or more base units

= 1000 (dm3 )

1dm3 = 1 liter ( L)

= (m3)volumem x m x m

= (g/cm3) = (g/ml)mass/volumedensity

= (kg/dm3)

Density

The mass of a substance that occupies one unit of volume

massvolume

Density =kg

dm3=

g

cm3=

g

ml=

Example

What is the density of a piece of concrete that has a mass of 8.76 g and a volume of 3.07 cm3

massvolume

Density =8.76g

3.07 cm3= = 2.85g/cm3

practice problem 1

A piece of metal with a mass of 147 g is placed ina graduated cylinder. The water level rises from 20 ml to 41 ml. what is the density of the metal.

mass

volumeDensity =146 g

21 ml= = 6.95 g/ml

20 ml41 ml =- 21 ml

practice problem 2

What is the volume of a sample that has a mass of 20 g and a density of 4 g/ml

= 5 ml20 g 4 g

mlx

Practice problem 3

A metal cube has a mass of 20 g and a volume of 5 cm3. Is the cube made of pure aluminum?

mass

volumeDensity =20 g

5 cm3= = 4 g/ml

density of Aluminum is 2.7 g/ml

Temperature

There are three systems for measuring temperature that are widely used:

Kelvin scale

Celsius scale

Fahrenheit scale

K = C˚ + 273.15

C˚ = K - 273.15

F˚ = C˚ (9/5) +32

C˚ = ( F˚ - 32) 5/9Used mainly in engineering

TemperatureKelvin scale Celsius scale Fahrenheit scale

373.15

273.15

233.15

100˚C

0˚C

- 40˚C

212˚F

32˚F

-40˚F

Handling Numbers

In chemistry we deal with very large and very small numbers

Scientific Notation

is a way of dealing with numbers that are either extremely large or extremely small

N x 10n

where N is a number between 1 and 10 and n is an exponent that can be a positive or negative integer

Exponents

0.001 = = 10-3

10 1

10 1

10 1

x x

10 x 10 = 102100 =

0.1 =10 1

= 10-1

Example

Express 568.762 in scientific notation.

568.762 = 5.68762 x 102

note that the decimal point moved to the left by two places and n = 2.

Example

Express 0.00000772 in scientific notation.

0.00000772 = 7.72 x 10–6

note that the decimal point moved to the right by six places and n = –6.

practice problem 12

Express the following quantities in scientific notation.

c. 4500000 m

d. 685000000000 m

.

.

= 4.5 x 106

= 6.85 x 1011

practice problem 12

Express the following quantities in scientific notation.

e. 0.0054 kg

f. 0.00000687 kg

.

.

= 5.4 x 10-3

= 6.87 x 10-6

Scientific Notation

To add or subtract using scientific notation, first write each quantity with the same exponent n. Then add or subtract the N parts of the numbers; the exponent parts remain the same.

practice problem 14e

(1.26 x 104 kg) + (2.5 x 103 kg)

= 1.51 x 104 kg

= (1.26 x 104 kg) + (0.25 x 104 kg)

practice problem 14f

(7.06 x 10-3 kg) + (1.2 x 10-4 kg)

= 7.18 x 10-3 kg

= (7.06 x 10-3 kg) + (0.12 x 10-3 kg)

Scientific Notation

To multiply numbers expressed in scientific notation, multiply the N parts of the numbers in the usual way, but add the exponent n’s together.

practice problem 15a - 15b

(4 x 102 cm) (1 x 108 cm)

= 4 x 1010 cm2

(2 x 10-4 cm) (3 x 10-2 cm)

= 6 x 10-6 cm2

Scientific Notation

To divide numbers expressed in scientific notation, divide the N parts of the numbers in the usual way, but subtract the exponent n’s together.

practice problem 16a - 16c

6 x 102 g / 1 x 108 cm3

= 3 x 101 g/cm3

= 3 x 106 g/cm3

9 x 105 g / 3 x 10-1 cm3

The Unit-Factor Method ofSolving Problems

also called “dimensional analysis”

it is a good idea to carry units in a calculation to ensure that the answer to the problem has the correct units

The Unit-Factor Method

2.54cm = 1 in dividing both sides of the equation by 2.54cm2.54cm2.54cm

1 in2.54cm

=1 we create an expression called a unit-factor

1 in

2.54cm=1 also called a

conversion factor

Example

What is the length of a 2.85cm pin in inches?

2.85 cm = 1.12 in1in2.54cmx

practice problem 17a

= 3.6 x 105 ms360 s 1 s

1000 msx

convert 360 s to ms

practice problem 17b

= 4.8 kg4800g 1000g

1 kgx

convert 4800 g to kg

550 m

1 s

Example 2 - 4

what is a speed of 550 meters per second in kilometers per minute

1 min

60 sx

1000 m

1 kmx

1 min

33 km=

60 min

1 hrx

How many seconds are there in 24 hours ?

24 hr1 min

60 sx = 8.64 x 104 s

practice problem 19

the density of gold is 19.3 g/mL.What is the gold’s density in decigrams per liter ?

practice problem 20

19.3 g

1 mL 1 L

1000 mLx

1 g

0.1 dgx

1 L

1930 dg=

Example

Where were you a billion seconds ago ?

1x109 sec24 hours

1 dayx

60 min

1 hourx

365 days

1 yearx = 31.7 years

1 min

60 secx