The Foundations of Chemistry

Plan

We use the equalities 1 Å
 1  10 ^10 m, 1 cm
 1  10 ^2 m, and 1 nm
 1  10 ^9 m to

construct the unit factors that convert 1.10 Å to the desired units.

Solution

__?cm
1.10 Å
1.10 10 ^8 cm

__?nm
1.10 Å
1.10 10 ^1 nm

You should now work Exercise 30.

EXAMPLE 1-5 Volume Calculation

Assuming a phosphorus atom is spherical, calculate its volume in Å^3 , cm^3 , and nm^3. The for-

mula for the volume of a sphere is V
(^43 ) r^3. Refer to Example 1-4.

Plan

We use the results of Example 1-4 to calculate the volume in each of the desired units.

Solution

__?Å^3 
(^43 ) (1.10 Å)^3 
 5.58 Å^3

__?cm^3 
( 3 ^4 ) (1.10 10 ^8 cm)^3 
 5.58 10 ^24 cm^3

__?nm^3 
( 3 ^4 ) (1.10 10 ^1 nm)^3 
 5.58 10 ^3 nm^3

You should now work Exercise 34.

EXAMPLE 1-6 Mass Conversion

A sample of gold has a mass of 0.234 mg. What is its mass in g? in kg?

Plan

We use the relationships 1 g
1000 mg and 1 kg
1000 g to write the required unit factors.

Solution

__?g
0.234 mg
2.34 10 ^4 g

__?kg
2.34 10 ^4 g
2.34 10 ^7 kg

Again, this example includes unit factors that contain only exact numbers.

1 kg



1000 g

1 g



1000 mg

1 nm



1  10 ^9 m

1.0 10 ^10 m



1 Å

1 cm



1  10 ^2 m

1  10 ^10 m



1 Å

All the unit factors used in this
example contain only exact numbers.

28 CHAPTER 1: The Foundations of Chemistry

Problem-Solving Tip:Conversions Within the Metric or SI System

The SI and metric systems of units are based on powers of ten. This means that many

unit conversions withinthese systems can be carried out just by shifting the decimal point.

For instance, the conversion from milligrams to grams in Example 1-6 just

Å n m n cm

Å n m n nm

1 Å
 10 ^10 m
 10 ^8 cm