The Foundations of Chemistry

We relate
(a) gallons to quarts, then
(b) quarts to liters, and then
(c) liters to milliliters.

30 CHAPTER 1: The Foundations of Chemistry

EXAMPLE 1-9 English–Metric Conversion

Express 1.0 gallon in milliliters.

Plan

We ask __?mL
1.0 gal and multiply by the appropriate factors.

gallons 88n quarts 88n liters 88n milliliters

Solution

__?mL
1.0 gal
3.8 103 mL

You should now work Exercise 32.

The fact that all other units cancel to give the desired unit, milliliters, shows that we used

the correct unit factors. The factors 4 qt/gal and 1000 mL/L contain only exact numbers.

The factor 1 L/1.06 qt contains three significant figures. Because 1.0 gal contains only

two, the answer contains only two significant figures.

Examples 1-1 through 1-9 show that multiplication by one or more unit factors

changes the units and the number of units, but not the amount of whatever we are

calculating.

PERCENTAGE

We often use percentages to describe quantitatively how a total is made up of its parts.

In Table 1-3, we described the amounts of elements present in terms of the percentage

of each element.

Percentages can be treated as unit factors. For any mixture containing substance A,

Mass A m88888888888888888888888888888888888888888n Mass mixture

If we say that a sample is 24.4% carbon by mass, we mean that out of every 100 parts (ex-

actly) by mass of sample, 24.4 parts by mass are carbon. This relationship can be repre-

sented by whichever of the two unit factors we find useful:

or

This ratio can be expressed in terms of grams of carbon for every 100 grams of sample,

pounds of carbon for every 100 pounds of sample, or any other mass or weight unit. The

next example illustrates the use of dimensional analysis involving percentage.

100 parts sample



24.4 parts carbon

24.4 parts carbon



100 parts sample

Parts A (by mass)



100 parts mixture (by mass)

% A



(by mass)

1-10

1000 mL



1 L

1 L



1.06 qt

4 qt



1 gal