The Foundations of Chemistry

Step 2: Now we know that 100.0 g of the compound contains 1.56 mol of S atoms and 3.12
mol of O atoms. We obtain a whole-number ratio between these numbers that gives the ratio
of atoms in the simplest formula.

1.00 S

SO 2

2.00 O

You should now work Exercise 52.

The solution for Example 2-12 can be set up in tabular form.

Relative Relative Number Smallest Whole-
Mass of of Atoms Divide by Number Ratio
Element Element (divide mass by AW) Smaller Number of Atoms

S 50.1 

5

3

0

2

.

.

1

1

1.56 

1

1

.

.

5

5

6

6

1.00 S

SO 2

O 49.9 

4

1

9

6

.

.

9

0

3.12 

3

1

.

.

1

5

2

6

2.00 O

This tabular format provides a convenient way to solve simplest-formula problems, as the
next example illustrates.

EXAMPLE 2-13 Simplest Formula

A 20.882-gram sample of an ionic compound is found to contain 6.072 grams of Na, 8.474
grams of S, and 6.336 grams of O. What is its simplest formula?

Plan

We reason as in Example 2-12, calculating the number of moles of each element and the ra-
tio among them. Here we use the tabular format that was introduced earlier.

Solution

3.12



1.56

1.56



1.56

A simple and useful way to obtain

whole-number ratios among several

numbers follows: (a) Divide each

number by the smallest, and then,

(b) if necessary, multiply all of the

resulting numbers by the smallest

whole number that will eliminate

fractions.

2-9 Derivation of Formulas from Elemental Composition 71

Relative Relative Number Convert Fractions Smallest Whole-
Mass of of Atoms Divide by to Whole Numbers Number Ratio
Element Element (divide mass by AW) Smallest Number (multiply by integer) of Atoms

Na 6.072 0.264 1.00 1.00
 2 2 Na

S 8.474 0.264 1.00 1.00
 2 2 S Na 2 S 2 O 3

O 6.336 0.396 1.50 1.50
 2 3 O

0.396



0.264

6.336



16.0

0.264



0.264

8.474



32.1

0.264



0.264

6.072



23.0

The “Relative Mass” column is

proportional to the mass of each

element in grams. With this

interpretation, the next column could

be headed “Relative Number of Moles

of Atoms.” Then the last column

would represent the smallest whole-

number ratios of molesof atoms. But

because a mole is always the same

number of items (atoms), that ratio is

the same as the smallest whole-number

ratio of atoms.