# Coal is not a pure chemical compound, but its elemental composition can be approximated by the formula C_135H_96NO_9S. What is the approximate percentage by mass of sulfur in coal?

Jun 21, 2017

1.8%

#### Explanation:

1. Use the formula:

% by mass = (mass of part / mass of whole) x 100

What to we need to know to use this formula?

We need the mass of the part (sulfur) and the mass of the whole (coal).

What are we solving for?

We are solving for % by mass of sulfur in coal.

2. To find the mass of the part (sulfur):

Look at the molecular formula and see how many sulfur atoms there are.

${C}_{135} {H}_{96} N O S$

There is just 1 sulfur (S) atom in the formula.

Since the atomic mass of sulfur is approximately 32.1 and there's only one sulfur atom here, the mass of the part is 32.1.

You can find information about atomic mass for any element on a periodic table.

3. To find the mass of the whole (coal):

First, count up the number of atoms of each element present in the formula.

C: 135 atoms
H: 96 atoms
N: 1 atom
O: 1 atom
S: 1 atom

Now multiply the # of atoms number by the atomic mass.

C: 135 atoms x 12.0
H: 96 atoms x 1.0
N: 1 atom x 14.0
O: 1 atom x 16.0
S: 1 atom x 32.1

C: 1620
H: 96
N: 14
O: 16
S: 32.1

Finally, add up your numbers to find the mass of the whole.

$1620 + 96 + 14 + 16 + 32.1 = 1778.1$

1778.1 is the mass of the part.

% by mass $= \left(\frac{32.1}{1778.1}\right) \cdot 100$
% by mass $= 1.80529779$
% by mass $\approx$ 1.8