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The simplest formula of a compound is the smallest set of possible
whole numbers for the atoms in a molecule. It
is not necessarily the same as the molecular
formula: for example, the simplest formula for benzene is CH, but benzene's
actual molecular formula is C6H6. The molecular formula is
always an integer multiple of the simplest formula. Some examples are shown in
the table below.
| Compound |
Simplest formula |
Molecular formula |
Multiple |
| Water |
H2O |
H2O |
1 |
| Hydrogen Peroxide |
HO |
H2O2 |
2 |
| Glucose |
CH2O |
C6H12O6 |
6 |
Many analytical instruments designed to give the compostion of a molecule
give either the total mass of each element or the percentage
mass for each. The procedure to convert this data back into a simplest
formula is fairly straightforward.
- Convert the mass of each element into the number of moles of that element.
(If given mass percents, convert these to grams by multiplying by 100 grams of
material: this will give you a set of masses of each element.)
- Divide all the moles by the smallest number of moles: this will give you
the mole ratio
- If the mole ratio is in whole numbers, you are done. If there are still
fractions, multiply all the ratios through by the smallest number that removes
the fraction
To get the molecular
formula, you must find some other method that measures the mass of the
molecule directly.
Example: A substance has the following elemental composition: 17.55%
Na, 39.70% Cr and 42.75% O. What is the simplest formula for this compound?
Solution: For this problem, we've been given mass percents: we can
convert these back into masses by picking an amount of the substance, say 100
grams, and multiplying through to get the masses of each element in 100 grams of
the compound.
- 17.55% Na * 100 g = 17.55 g Na
- 39.70% Cr * 100g = 39.70 g Cr
- 42.75% O * 100 g = 42.75 g O
Next, we convert each of these to a
number of moles by dividing by the molecular weight
- 17.55 g Na/22.99 g/mole = 0.7634 moles Na
- 39.70 g Cr/52.00 g/mole = 0.7634 moles Cr
- 42.75 g O/16.00 g/mole = 2.672 mole O
Now, divide each by the
smallest number of moles to get the mole ratio: the smallest number is 0.7634
moles
- 0.7634 moles Na/0.7634 moles = 1 Na
- 0.7634 moles Cr/0.7634 moles = 1 Cr
- 2.672 moles O/0.7634 moles = 3.5 O
If these were whole numbers we'd
be done: the formula would be the ratio above. Since they are not, we need to
multiply by an integer. If we multiply by 2, the 3.5 turns into 7, and we'll
have a nice integer ratio:
- 1 Na * 2 = 2 Na
- 1 Cr * 2 = 2 Cr
- 3.5 O * 2 = 7 O
The simplest formula is
Na2Cr2O7, sodium dichromate.
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