Ratio of Atoms in a Compound

NOTE: Formula -> chemical formula

Empirical (Simple) Formula

Intuition

Imagine you have 2 samples of a chemical containing copper and oxygen. You could have copper () or copper (), which would have different percentages of copper.

Info

The simple formula can be determined from the experimental analysis of the % composition of each element. It tells us the simplest whole-number ratio of the atoms in the compound

The simple formula is not always the Molecular True Formula, it only tells us the lowest whole number ratio.

Steps

  1. Mass: assume 100g, so the percentages convert nicely
  2. Moles: divide by molar mass
  3. Ratio: divide molar mass by smallest molar mass, and round

Example

A compound is found to contain carbon, hydrogen, and fluorine. Find the simplest formula.

solution

Atom Mass (g) Moles Ratio
C 63.1
H 11.9
F 25.0

Therefore the formula is

Example

When 25 g of a hydrocarbon is burned, 68.58 g is produced. What is the empirical formula of the hydrocarbon?

Notes:

  • A hydrocarbon contains only and
  • During combustion a hydrocarbon reacts with to produce and
  • Unbalanced combustion equation:
  • All of the carbon in the hydrocarbon is converted to carbon in the

solution

Find the number of moles of :

Then we have .
To find the number of moles of , first find the mass of :

Then, to find the mass of , .
Then find the moles of :

Since , we have .

Molecular (True) Formula

An ionic compound is always represented in the smallest whole number ratio, for example

Copper (II) Oxide Magnesium Oxide

However, a molecular compound might not be represented in the smallest whole number ratio, so the empirical formula may not match the true molecular formula:
1:2 1:2 1:4

Note that and are NOT the same

Important

The molecular formula is always a multiple of the empirical formula

To calculate the true formula, the molar mass of the molecule MUST be provided

Example

What is the molecular formula for a compound whose molar mass is 90 g/mol, and whose empirical was determined to be ?

solution

  1. Calculate molar mass
  2. Calculate the multiple, since the true formula is some multiple of the empirical formula
  3. Calculate the true formula by multiplying the empirical formula coefficients by the multiple
Example

A compound is found to contain carbon, hydrogen, nitrogen, and oxygen. The molar mass is . Find the true formula.

solution

  1. Determine empirical formulaso the empirical formula is
  2. Calculate molar mass
  3. Calculate the multiple
  4. Calculate the true formula
Example

Cortisol (), is a key factor in the synthesis of proteins. Its profound effect on the reduction of inflammation explains its use in the treatment of rheumatoid arthritis.
Cortisol is 69.6% C, 8.34% H, and 22.1% O by mass. What is its molecular formula?

solution
Assume 100 grams.

Ratios:

  • C:
  • H:
  • O:

The molecular mass of an "empirical" formula constructed with these values is:

Ratio of this molar mass to the given molecular weight:

So

  • C:
  • H:
  • O:

Molecular formula: