Molecular and empirical formulae

​​In a nutshell 

Molecular and empirical formulas show how many of each type of atom a compound contains. The molecular formula represents the number and type of each atom, whereas the empirical formula will include a ratio. 

Molecular formula 

Definition

The molecular formula of a compound will provide the number of each type of atom that the compound contains. 

Example

The hydrocarbon ethane has two carbon atoms ($$C_2$$) and six hydrogen atoms ($$H_6$$) in its structure, so the molecular formula is $${C_2H_6}$$.

Empirical formula 

Definition

The empirical formula of a compound is the simplest whole number ratio of each type of atom in a compound. 

The molecular formula can be used to work out an empirical formula. 

procedure 

Example

The molecular formula of hydrogen peroxide is $$H_2O_2$$. What is the empirical formula of hydrogen peroxide?

Molecular formula of hydrogen peroxide:

$$H_2O_2$$​​

Divided by the highest common factor, both $$H_2$$ and $$O_2$$ will divide by $$2$$​:

$$\frac{H_2O_2}{2}=HO$$

The empirical formula of hydrogen peroxide is $$\underline{HO}$$.​

​

Calculating molecular formula from the empirical formula

Just as the empirical formula can be calculated form the molecular formula; the molecular formula can be calculated from the empirical formula. 

In order to do this you must have the $$M_r$$ of the compound. ​

procedure 

Example

The empirical formula for a compound is $$C_{7}H_{15}$$​. The compound has a $$M_r$$ of $$198$$, what is the molecular formula for this hydrocarbon?

Work out the $$M_r$$ for the empirical formula of the compound:

$$M_r=(7\times12)+(15\times1)=99$$​​

Divide the $$M_r$$ of the compound by the $$M_r$$​ of the empirical formula:

$$\frac{198}{99}=2$$​​

Multiply everything in the empirical formula by $$2$$:

$$C_{(7\times2)}H_{(15\times2)}=C_{14}H_{30}$$

The molecular formula is therefore, $$\underline{C_{14}H_{30}}$$.

Calculating the empirical formula from mass

You can also calculate the empirical formula of a compound if you know the mass of its constituent elements. 

Example

A hydrocarbon contains $$60\ g$$ of carbon and $$20\ g$$ of hydrogen. What is the empirical formula?​

Work out the number of moles of each constituent element:

$$moles = \frac{mass}{A_r}\\ \ \\ \ \\ \ A_r(C)=12\\ \ \\ \ \\ \ A_r(H)=1\\ \ \\ \ \\ \ moles (C)=\frac{60}{12}=5\ moles\\ \ \\ \ \\ \ moles (H)=\frac{20}{1}=20\ moles$$​​

Write down the ratio of moles of carbon to hydrogen and then simplify it:

$$C:H\\5:20\\1:4$$​​

This is your empirical formula. The empirical formula is therefore $$\underline{CH_4}$$​