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

1.	You are given the molecular formula for a compound.
2.	Divide the number of each type of atom by the highest common factor.
3.	The empirical formula for the compound is left.

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

1.	Find the $M_r$ of the empirical formula, using the $A_r$ of each element.
2.	Divide the $M_r$ of the whole compound by the $M_r$ of the empirical formula.
3.	Multiply the number of each element in the empirical formula by the answer value from step 2.
4.	The molecular formula for the compound is left.

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 $\underline{CH_4}$ 