# The elemental mass percent composition of succinic acid is C 40.68% , H 5.12% , and O 54.19%. What is the empirical formula of succinic acid?

Jul 14, 2015

The empirical formula of succinic acid is ${C}_{2} {H}_{3} {O}_{2}$.

#### Explanation:

In order to be able to determine the empirical formula of succinic acid, you must first determine what the mole ratio between the atoms that make up the molecule is.

To do that, you'll use the mass percent composition of carbon, hydrogen, and oxygen.

A mass percent composition of 40.68% for carbon means that, for every 100 g of succinic acid, you'll get 40.68 g of carbon.

The same is true for the other two elements - every 100 g of succinic acid will contain 5.12 g of hydrogen and 54.19 g of oxygen.

To make the calculations easier, assume that you're dealing with a 100-g sample of succinic acid.

To determine how many moles of each element are present in the sample, use carbon, hydrogen, and oxygen's molar masses.

$\text{For C": (40.68cancel("g"))/(12.011cancel("g")/"mol") = "3.387 moles}$

$\text{For H": (5.12 cancel("g"))/(1.001cancel("g")/"mol") = "5.115 moles}$

$\text{For O": (54.19cancel("g"))/(15.9994cancel("g")/"mol") = "3.387 moles}$

The mole ratio these elements have in the compound can be determined by dividing these values by the smallest of the group.

"For C": (3.387cancel("moles"))/(3.387cancel("moles")) = 1

"For H": (5.115cancel("moles"))/(3.387cancel("moles")) = 1.51 ~= 1.5

"For O": (3.387cancel("moles"))/(3.387cancel("moles")) = 1

The first draft of the empirical formula will be

${C}_{1} {H}_{1.5} {O}_{1}$

SInce you can't have fractional subscripts, multiply every subscript by $\textcolor{b l u e}{2}$ to get the empirical formula of succinic acid

${C}_{\textcolor{b l u e}{2} \cdot 1} {H}_{\textcolor{b l u e}{2} \cdot 1.5} {O}_{\textcolor{b l u e}{2} \cdot 1} \implies \textcolor{g r e e n}{{C}_{2} {H}_{3} {O}_{2}}$