Chapter 12, Problem 101A

Interpretation Introduction

Interpretation: The molecular formula of oxalic acid molar mass $90{\text{ g mol}}^{-1}$ is to be determined.

Concept Introduction: The molecular formula is an expression that describes the number of atoms of each element in a molecule. It indicates the exact number of atoms in a molecule.

Answer to Problem 101A

The molecular formula of oxalic acid is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_4$ .

Explanation of Solution

The given compound is oxalic acid.

The given molar mass of oxalic acid is $90{\text{ g mol}}^{-1}$ .

The $\text{\%C}$ is $26.7\%$ .

The $\text{\%H}$ is $2.2\%$ .

The $\text{\%O}$ is $71.1\%$ .

The molar mass of $\text{C}$ is $12.01{\text{ g mol}}^{-1}$ .

The molar mass of $\text{H}$ is $1.008{\text{ g mol}}^{-1}$ .

The molar mass of $\text{O}$ is $16.00{\text{ g mol}}^{-1}$ .

The ratio of the number of atoms is as follows:

  $\begin{array}{l}\text{C:H:O}=\frac{\%\text{C}}{\text{Molar mass of C}}:\frac{\%\text{H}}{\text{Molar mass of H}}:\frac{\%\text{O}}{\text{Molar mass of O}}\\ =\frac{26.7}{12.01\times 100}:\frac{2.2}{1.008\times 100}:\frac{71.1}{16.00\times 100}\\ =0.0222:0.0218:0.0444\end{array}$

Divide the number with the smallest number, $0.0218$ as follows:

  $\begin{array}{l}\text{C:H:O}=\frac{0.0222}{0.0218}:\frac{0.0218}{0.0218}:\frac{0.0444}{0.0218}\\ =1:1:2\end{array}$

The empirical formula of oxalic acid is ${\text{CHO}}_{\text{2}}$ .

The molar mass of ${\text{CHO}}_{\text{2}}$ is calculated as follows:

  $\begin{array}{c}{\text{Molar mass CHO}}_{\text{2}}=\text{Molar mass C+Molar mass H+2}\times \text{Molar mass O}\\ =12.01{\text{ g mol}}^{-1}+1.008{\text{ g mol}}^{-1}+2\times 16.00{\text{ g mol}}^{-1}\\ =45.018{\text{ g mol}}^{-1}\end{array}$

Therefore, the molar mass of ${\text{CHO}}_{\text{2}}$ is $45.018{\text{ g mol}}^{-1}$ ,

The ratio of molecular molar mass to the ratio of the empirical molar mass of oxalic acid is calculated as follows:

  $\frac{90\bcancel{{\text{g mol}}^{-1}}}{45.018\bcancel{{\text{g mol}}^{-1}}}=2$

The molecular formula of oxalic is calculated as follows:

  $\begin{array}{c}\text{Molecular formula}=2\times {\text{CHO}}_{\text{2}}\\ ={\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_4\end{array}$

Therefore, the molecular formula of oxalic acid is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_4$ .

Conclusion

The molecular formula of oxalic acid is ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_4$ .