Chapter 6, Problem 10STP

Interpretation Introduction

Interpretation: The molecular formula of the compound needs to be determined.

Concept Introduction: The empirical formula is the simplest ratio of atoms of elements present in the compound. It does not tell about the actual number of atoms present in it. Some molecules have empirical formula equal to their molecular formula.

Answer to Problem 10STP

Correct Answer: Option D.

Explanation of Solution

The atoms of element present in the given compound are carbon, hydrogen and oxygen. There is 40% C and 6.71% H. The mass and number of moles of sample of compound is 9 g and 0.050 mol respectively.

The mass of compound is given 9 g. Thus, from given percentage of C and H atom, the mass of C and H can be calculated as follows:

  $\begin{array}{l}{m}_C=\frac{40}{100}\times 9=3.6\text{ g}\\ m_H=\frac{6.71}{100}\times 9=0.604\text{ g}\end{array}$

Now, mass of O will be:

  $m_{\text{O}}=9-3.6-0.604=4.796\text{ g}$

Now, molar mass of C, H and O is 12.01 g/mol, 1.008 g/mol and 15.99 g/mol respectively. Thus, number of moles can be calculated as follows:

  $n=\frac{m}{M}$

Thus, number of moles of C, H and O will be:

  $\begin{array}{l}{n}_C=\frac{3.6\text{ g}}{12.01\text{ g/mol}}=0.3\\ n_H=\frac{0.604\text{ g}}{1.008\text{ g/mol}}=0.6\\ n_O=\frac{4.796\text{ g}}{15.99\text{ g/mol}}=0.3\end{array}$

The ratio of number of moles of C:H:O will be 0.3:0.6:0.3 or 1:2:1. Thus, empirical formula of compound will be ${\text{CH}}_{\text{2}}\text{O}$ .

Now, calculate the empirical mass:

  ${\text{CH}}_{\text{2}}\text{O=12}\text{.01+2}\left(1.008\right)+15.99=30.016\text{ g/mol}$

The molecular formula can be calculated from number of moles and mass as follows:

  $\begin{array}{l}n=\frac{m}{M}\\ \text{Or,}\\ M=\frac{m}{n}\end{array}$

Putting the values,

  $M=\frac{9\text{ g}}{0.05\text{ mol}}=180\text{ g/mol}$

The ratio of molecular mass of compound and empirical mass will be:

  $R=\frac{180\text{ g/mol}}{30.016\text{ g/mol}}=6$

Thus, molecular formula of compound will be:

  ${\text{C}}_6{\text{H}}_{\text{12}}{\text{O}}_6$

Conclusion

Therefore, option (D) is correct.