Chapter 10.4, Problem 63PP

Interpretation Introduction

Interpretation:

The molecular formula of the liquid needs to be determined.

Concept introduction:

The empirical formula tells about the simplest ratio of atoms of present in the molecule. It does not give the actual number of atoms present in the molecule. The molecular formula shows the actual number of atoms present in the molecule.

Answer to Problem 63PP

The molecular formula of the liquid is N₂O₂.

Explanation of Solution

Given information:

A colorless liquid composed of $46.68\%N$ and $53.32\%O$ has a molar mass of $60.01$ g/mol.

Calculation: The relation between number of moles, mass and molar mass is as follows:

$n=\frac{m}{M}$

Taking mass of compound to be $100$ g, the mass of N and O atoms will be 46.88 g and 53.32 g respectively.

The molar mass of N and O is 14 g/mol and 16 g/mol respectively thus, number of moles of N and O can be calculated as follows:

$\begin{array}{l}{n}_N=\frac{46.88\text{ g}}{14\text{ g/mol}}=3.3\\ n_O=\frac{53.32\text{ g}}{16\text{ g/mol}}=3.3\end{array}$

Thus, the simplest ratio of N to O atom is 1:1 and empirical formula $=NO$

Empirical mass $=14+16=3\text{0 g/mol}$

Molar mass $=60.01g/mol$

The ratio of molar mass to empirical mass will be:

$x=\frac{60.01\text{ g/mol}}{30\text{ g/mol}}\simeq 2$

Hence, Molecular formula $={\text{N}}_{\text{2}}{\text{O}}_{\text{2}}$

Conclusion

The molecular formula of the liquid is ${\text{N}}_{\text{2}}{\text{O}}_{\text{2}}$.