Chapter 10, Problem 196A

Interpretation Introduction

Interpretation:

Empirical formula and molecular formula of naphthalene must be found for which % of C and H are is 93.7 and 6.3 respectively. Molar mass of naphthalene is 128 g/mol.

Concept introduction:

Empirical formula of a molecule is the smallest unit which is repeated in the molecule.

Molecular formula ${\text{=(empirical formula)}}_{\text{n}}$

Where n is the number of times the empirical formula is present in the molecular formula, n can be 1, 2, 3 etc.

Answer to Problem 196A

The empirical formula is C₅H₄and molecular formula is C₁₀H₈.

Explanation of Solution

% of C and H are 93.7 and 6.3 respectively.

Considering 100 g of compound, the mass of C and H is 93.7 g and 6.3 g respectively.

The molar mass of C and H is 12 g/mol and 1 g/mol respectively.

The number of moles of C and H is calculated as follows:

Moles of C $\text{=}\frac{\text{93}\text{.7 g}}{\text{12 g/mol}}\text{=7}\text{.81 mol}$

Moles of H $=\frac{6.3\text{ g}}{1\text{ g/mol}}=6.3\text{ mol}$

Smallest mole ratio C: H is as follows:

$\begin{array}{l}=\frac{7.81}{6.3}:\frac{6.3}{6.3}\\ =1.2:1=4.8:4\approx 5:4.\end{array}$

Thus empirical formula is C₅H₈.

Now,

$\begin{array}{l}$ {{\text{(C}}_{\text{5}}{\text{H}}_4\text{)}}_{\text{n}}\text{=128}$\text{Or, (5}\times \text{12+1}\times 4\text{)×n=128}\\ \text{Or, n=}\frac{128}{\text{64}}\text{=2}\text{.}\end{array}$

Conclusion

Empirical formula of the molecule is C₅H₄ and molecular formula is C₁₀H₈.