Chapter 11.2, Problem 13PP

Interpretation Introduction

Interpretation:

The obtained mass in grams of chlorine gas from the given decomposition of sodium chloride needs to be calculated.

Concept introduction:

The ratio of mass of substance to its molar mass is said to be number of moles of that substance.

Answer to Problem 13PP

The obtained mass in grams of chlorine gas from the given decomposition of sodium chloride is $88.63\text{ g}$.

Explanation of Solution

Given:

The reaction for the decomposition of sodium chloride to sodium and chlorine is:

$\text{NaCl }\stackrel{\text{electric energy}}{\to }{\text{ Na + Cl}}_{\text{2}}$

The above reaction is not balanced as the number of Cl atoms on the reactant side is 1 and on the product side is 2. So, in order to balance the reaction coefficient, 2 is written before $\text{NaCl}$ in the reactant side and 2 before $\text{Na}$ on the product side. Thus, the balanced reaction is:

$\text{2NaCl }\stackrel{\text{electric energy}}{\to }{\text{ 2Na + Cl}}_{\text{2}}$

From the balanced chemical reaction, the mole ratio of $\text{NaCl}$ and ${\text{Cl}}_{\text{2}}$ is 2:1 that means 2 moles of $\text{NaCl}$ produces 1 mol of ${\text{Cl}}_{\text{2}}$, so the number of moles of ${\text{Cl}}_{\text{2}}$ produced from 2.50 moles of $\text{NaCl}$ will be:

$\text{2}\text{.50 mol of NaCl ×}\frac{{\text{1 mol of Cl}}_{\text{2}}}{\text{2 mol of NaCl}}\text{ = 1}{\text{.25 mol of Cl}}_{\text{2}}$

Now, the mass of ${\text{Cl}}_{\text{2}}$ obtained is calculated as:

The molar mass of ${\text{Cl}}_{\text{2}}$ is 70.906 g/mol. So,

$\begin{array}{l}{\text{Number of moles of Cl}}_{\text{2}}=\frac{{\text{Mass of Cl}}_{\text{2}}}{{\text{Molar mass of Cl}}_{\text{2}}}\\ \text{1}\text{.25 mol}=\frac{{\text{Mass of Cl}}_{\text{2}}}{\text{70}\text{.906 g/mol}}\\ {\text{Mass of Cl}}_{\text{2}}\text{ = }1.25\text{ mol}\times 70.906\text{ g/mol}\\ {\text{Mass of Cl}}_{\text{2}}\text{ = }88.63\text{ g}\end{array}$

Hence, the obtained mass in grams of chlorine gas from the given decomposition of sodium chloride is $88.63\text{ g}$.