Chapter 24, Problem 79QP

Interpretation Introduction

Interpretation:

The volume of chlorine gas required to oxidize all the bromide ions is to be calculated.

Concept introduction:

A balanced chemical equation must contain an equal number of similar atoms on each side.

The ideal gas equation is given as follows:

$PV=n\text{R}T$

Here, $P,V,n,\text{R,}\text{and}T$ are pressure, volume, number of moles, gas constant, and temperature, respectively.

The moles of a substance are calculated by the ratio of the mass of the substance to the molar mass of the substance.

$\text{Number of }\text{}\text{moles = }\frac{\text{Given mass}}{\text{Molar mass}}$

The mass of compound can be calculated as: $m=n\times M$

Here, $n$ is the number of moles, $m$ is the mass, and $M$ is the molar mass.

The number of moles of chlorine needed is calculated as:

$\text{number of moles of chlorine = }\frac{\text{given}\text{mass}\text{of}\text{bromine}}{\text{molar}\text{mass}\text{of}\text{bromine}}\text{×}\frac{\text{1}\text{mol}\text{chlorine}}{\text{2}\text{mol}\text{bromine}}$

Answer to Problem 79QP

Solution: $25.3\text{L}$

Explanation of Solution

The balanced chemical reaction is as follows:

$2{\text{Br}}^{-}\left(g\right)+{\text{ Cl}}_{\text{2}}\left(g\right)\to 2{\text{Cl}}^{-}\left(aq\right)+{\text{ Br}}_{\text{2}}\left(l\right)$

$\text{2}\text{moles}\text{of}\text{bromine}\text{reacts}\text{with}\text{1}\text{mole}\text{ofchlorine}$

The number of moles of chlorine needed is calculated as follows:

$\text{number of moles of chlorine = }\frac{\text{given}\text{mass}\text{of}\text{bromine}}{\text{molar}\text{mass}\text{of}\text{bromine}}\text{×}\frac{\text{1}\text{mol}\text{chlorine}}{\text{2}\text{mol}\text{bromine}}$

$\left(167\cancel{\text{g}{\text{Br}}^{-}}\right)\text{×}\left(\frac{\text{1}\cancel{\text{mol}{\text{Br}}^{-}}}{79.90\cancel{\text{g}{\text{Br}}^{-}}}\right)\text{×}\left(\frac{1\text{mol}{\text{Cl}}_{\text{2}}}{2\cancel{\text{mol}{\text{Br}}^{-}}}\right)\text{=}1.05\text{mol}{\text{Cl}}_{\text{2}}\text{(}g\text{)}$

The volume of chlorine gas needed is calculated by using the ideal gas equation as follows:

$\begin{array}{c}{V}_{{\text{Cl}}_{\text{2}}}\text{=}\frac{n\text{R}T}{P}\\ \text{=}\frac{\text{(}1.05\cancel{\text{mol}}\text{)(}0.0821\text{L×}\cancel{\text{atm}}\text{/}\cancel{\text{K}}\text{×}\cancel{\text{mol}}\text{)(}293\cancel{\text{K}}\text{)}}{\text{(}1\cancel{\text{atm}}\text{)}}\\ \text{= }25.3\text{L}\end{array}$

Conclusion

The volume of chlorine gas required to oxidize all the bromide ions is $25.3\text{ L}$.