Question

For the following reactions, predict whether the mole fraction of the reactants or products increases or remains the same when the volume of the reaction vessel is increased.

$$\begin{gathered} \mathit{a}\mathbf{.}\mathbf{}\mathit{B}{\mathit{r}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{2}\mathit{H}\mathit{B}\mathit{r}\mathbf{\left(}\mathit{g}\mathbf{\right)} \\ \mathit{b}\mathbf{.}\mathbf{}\mathbf{2}\mathit{C}{\mathit{H}}_{\mathbf{4}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathit{C}}_{\mathbf{2}}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)} \\ \mathit{c}\mathbf{.}\mathbf{}\mathbf{2}\mathit{H}\mathit{I}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathit{I}}_{\mathbf{2}}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)} \end{gathered}$$

Short answer

a. The mole fraction remains the same.

b. The mole fraction of the products increases when the volume is increased.

c. The mole fraction of the reactants increases when the volume is increased.

Step-by-step solution

Predict whether the mole fraction of the reactants or products increases or remains the same.

For the given reaction,$B{r}_2\left(g\right)+H_2\left(g\right)\rightleftharpoons 2HBr\left(g\right)$:

There is no change. Since the stoichiometric equation has the same total number of reactant and product moles of the gases. As a result, a volume change has no effect on the equilibrium.

Predict whether the mole fraction of the reactants or products increases or remains the same.

For the given reaction:

$2C{H}_4\left(g\right)\rightleftharpoons C_2{H}_2\left(g\right)+3H_2\left(g\right)$

Increasing the volume will increase the mole fraction of the products. Because there are more moles of gas molecules of the products on the right side than on the left side. So, the reaction will shift to the right. Hence, the mole fraction of the products increases.

Predict whether the mole fraction of the reactants or products increases or remains the same.

For the given reaction:

$2HI\left(g\right)\rightleftharpoons I_2\left(s\right)+H_2\left(g\right)$

With an increase in volume, the mole fraction of reactants will rise. There are more reactant molecules than the product molecules in the balanced chemical equation (pure solids are omitted). The reaction changes to the side with greater number of gas molecules as the volume increases. Hence, the mole fraction of the reactants increases.