Calculate the amount of work done in the oxidation of 1 mole of...

The given reaction is:

$4\text{HCl(g)} + \text{O}_2\text{(g)} \rightarrow 2\text{Cl}_2\text{(g)} + 2\text{H}_2\text{O(g)}$

For the oxidation of $4$ moles of $\text{HCl}$, the change in the number of gaseous moles is:

$\Delta n_g = (2 + 2) - (4 + 1) = -1$

For the oxidation of $1$ mole of $\text{HCl}$, the change in the number of gaseous moles is:

$\Delta n_g = -\dfrac{1}{4}$

The given temperature is T = 127^{}^{\circ}\text{C} = 127 + 273 = 400\text{ K}.

The work done is given by the formula:

$W = -\Delta n_g R T$

Substituting the values:

$W = -\left(-\dfrac{1}{4}\right) \times 8.314 \times 400$

$W = 8.314 \times 100 = 831.4\text{ J}$

Answer: $831.4$ J