Question

Of the reactions given below, the reaction whose number of moles of products increases by the addition of inert gases into the reaction chamber at constant pressure and temperature is \((a) \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) \((b) \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) \((c) \mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}\) \((d) \mathrm{N}_{2} \rightleftharpoons 2 \mathrm{N}\) \((e)\) all of the above

Short answer

a) \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) b) \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) c) \(\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}\) d) \(\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{N}\) Answer: d) \(\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{N}\)

Step-by-step solution

Analyze each reaction

Let's first gather some information about each reaction based on their stoichiometric coefficients. For reaction a: \(\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\) Number of moles on the reactants' side: \(1 + 0.5 = 1.5\) Number of moles on the products' side: \(1\) For reaction b: \(\mathrm{CO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) Number of moles on the reactants' side: \(1 + 0.5 = 1.5\) Number of moles on the products' side: \(1\) For reaction c: \(\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}\) Number of moles on the reactants' side: \(1 + 1 = 2\) Number of moles on the products' side: \(2\) For reaction d: \(\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{N}\) Number of moles on the reactants' side: \(1\) Number of moles on the products' side: \(2\)

Apply Le Chatelier's principle

As per the Le Chatelier's principle, we need to identify when the number of moles of products increases when an inert gas is added at a constant pressure and a constant temperature. When an inert gas is added at a constant pressure, the volume of the system increases. According to the Le Chatelier's principle, the side with a higher number of moles will be favored. So, let's see which reaction matches this condition. For reaction a: As there are more moles on the reactants' side, the addition of an inert gas at constant pressure will favor the reactants, so the number of moles of products won't increase. For reaction b: As there are more moles on the reactants' side, the addition of an inert gas at constant pressure will favor the reactants, so the number of moles of products won't increase. For reaction c: As there are equal number of moles on both sides, the addition of an inert gas at constant pressure will make no difference. So, the number of moles of products won't increase. For reaction d: As there are more moles on the products' side, the addition of the inert gas at constant pressure will favor the products. So, the number of moles of products will increase.

Identify the correct answer

From the analysis in the previous steps, we can conclude that the correct option is (d) \(\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{N}\). This is the reaction that exhibits an increase in the number of moles of products when an inert gas is added to the reaction chamber at constant pressure and temperature.