Question

For the reaction \(2 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{g}) ; \Delta H=\) 80 kcal. The highest yicld of \(Z\) at cquilibrium occurs at (1) \(1000 \mathrm{~atm}\) and \(500^{\circ} \mathrm{C}\) (2) \(500 \mathrm{~atm}\) and \(500^{\circ} \mathrm{C}\) (3) \(1000 \mathrm{~atm}\) and \(100^{\circ} \mathrm{C}\) (4) \(500 \mathrm{~atm}\) and \(100^{\circ} \mathrm{C}\)

Short answer

Option (1) 1000 atm and 500°C is the best condition for the highest yield of Z.

Step-by-step solution

- Understand the Reaction and \(\Delta H\)

The reaction given is \(2 \mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{g})\). \(\Delta H = 80 \text{kcal}\) indicates that the reaction is endothermic (heat is absorbed).

- Le Chatelier’s Principle

According to Le Chatelier’s Principle, for an endothermic reaction, increasing the temperature will favor the formation of products. Thus, higher temperatures will shift the equilibrium towards producing more \(\text{Z}\).

- Effect of Pressure

In the given reaction, the number of gas molecules on the left side is 3 (2X + Y) and on the right side is 2 (2Z). According to Le Chatelier's Principle, increasing the pressure will favor the side with fewer gas molecules. Thus, higher pressures will favor the production of \(\text{Z}\).

- Analyze the Options

Examine the given options and choose the one with both the highest temperature and highest pressure because both these conditions favor the production of \(\text{Z}\).

Key concepts

Endothermic Reaction

An endothermic reaction is a chemical reaction that absorbs heat from its surroundings. In the reaction given, \( 2 \text{X}(g) + \text{Y}(g) \rightleftharpoons 2 \text{Z}(g) \) with \( \Delta H = 80 \text{kcal} \, \), the positive enthalpy change \( (\Delta H) \) indicates that this reaction is endothermic.

This implies that the system needs to take in heat for the reaction to proceed efficiently.

Therefore, adding heat (increasing temperature) will shift the equilibrium towards the production of more \( Z \, \).

Essentially, the system absorbs heat and converts more of the reactants (\text{X} and \text{Y}) into products \( (Z) \, \).

This concept is crucial to understand as it helps predict how the reaction will behave when temperature changes.

Effect of Pressure on Equilibrium

The effect of pressure on a reaction that involves gases is essential for determining the equilibrium position, especially when the number of gas molecules differs on each side.

In the given reaction, \( 2 \text{X}(g) + \text{Y}(g) \rightleftharpoons 2 \text{Z}(g) \), there are three gas molecules on the reactants side and two gas molecules on the products side.

According to Le Chatelier’s Principle, increasing the pressure will shift the equilibrium towards the side with fewer gas molecules.

Therefore, by increasing the pressure, the system will favor the production of \( Z \, \), because there are fewer gas molecules on the product side compared to the reactant side.

This means that higher pressures will help in achieving a higher yield of \( Z \, \).

Temperature Effect on Equilibrium

Temperature plays a vital role in affecting the equilibrium of a chemical reaction, particularly for endothermic reactions.

As per Le Chatelier’s Principle, for an endothermic reaction, like the one given \( 2 \text{X}(g) + \text{Y}(g) \rightleftharpoons 2 \text{Z}(g) \), increasing the temperature will favor the formation of the products.

Given that the reaction absorbs heat (endothermic), adding more heat will shift the equilibrium toward producing more \( Z \, \).

Consequently, selecting the conditions with a higher temperature inherently supports the production of more \( Z \, \).

To achieve the highest yield of \( Z \, \), a combination of high temperature and high pressure is optimal according to the provided choices.