Problem 36 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \leftrightarrow 2 \mathrm{HI}(\mathrm{g})\) the equilib- rium constant \(\mathrm{K}_{\mathrm{p}}\) changes with (a) catalyst (b) temperature (c) total pressure (d) the amounts of \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) present

Step-by-Step Solution

Answer

\( \mathrm{K}_{\mathrm{p}} \) changes with temperature only.

Step 1: Understand the Reaction Dynamics

The given reaction is \( \mathrm{H}_{2}(\mathrm{~g}) + \mathrm{I}_{2}(\mathrm{~g}) \leftrightarrow 2 \mathrm{HI}(\mathrm{g}) \), an equilibrium between hydrogen, iodine, and hydrogen iodide gases. The equilibrium constant, \( \mathrm{K}_{\mathrm{p}} \), indicates the ratio of product to reactant pressures at equilibrium.

Step 2: Analyze the Effect of Catalyst

A catalyst speeds up the rate at which equilibrium is achieved without affecting the position of equilibrium or the equilibrium constant \( \mathrm{K}_{\mathrm{p}} \). Therefore, a catalyst does not change the value of \( \mathrm{K}_{\mathrm{p}} \).

Step 3: Examine the Influence of Temperature

The equilibrium constant \( \mathrm{K}_{\mathrm{p}} \) is temperature-dependent. According to Le Chatelier's principle, a change in temperature will shift the position of equilibrium, thus changing \( \mathrm{K}_{\mathrm{p}} \). Therefore, temperature affects \( \mathrm{K}_{\mathrm{p}} \).

Step 4: Consider the Impact of Total Pressure

For reactions involving only gaseous reactants and products, if the number of moles of gas changes during the reaction, pressure can shift equilibrium positions. However, \( \mathrm{K}_{\mathrm{p}} \) itself is not dependent on pressure; it depends on temperature alone.

Step 5: Investigate Changes in Reactant Amounts

Changing the amounts of \( \mathrm{H}_{2} \) or \( \mathrm{I}_{2} \) shifts the position of equilibrium but does not affect the value of \( \mathrm{K}_{\mathrm{p}} \) itself. The system will adjust to re-establish equilibrium, but \( \mathrm{K}_{\mathrm{p}} \) will remain the same since it is only altered by temperature.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_p \) for reactions involving gases, is a crucial concept in chemical equilibrium. It represents the ratio of the partial pressures of the products to the partial pressures of the reactants, each raised to the power of their stoichiometric coefficients. For the reaction \( \mathrm{H}_{2}(\mathrm{~g}) + \mathrm{I}_{2}(\mathrm{~g}) \leftrightarrow 2 \mathrm{HI}(\mathrm{g}) \), the expression for the equilibrium constant \( K_p \) is:
\[ K_p = \frac{{(P_{\mathrm{HI}})^2}}{{P_{\mathrm{H}_2} \cdot P_{\mathrm{I}_2}}} \]
Here, \( P_{\mathrm{HI}} \), \( P_{\mathrm{H}_2} \), and \( P_{\mathrm{I}_2} \) represent the partial pressures of hydrogen iodide, hydrogen, and iodine gases, respectively.

• \( K_p \) is a constant only at a given temperature; the same reaction at a different temperature will have a different \( K_p \).
• It provides insight into the extent of a reaction at equilibrium.
• A high \( K_p \) indicates a product-favored reaction, while a low \( K_p \) suggests a reactant-favored reaction.

Understanding \( K_p \) helps in predicting the behavior of a system under various conditions, except when the temperature changes.

Le Chatelier's Principle

Le Chatelier's Principle is a powerful tool for predicting the effect of changing conditions on a chemical equilibrium. It states that if you change the conditions of a system at equilibrium, the system will adjust to counteract that change and restore a new equilibrium state.
Some common changes that can affect equilibrium include:

• Concentration: Increasing the concentration of a reactant or product will shift the equilibrium to oppose the change.
• Pressure: For gaseous reactions, changing the total pressure can shift equilibrium, especially if the number of gas moles is different on either side of the equation.
• Temperature: Raising the temperature shifts the equilibrium in the endothermic direction; lowering it shifts in the exothermic direction.

In the context of our reaction \( \mathrm{H}_{2}(\mathrm{~g}) + \mathrm{I}_{2}(\mathrm{~g}) \leftrightarrow 2 \mathrm{HI}(\mathrm{g}) \), if we increase the concentration of \( \mathrm{H}_2 \) or \( \mathrm{I}_2 \), the system will generate more \( \mathrm{HI} \) to offset this change.
Le Chatelier's Principle helps predict how reactions respond to disturbances, crucial for industrial applications and laboratory settings.

Catalyst Effect

A catalyst plays an essential role in speeding up the rate at which a chemical reaction achieves equilibrium without affecting the equilibrium position itself. It lowers the activation energy required for the reaction to proceed, thereby increasing the rate of forward and backward reactions equally.
Thus, while a catalyst helps a system to achieve equilibrium faster, it does not alter the value of the equilibrium constant \( K_p \).
Here are a few key points about catalysts:

• Catalysts do not change \( K_p \) because they do not impact the relative concentrations of reactants and products at equilibrium.
• They are not consumed in the reaction and can be used repeatedly.
• In industrial processes, catalysts are crucial because they can reduce the time and energy required to reach equilibrium.

In our given reaction involving hydrogen, iodine, and hydrogen iodide, adding a catalyst would mean the reaction reaches equilibrium quicker but does not change \( K_p \). This understanding is essential for accurately predicting reaction dynamics in real-world applications.

Temperature Dependence

Temperature has a distinct effect on the equilibrium constant \( K_p \) and is the only condition in our list that changes its value. According to Le Chatelier's Principle, a change in temperature will shift the position of equilibrium, which then affects \( K_p \). For endothermic reactions, an increase in temperature drives the reaction toward the formation of products, increasing \( K_p \). Conversely, for exothermic reactions, increasing temperature shifts equilibrium towards reactants, decreasing \( K_p \).
Consider the general reaction \( \mathrm{A} + \mathrm{B} \leftrightarrow \mathrm{C} + \Delta \,\text{(heat)} \):

• If the reaction is exothermic, increasing temperature favors the backward reaction, shifting equilibrium to the left.
• If the reaction is endothermic, increasing temperature favors the forward reaction, shifting equilibrium to the right.

For our specific reaction of hydrogen and iodine forming hydrogen iodide, if it exhibits exothermic characteristics, increasing temperature would make \( K_p \) smaller as the system favors reactants. Understanding how temperature affects \( K_p \) is crucial in controlling and optimizing reactions in various scientific and industrial processes.