Problem 46 - A Complete Resource Book in Chemistry for JEE Main

Question

Reaction quotient for the reaction, \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) is given by \(\mathrm{Q}=\frac{\left[\mathrm{NH}_{3}\right]^{2}}{\left[\mathrm{~N}_{2}\right]\left[\mathrm{H}_{2}\right]^{3}}\) the reaction will proceed from right to left, if \(\mathrm{K}_{c}\) is equilibrium constant (a) \(\mathrm{Q}<\mathrm{K}_{\mathrm{c}}\) (b) \(\mathrm{Q}=0\) (c) \(\mathrm{Q}>\mathrm{K}_{\mathrm{c}}\) (d) \(\mathrm{Q}=\mathrm{K}_{\mathrm{c}}\)

Step-by-Step Solution

Answer

The reaction proceeds from right to left if \( Q > K_c \), which is option (c).

Step 1: Understanding the Reaction Quotient (Q)

The reaction quotient, \( Q \), is used to determine the direction in which the reaction will proceed. It is calculated by substituting the current concentrations of the reactants and products into the equilibrium expression.

Step 2: Comparing Q with Kc

The equilibrium constant \( K_c \) is given at equilibrium conditions. To predict the direction of the reaction, compare \( Q \) with \( K_c \): if \( Q < K_c \), the reaction will proceed to the right (towards products), if \( Q = K_c \), the reaction is at equilibrium, and if \( Q > K_c \), the reaction will proceed to the left (towards reactants).

Step 3: Analyzing the Given Options

The options are comparing \( Q \) and \( K_c \) to determine the direction. Since the reaction proceeds from right to left when \( Q > K_c \), option (c) \( Q > K_c \) correctly describes the condition under which the reaction will proceed in this manner.

Key Concepts

Understanding the Reaction Quotient (Q)

The reaction quotient, often denoted as \( Q \), gives us insight into the current state of a reaction compared to its equilibrium. Unlike the equilibrium constant \( K_c \), which is only defined when a reaction is at equilibrium, \( Q \) can be defined at any concentration point in time. To calculate \( Q \), insert the concentrations of the reactants and products into the equilibrium expression. Let's take the example of the reaction \( \text{N}_2(\text{g}) + 3 \text{H}_2(\text{g}) \rightleftharpoons 2 \text{NH}_3(\text{g}) \).- The expression for \( Q \) is \( \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} \).- Here, the brackets '[ ]' denote concentrations of substances at any given point, not necessarily at equilibrium.Using \( Q \), we can compare it with \( K_c \) to find out which direction the reaction is shifting to reach equilibrium.

Predicting the Direction of Reaction

The comparison between the reaction quotient \( Q \) and the equilibrium constant \( K_c \) is fundamental in predicting which direction a chemical reaction will shift. Here's how it works:- If \( Q < K_c \): The reaction has not reached equilibrium. More products need to be formed, so the reaction will shift to the right.- If \( Q > K_c \): There are more products than at equilibrium, causing the system to produce more reactants, shifting the reaction to the left.- If \( Q = K_c \): The reaction is already at equilibrium and no net change will occur.By evaluating \( Q \) against \( K_c \), one can understand the current phase of the reaction and its progression towards equilibrium. For the exercise, if \( Q > K_c \), the reaction proceeds from right to left, consistent with the movement towards more reactants.

Equilibrium Constant \( K_c \) and Its Role

The equilibrium constant, \( K_c \), is a critical parameter in chemical reactions. It reflects the ratio between the concentrations of products and reactants at equilibrium for a given reaction at a specific temperature. The formula for \( K_c \) uses the same form as the expression for \( Q \) but is applicable strictly at the equilibrium stage. - For \( \text{N}_2(\text{g}) + 3 \text{H}_2(\text{g}) \rightleftharpoons 2 \text{NH}_3(\text{g}) \), \( K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} \) at equilibrium.A stable \( K_c \) value at a given temperature implies:- High \( K_c \): Indicates a product-favored reaction, where products dominate at equilibrium.- Low \( K_c \): Implies a reactant-favored reaction, with a higher presence of reactants at equilibrium.Understanding \( K_c \) in the context of \( Q \) comparisons allows chemists to manipulate conditions to favor desired reaction outcomes, providing control over reaction dynamics.