Problem 49 - A Complete Resource Book in Chemistry for JEE Main

Question

The reaction quotient (Q) 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 (a) \(Q>K_{c}\) (b) \(Q=0\) (c) \(\mathrm{Q}=\mathrm{K}_{c}\) (d) \(\mathrm{Q}<\mathrm{K}_{\mathrm{c}}\)

Step-by-Step Solution

Answer

The reaction will proceed from right to left if \( Q > K_{c} \), so option (a) is correct.

Step 1: Understand the Reaction Quotient

The reaction quotient, \(Q\), is a measure of the relative amounts of products and reactants present in a reaction at any given point in time. It is related to equilibrium constant, \(K_{c}\), but is measured under non-equilibrium conditions.

Step 2: Expression for Q and Kc

For the given reaction \( \text{N}_{2}(\text{g}) + 3 \text{H}_{2}(\text{g}) \rightleftharpoons 2 \text{NH}_{3}(\text{g}) \), the expression for the reaction quotient \( Q \) is:\[ Q = \frac{[\text{NH}_{3}]^{2}}{[\text{N}_{2}][\text{H}_{2}]^{3}} \]Similarly, \( K_{c} \) is the equilibrium constant with the same expression as \( Q \), following the balanced chemical equation.

Step 3: Direction of Reaction

To know in which direction the reaction will proceed, we compare \( Q \) with \( K_{c} \):- If \( Q < K_{c} \), the reaction will proceed in the forward direction (left to right) to reach equilibrium.- If \( Q > K_{c} \), the reaction will move in the reverse direction (right to left) to reach equilibrium.

Step 4: Determine the Correct Option

According to the problem, for the reaction to proceed from right to left, it must be that \( Q > K_{c} \). Therefore, the correct answer is option (a): \( Q > K_{c} \).

Key Concepts

Understanding the Reaction Quotient

The reaction quotient, commonly denoted as \( Q \), is an essential tool in chemistry for understanding the progress of a chemical reaction at any particular moment. Unlike the equilibrium constant, which provides a picture of the reaction at equilibrium, \( Q \) can be calculated at any point before the reaction reaches that equilibrium state. Here's how it works:

• \( Q \) involves the same expression as the equilibrium constant, employing the concentrations of reactants and products raised to the power of their coefficients from the balanced chemical equation.
• It allows chemists to determine whether a reaction has reached, or will shift towards, chemical equilibrium.
• If you know the concentrations of all species in the reaction, you can calculate \( Q \).

The status of the reaction can be deduced by comparing \( Q \) to the equilibrium constant \( K_c \): if \( Q = K_c \), the system is at equilibrium. Otherwise, the reaction will shift towards equilibrium. Knowing \( Q \) helps chemists predict the direction in which the reaction will proceed, to become more stable.

Equilibrium Constant: A Snapshot of Stability

The equilibrium constant, \( K_c \), is fundamental for telling us about the balance or equilibrium of a reversible chemical reaction. Here's what makes \( K_c \) so crucial:

• It quantifies the ratio of products to reactants at equilibrium, guiding us on how far a reaction will tend to go before stopping.
• Specific to each chemical reaction, \( K_c \) can change only with a change in temperature.
• The expression for \( K_c \) is determined by taking the concentration of products over reactants, each raised to the power of their respective coefficients from the balanced equation.

For the reaction between nitrogen and hydrogen to form ammonia \( \text{N}_2 + 3 \text{H}_2 \rightleftharpoons 2 \text{NH}_3 \), the \( K_c \) helps predict how much ammonia is formed at equilibrium. If \( Q > K_c \), the reaction is product-heavy, and will shift left. In contrast, if \( Q < K_c \), it is reactant-heavy, indicating a need for more products to form. Therefore, \( K_c \) serves as a benchmark for predicting reaction behavior.

Influence of Le Chatelier's Principle

Le Chatelier's Principle is a classic theory in chemistry that provides insights into how a system at equilibrium responds to external changes. Its essence can be summarized as follows: if an external condition such as concentration, pressure, or temperature is changed, the system will shift in a direction that aims to counteract that change and re-establish equilibrium. Here's how it plays out:

• An increase in concentration of a reactant typically shifts the equilibrium towards the products, supporting the forward reaction.
• If the concentration of a product rises, the equilibrium may shift back to create more reactants, signaling a reverse reaction.
• Changes in pressure or temperature can similarly cause shifts, with increased pressure favoring the side with fewer gas molecules, and temperature changes affecting \( K_c \).

This principle helps chemists manipulate reaction conditions to optimize production or control reactions. In the context of the nitrogen, hydrogen, and ammonia system, if \( Q > K_c \), Le Chatelier's Principle tells us the reaction will naturally shift back towards reactants until equilibrium is re-attained. This intricate dance ensures reactions remain dynamic and balanced under varying conditions.