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) \(\mathrm{Q}>\mathrm{K}_{c}\) (b) \(Q=0\) (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 when \( Q > K_c \).

Step 1: Understanding the Reaction Quotient (Q)

The reaction quotient, \( Q \), measures the relative quantities of products and reactants present during a reaction at any point in time. For the reaction \( \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) \), \[ \mathrm{Q} = \frac{[\mathrm{NH}_{3}]^2}{[\mathrm{N}_{2}][\mathrm{H}_{2}]^3} \].

Step 2: Comparing Q to the equilibrium constant (Kc)

\( K_c \) is the equilibrium constant for the reaction, which indicates the ratio of product to reactant concentrations at equilibrium. Comparing \( Q \) to \( K_c \) helps determine the direction the reaction will shift to reach equilibrium. If \( Q eq K_c \), the reaction is not at equilibrium.

Step 3: Identifying Reaction Direction When Q > Kc

If \( Q > K_c \), the current concentration of products is greater than at equilibrium, so the reaction will shift from products back to reactants to reach equilibrium. Hence, the reaction proceeds from right to left.

Step 4: Analyzing Other Given Options

Consider the incorrect options: (b) \( Q=0 \), where there are no products present; (c) \( Q=K_c \), indicating the system is at equilibrium; (d) \( Q

Key Concepts

Reaction Quotient

In any chemical reaction, the reaction quotient, noted as \( Q \), serves as a snapshot of a reaction's progress at a specific moment. It quantifies the ratio of reactant and product concentrations. The formula for \( Q \) is similar in form to that of the equilibrium constant \( K \): however, \( Q \) can be calculated at any point in the reaction, not just at equilibrium.
To calculate \( Q \) for a given reaction such as \( \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \rightleftharpoons 2\mathrm{NH}_3(g) \), use the expression: \[\mathrm{Q} = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]

• Numerator: Concentration of the products raised to the power of their coefficients.
• Denominator: Concentration of the reactants raised to the power of their coefficients.

The calculated \( Q \) value helps to determine if a reaction is currently making progress towards equilibrium, already at equilibrium, or moving away from equilibrium.

Equilibrium Constant

The equilibrium constant, noted as \( K_c \), is a fundamental concept in chemical equilibrium that captures the concentration ratio of products to reactants at the reaction’s equilibrium point.
This ratio is mathematically represented similar to \( Q \) but specifically pertains to the point when the forward and reverse reactions occur at the same rate, meaning the reactant and product concentrations no longer change over time. For our example, the equilibrium constant expression is: \[K_c = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]
The equilibrium condition aligns with the value of \( K_c \):

• If \( Q = K_c \), the reaction is at dynamic equilibrium, meaning no net change is observed.
• If \( Q eq K_c \), this signals that adjustments in concentrations will occur to reach equilibrium.

The differences between \( Q \) and \( K_c \) at any given moment determine the direction in which a reaction must shift to achieve balance.

Le Chatelier's Principle

Le Chatelier’s Principle provides insight into how a system at equilibrium responds to external changes such as concentration, pressure, or temperature.
Essentially, if a change is imposed on a system at equilibrium, the system will adjust itself to counteract the change and re-establish equilibrium.

• If \( Q > K_c \), there are too many products compared to equilibrium conditions. The reaction will shift to the left to form more reactants.
• If \( Q < K_c \), there are more reactants compared to products than at equilibrium. The reaction will shift to the right to generate more products.

This principle is key to predicting the behavior of chemical reactions when subjected to different conditions. Understanding this can significantly aid in the control and optimization of reactions in industrial applications.

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Other exercises in this chapter

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For the reaction, \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\), the equilibrium concentrations of \(\mathrm{H}_{2}, 1_{2}\) and \(\mathrm{

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Problem 48

In which of the following case, the value of \(\mathrm{K}_{\mathrm{p}}\) is less than \(\mathrm{K}_{\mathrm{c}} ?\) (a) \(\mathrm{N}_{2}+\mathrm{O}_{2} \rightle

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Problem 51

For the reaction \(\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}\) (l)

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Problem 52

The enthalpy and entropy change for the reaction, \(\mathrm{Br}_{2}(\mathrm{l})+\mathrm{Cl}_{2}(\mathrm{~g})\) \(2 \mathrm{BrCl}(\mathrm{g})\) are \(30 \mathrm{

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Key Concepts

Reaction Quotient

In any chemical reaction, the reaction quotient, noted as \( Q \), serves as a snapshot of a reaction's progress at a specific moment. It quantifies the ratio of reactant and product concentrations. The formula for \( Q \) is similar in form to that of the equilibrium constant \( K \): however, \( Q \) can be calculated at any point in the reaction, not just at equilibrium.
To calculate \( Q \) for a given reaction such as \( \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \rightleftharpoons 2\mathrm{NH}_3(g) \), use the expression: \[\mathrm{Q} = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]

• Numerator: Concentration of the products raised to the power of their coefficients.
• Denominator: Concentration of the reactants raised to the power of their coefficients.

The calculated \( Q \) value helps to determine if a reaction is currently making progress towards equilibrium, already at equilibrium, or moving away from equilibrium.

Equilibrium Constant

The equilibrium constant, noted as \( K_c \), is a fundamental concept in chemical equilibrium that captures the concentration ratio of products to reactants at the reaction’s equilibrium point.
This ratio is mathematically represented similar to \( Q \) but specifically pertains to the point when the forward and reverse reactions occur at the same rate, meaning the reactant and product concentrations no longer change over time. For our example, the equilibrium constant expression is: \[K_c = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]
The equilibrium condition aligns with the value of \( K_c \):

• If \( Q = K_c \), the reaction is at dynamic equilibrium, meaning no net change is observed.
• If \( Q eq K_c \), this signals that adjustments in concentrations will occur to reach equilibrium.

The differences between \( Q \) and \( K_c \) at any given moment determine the direction in which a reaction must shift to achieve balance.

Le Chatelier's Principle

Le Chatelier’s Principle provides insight into how a system at equilibrium responds to external changes such as concentration, pressure, or temperature.
Essentially, if a change is imposed on a system at equilibrium, the system will adjust itself to counteract the change and re-establish equilibrium.

• If \( Q > K_c \), there are too many products compared to equilibrium conditions. The reaction will shift to the left to form more reactants.
• If \( Q < K_c \), there are more reactants compared to products than at equilibrium. The reaction will shift to the right to generate more products.

This principle is key to predicting the behavior of chemical reactions when subjected to different conditions. Understanding this can significantly aid in the control and optimization of reactions in industrial applications.