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 \(Q=\frac{\left[\mathrm{NH}_{3}\right]^{2}}{\left[\mathrm{~N}_{2}\right]\left[\mathrm{H}_{2}\right]^{3}}\) 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) \(Q>K_{c}\) (d) \(Q=K_{c}\)

Step-by-Step Solution

Answer

The correct answer is (c): \( Q > K_c \). The reaction proceeds from right to left.

Step 1: Understanding Reaction Quotient

The reaction quotient, or \( Q \), is a measure of the relative amounts of products and reactants present during a reaction at a particular point in time, not at equilibrium. For the given reaction, \( \mathrm{Q} \) is calculated using the concentrations of \( \mathrm{NH}_3 \), \( \mathrm{N}_2 \), and \( \mathrm{H}_2 \).

Step 2: Equilibrium Constant Concept

The equilibrium constant, \( \mathrm{K}_c \), represents the ratio of the concentrations of products to reactants at equilibrium for the reaction. At equilibrium, \( \mathrm{Q} = \mathrm{K}_c \).

Step 3: Determining Reaction Direction

To determine the direction of the reaction, we compare \( \mathrm{Q} \) to \( \mathrm{K}_c \). If: - \( \mathrm{Q} < \mathrm{K}_c \), the reaction proceeds forward (left to right)- \( \mathrm{Q} > \mathrm{K}_c \), the reaction proceeds backwards (right to left)- \( \mathrm{Q} = \mathrm{K}_c \), the reaction is at equilibrium.

Step 4: Conclusion

Given that the reaction proceeds from right to left when \( \mathrm{Q} > \mathrm{K}_c \), option (c) is correct: \( Q > K_c \).

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_c \), is a fundamental concept in the study of chemical reactions. It provides a quantitative measure of the ratio of product concentrations to reactant concentrations at equilibrium for a given reaction.
This constant is specific to each particular reaction and is influenced by factors such as temperature.

An important aspect of the equilibrium constant is that it remains constant for a reaction at a specific temperature, even if concentrations of reactants and products are different at equilibrium.
This means that equilibrium can be established in various ways, but the ratio determined by \( K_c \) will always prevail at a given temperature.

For the reaction \( \mathrm{N}_2 + 3\mathrm{H}_2 \rightleftharpoons 2\mathrm{NH}_3 \), the equilibrium constant expression is given by:

\[ K_c = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]
Understanding \( K_c \) helps in predicting reaction behaviors and the concentrations of species at equilibrium.

Chemical Equilibrium

Chemical equilibrium occurs in a closed system when the rate of the forward reaction equals the rate of the reverse reaction. This results in stable concentrations of reactants and products over time.
This does not necessarily mean that the amounts of reactants and products are equal but that their ratios remain constant.

The concept of dynamic equilibrium emphasizes that even while concentrations remain constant, the molecular action continues.
Molecules of reactants and products keep reacting but at rates that cancel each other out.

• In practical terms, reaching equilibrium means the system has no net change in concentration over time.
• Reactions halt visible change but continue on a molecular level.

Using the equilibrium concept, scientists can manipulate external conditions, such as pressure or temperature, to shift the equilibrium position and alter the yield of products or reactants.

Reaction Direction Analysis

Reaction direction analysis helps to determine whether a reaction will proceed forward, backward, or remain unchanged.
By comparing the reaction quotient \( Q \) and the equilibrium constant \( K_c \), we can predict the movement of a chemical system toward equilibrium.

The reaction quotient \( Q \) is calculated using the same formula as \( K_c \) but uses instant concentrations instead of equilibrium concentrations.
The comparison between \( Q \) and \( K_c \) provides the following:

• \( Q < K_c \): The reaction will go forward, from left to right, favoring the formation of products.
• \( Q = K_c \): The reaction is at equilibrium, no net change occurs, though molecular activity persists.
• \( Q > K_c \): The reaction will proceed backward, shifting from right to left, favoring reactants over products.

For the example reaction, if we find \( Q > K_c \), we know the system is overrun with products and will move towards forming more reactants to re-establish equilibrium.