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 \(\mathrm{K}_{\mathrm{c}}\) is equilibrium constant (a) \(\mathrm{Q}<\mathrm{K}_{c}\) (b) \(\mathrm{Q}=0\) (c) \(\mathrm{Q}>\mathrm{K}_{c}\) (d) \(Q=K_{c}\)

Step-by-Step Solution

Answer

The reaction proceeds from right to left if \( Q > K_c \), so the answer is (c).

Step 1: Understanding Reaction Quotient

The reaction quotient \( Q \) is a measure of the relative amounts of products and reactants present during a reaction at a given point in time. It is calculated using the formula \( Q = \frac{[\mathrm{NH}_{3}]^2}{[\mathrm{N}_{2}][\mathrm{H}_{2}]^3} \). \( Q \) helps determine the direction in which the reaction will proceed.

Step 2: Comparing Q and Kc

\( K_c \) is the equilibrium constant, which is the value of \( Q \) when the reaction is at equilibrium. To predict the direction of the reaction, compare \( Q \) against \( K_c \).

Step 3: Analyzing Q > Kc

When \( Q > K_c \), it indicates that the concentration of products is higher than that at equilibrium. As a result, the reaction will shift from products to reactants, meaning it will proceed from right (products) to left (reactants).

Step 4: Conclusion

The reaction will proceed from right to left if \( Q > K_c \), thus, the correct answer is option (c): \( Q > K_c \).

Key Concepts

Equilibrium Constant

In the world of chemistry, the equilibrium constant, denoted as \( K_c \), is a vital concept that helps us understand how far a reaction will proceed before reaching a balance. It is at this point that the concentrations of reactants and products remain constant over time. The equilibrium constant is influenced by temperature but is independent of the initial concentrations of the substances involved.
The value of \( K_c \) is the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients from the balanced chemical equation. For instance, in the reaction \( \mathrm{N}_2(g) + 3 \mathrm{H}_2(g) \rightleftharpoons 2 \mathrm{NH}_3(g) \), the equilibrium constant \( K_c \) is expressed as:

• \[ K_c = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]

The value of \( K_c \) provides insight into the position of equilibrium; if \( K_c \) is large, it suggests that products predominate at equilibrium, whereas a small \( K_c \) indicates that reactants are favored.

Chemical Equilibrium

Chemical equilibrium is a dynamic state where the rate of the forward reaction equals the rate of the backward reaction in a closed system. This does not mean that the reactants and products are in equal concentrations, but rather that their concentrations remain constant over time as the two opposing processes balance each other.
At equilibrium, the reaction quotient \( Q \), which represents the ratio of product concentrations to reactant concentrations at any given moment, equals the equilibrium constant \( K_c \). If \( Q \) differs from \( K_c \), the reaction will adjust to reach this state of balance by shifting to either the right (towards products) or to the left (towards reactants):

• If \( Q < K_c \), the system has more reactants and will shift to form more products.
• If \( Q > K_c \), the system has more products and will shift to form more reactants.
• If \( Q = K_c \), the system is already at equilibrium and no shift is necessary.

This balance is crucial in many industrial and natural processes, ensuring reactions can efficiently reach a point where input and output are optimized.

Le Chatelier's Principle

Le Chatelier's Principle gives us a way to predict how a chemical equilibrium will respond to changes in conditions. This principle states that if an external change is applied to a system at equilibrium, the system adjusts itself to counteract that change and a new equilibrium is established.
In practical terms, this means:

• If the concentration of a reactant or product is changed, the equilibrium will shift in the direction that opposes this change.
• An increase in temperature typically favors the endothermic direction of a reaction (absorbing heat), and a decrease will favor the exothermic direction (releasing heat).
• Pressure changes, relevant to gases, will shift equilibrium toward the side with fewer moles of gas if pressure is increased, and toward the side with more moles of gas if pressure is decreased.

For example, in our reaction \( \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \rightleftharpoons 2\mathrm{NH}_3(g) \), increasing the pressure will favor the side with fewer gas moles, which is the product side (2 moles of \( \mathrm{NH}_3 \)). Le Chatelier's Principle helps chemists optimize reaction conditions for maximum yield, an invaluable tool in both laboratory and industrial chemical processes.