Question

The equilibrium constant of a reaction depends mainly on:

• A. Pressure
• B. Temperature
• C. Volume
• D. Catalyst

Hint:

Remember the Van 't Hoff equation: the change in the equilibrium constant with temperature depends on whether the reaction is exothermic or endothermic. No other physical parameter can alter \( K \).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the primary variable that determines the value of the thermodynamic equilibrium constant (\( K \)) of a chemical reaction.

Step 2: Key Formula or Approach:
The relationship between the standard Gibbs free energy change (\( \Delta G^\circ \)) and the equilibrium constant (\( K \)) is expressed as:
\[ \Delta G^\circ = -R T \ln K \]
Rearranging this equation gives:
\[ \ln K = -\frac{\Delta G^\circ}{R T} \]
Further, substituting \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) yields:
\[ \ln K = -\frac{\Delta H^\circ}{R T} + \frac{\Delta S^\circ}{R} \]

Step 3: Detailed Explanation:

• Temperature Dependence: The standard Gibbs free energy change (\( \Delta G^\circ \)) is defined for reactants and products in their standard states, which makes it independent of pressure and concentration.
Consequently, \( \Delta G^\circ \) and the equilibrium constant (\( K \)) depend exclusively on temperature.

• Effect of Other Parameters:
-

Pressure and Volume (Options A and C) can shift the position of equilibrium (as described by Le Chatelier's principle) but do not change the actual value of the equilibrium constant \( K \) for a gas-phase reaction behaving ideally.
-

Catalysts (Option D) increase the rate of both forward and reverse reactions equally, reducing the time to reach equilibrium without altering the equilibrium composition or the value of \( K \).


Step 4: Final Answer:
Thus, the equilibrium constant of a reaction depends mainly on temperature, corresponding to Option (B).