In an equilibrium reaction, which of the following conditions indicates that maximum yield of the product will be obtained?

Analysis

The question asks for the condition that signifies the maximum yield of products in a chemical equilibrium reaction. We need to relate the equilibrium constant ($K$) to the spontaneity and extent of the reaction.

Concept Explanation

In chemical thermodynamics, the relationship between the standard Gibbs free energy change ($\Delta G^\circ$) and the equilibrium constant ($K$) is given by the equation:

• If $K$ is very large ($K \gg 1$): The value of $\ln K$ is a large positive number. This makes $\Delta G^\circ$ a large negative number. A large negative $\Delta G^\circ$ indicates that the reaction is spontaneous and proceeds far to the right, favoring the formation of products. Therefore, a large $K$ means the equilibrium position lies heavily toward the product side, resulting in a maximum yield.
• If $K$ is very small ($K \ll 1$): The value of $\ln K$ is a large negative number, making $\Delta G^\circ$ positive. This indicates the reaction is non-spontaneous and favors the reactants, resulting in a low yield.
• Regarding $\Delta G = \Delta H - T\Delta S$: For a reaction to be spontaneous, $\Delta G$ must be negative. Setting $\Delta H - T\Delta S = 0$ actually represents the point of equilibrium where the system is neither moving forward nor backward, not the condition for maximum product yield.

Step-by-Step Solution

1. Evaluate the relationship: The yield of a product in an equilibrium reaction is determined by the position of equilibrium.
2. Analyze the equilibrium constant ($K$): $K = \frac{[\text{Products}]}{[\text{Reactants}]}$. For the yield of products to be maximum, the numerator must be much larger than the denominator. This mathematically results in a very large value for $K$.
3. Check the options: • Option A: A large $K$ implies the concentration of products is significantly higher than reactants at equilibrium. This is correct. • Option B: $\Delta H - T\Delta S = 0$ means $\Delta G = 0$, which is the definition of the equilibrium state itself, not a condition for maximum yield. • Option C: $\Delta H > T\Delta S$ implies $\Delta G > 0$, meaning the reaction is non-spontaneous and will not favor products. • Option D: An equilibrium constant cannot be less than zero (it must be a positive value).

Conclusion

The condition that indicates the maximum yield of products is a very large equilibrium constant, as it shows the reaction strongly favors the product side.

Exam Tip: Always remember the "K-Rule": If $K > 1$, products are favored (high yield). If $K < 1$, reactants are favored (low yield). If $K = 1$, the concentration of products and reactants is roughly equal.