What happens to the value of the equilibrium constant (Kc) for a reaction if the reaction is reversed?

Analysis

The question asks how the equilibrium constant ($K_c$) of a chemical reaction changes when the direction of the reaction is reversed.

Concept Explanation

The equilibrium constant ($K_c$) is defined as the ratio of the concentration of products to the concentration of reactants, each raised to the power of their stoichiometric coefficients.

For a general reversible reaction:

The equilibrium constant is:

When you reverse the reaction, the products become the reactants, and the reactants become the products:

The new equilibrium constant ($K_{c}'$) for this reversed reaction is:

Step-by-Step Solution

1. Compare the expression for the original reaction with the expression for the reversed reaction.
2. You will notice that $K_{c}'$ is exactly the inverse (or reciprocal) of $K_c$.
3. Mathematically, this is expressed as: $$K_{c}' = \frac{1}{K_c}$$
4. Therefore, if the original constant was $K_c$, the new constant is $1/K_c$.

Conclusion

When a reaction is reversed, the new equilibrium constant is the reciprocal of the original equilibrium constant. This matches option D.

Exam Tip: Remember that $K_c$ is temperature-dependent. If you change the temperature, the value of $K_c$ changes. However, changing the concentration, pressure, or adding a catalyst does not change the value of $K_c$. Reversing the reaction is the only way to mathematically invert the constant.