Explanation:

Equilibrium Constant (K) and Temperature:
The equilibrium constant (K) of a reaction is a measure of the extent to which the reactants are converted into products at a given temperature. The value of K is determined by the ratio of the concentrations (or pressures) of the products to the concentrations (or pressures) of the reactants, each raised to the power of their respective stoichiometric coefficients.

Variation of K with Temperature:
The equilibrium constant (K) for a reaction is dependent on the temperature. As the temperature changes, the value of K also changes. The relationship between K and temperature is described by the Van't Hoff equation:

ln(K2/K1) = ∆H/R * (1/T1 - 1/T2)

Where K1 and K2 are the equilibrium constants at temperatures T1 and T2 respectively, ∆H is the enthalpy change of the reaction, R is the gas constant, and T1 and T2 are the initial and final temperatures.

Given Information:
At 300 K, the equilibrium constant (K) is 25.
At 400 K, the equilibrium constant (K) is 10.

Analysis:
From the given information, we can observe that as the temperature increases from 300 K to 400 K, the value of the equilibrium constant (K) decreases from 25 to 10. This indicates that the forward reaction is favored at lower temperatures (300 K) while the backward reaction is favored at higher temperatures (400 K).

Activation Energy and Reaction Rates:
The activation energy of a reaction is the minimum energy required for a reaction to occur. It is the energy barrier that must be overcome for the reactants to convert into products. The forward reaction and the backward reaction of a reversible reaction have different activation energies.

Explanation of the Correct Answer:
Based on the provided information, we can conclude that the backward reaction will have a greater activation energy than the forward reaction. This can be explained by the reaction rates at different temperatures.

- At 300 K (lower temperature), the value of the equilibrium constant (K) is 25. This indicates that the forward reaction is favored, and the reaction rate of the forward reaction is higher than the backward reaction. Therefore, the activation energy of the forward reaction is relatively lower compared to the backward reaction.

- At 400 K (higher temperature), the value of the equilibrium constant (K) is 10. This indicates that the backward reaction is favored, and the reaction rate of the backward reaction is higher than the forward reaction. Therefore, the activation energy of the backward reaction is relatively higher compared to the forward reaction.

Hence, the correct answer is option 'C' - the activation energy of the backward reaction is greater than that of the forward reaction.

K decreases with increase in temperature. Thus, forward reaction is exothermic.