K_p is constant only at constant temperature

Steps:

• K_p is defined as K_p = (P_HI)^2 / (P_H2 * P_I2) at equilibrium.
• This ratio remains constant for a given reaction under ideal gas conditions.
• The value of K_p varies with temperature, as shown by the van't Hoff equation.
• Thus, constant temperature is required for K_p to be fixed.

Why D is correct:

• K_p depends on temperature via ΔH in the van't Hoff equation: ln(K_p) = -ΔH/RT + constant, so T must be constant for K_p to hold a specific value.

Why the others are wrong:

• A: Partial pressures satisfy the K_p expression but are not required to be equal.
• B: Total pressure can change at constant T without altering K_p for this Δn=0 reaction.
• C: Equilibrium means equal forward and reverse rates, not stopped reactions.

Final answer: D