K_p is temperature-dependent for equilibrium constants

Steps:

• Recall that K_p is defined as K_p = (P_HI)^2 / (P_H2 * P_I2), where P denotes partial pressures at equilibrium.
• Note that equilibrium constants like K_p vary with temperature according to the van 't Hoff equation, which relates ln K to ΔH/T.
• Identify that for K_p to be a fixed value in a given system, temperature must remain constant, as changes in T shift equilibrium and alter K_p.
• Eliminate options unrelated to the definition of K_p, confirming temperature constancy is essential.

Why D is correct:

• The van 't Hoff equation shows K_p = e^(-ΔH/RT + constant), so K_p changes with temperature T; constancy of T ensures K_p is well-defined and constant.

Why the others are wrong:

• A: Partial pressures at equilibrium satisfy K_p but are not required to be equal; they depend on initial conditions.
• B: External pressure affects position but not the value of K_p, which uses partial pressures.
• C: At equilibrium, rates are equal, not stopped; reactions continue dynamically.

Final answer: D