Question

Vessel (A) contains 1 mole each of H$_2$ and I$_2$, and vessel (B) contains 2 moles each of H$_2$ and I$_2$. Both vessels are at the same temperature and reach equilibrium for the reaction H$_2$(g) + I$_2$(g) $\rightleftharpoons$ 2HI(g). What is the ratio of the equilibrium constants $K_p$ for vessels A and B?

• A. $K_p$ for A and B are in the ratio of 1 : 2
• B. $K_p$ for A and B are in the ratio of 1 : 1
• C. $K_p$ for A and B are equal
• D. $K_p$ for A and B are in the ratio of 2 : 1

Hint:

The equilibrium constant $K_p$ depends only on temperature for a given reaction, not on the initial concentrations or amounts of reactants.

Answer 1

The Correct Option is C

For the reaction H$_2$(g) + I$_2$(g) $\rightleftharpoons$ 2HI(g), the equilibrium constant is:
$K_p = \frac{(P_{{HI}})^2}{(P_{{H}_2})(P_{{I}_2})}$.
Since $K_p$ depends only on temperature and reaction stoichiometry, and both vessels are at the same temperature, $K_p$ remains the same for both.
Vessel A has 1 mol each of H$_2$ and I$_2$, while Vessel B has 2 moles each of H$_2$ and I$_2$.
The initial amounts do not affect $K_p$; only the equilibrium partial pressures adjust to satisfy the same $K_p$.
Thus, $K_p$ for A and B are equal.