For the gaseous reaction , let be the equilibrium constant expressed strictly in terms of mole fract — Chemical Equilibrium Chemistry Question
Question
For the gaseous reaction $aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$, let $K_x$ be the equilibrium constant expressed strictly in terms of mole fractions. If $\Delta n_g = (c+d) - (a+b)$, which of the following analytical expressions is/are correct?
💡 Solution & Explanation
The partial pressure of a gas is its mole fraction multiplied by total pressure ($P_i = X_i P_{total}$). Substituting this into the $K_p$ expression yields $K_p = K_x(P_{total})^{\Delta n_g}$ (A is correct), which rearranges to $K_x = K_p(P_{total})^{-\Delta n_g}$ (B is correct). If $\Delta n_g = 0$, then $P_{total}^0 = 1$, making $K_p = K_x$, and similarly $K_p = K_c(RT)^0 = K_c$ (C is correct). $K_x$ depends on total pressure if $\Delta n_g eq 0$ (D is false).