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For the gas-phase reaction CO(g) + \tfrac{1}{2}O_2(g) \rightleftharpoons CO_2(g), the relationship between equilibrium constants in terms of pressure and concentration is determined by \(\Delta n_g\). Since \(\Delta n_g = 1 - (1 + 0.5) = -0.5\), which expression is correct?

1. Kₚ = Kc(RT)^Δn_g
2. Kₚ/Kc = 1/(RT)^(1/2)
3. Kₚ = Kc(RT)^(-1/2)
4. Kₚ = Kc(RT)^(1/2)

Correct answer: Kₚ/Kc = 1/(RT)^(1/2)

Solution

For gaseous equilibria, \(K_p = K_c(RT)^{\Delta n_g}\). Here, \(\Delta n_g = 1 - 1.5 = -0.5\), so \(K_p = K_c(RT)^{-1/2}\). This is equivalent to \(K_p/K_c = 1/(RT)^{1/2}\).

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