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For the gaseous reaction \(\mathrm{CO(g) + \tfrac{1}{2}O_2(g) \rightleftharpoons CO_2(g)}\), what is the relation between \(K_p\) and \(K_c\)?

1. (RT)^(1/2)
2. (RT)^(-1/2)
3. RT
4. (RT)⁻¹

Correct answer: (RT)^(-1/2)

Solution

For gaseous equilibria, \(K_p = K_c(RT)^{\Delta n}\), where \(\Delta n\) is the change in moles of gaseous species. Here, \(\Delta n = 1 - \left(1 + \tfrac{1}{2}\right) = -\tfrac{1}{2}\). Hence, \(K_p = K_c(RT)^{-1/2}\).

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