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For the gaseous equilibrium A(g) <=> B(g) + (1/2)C(g) with degree of dissociation alpha and total equilibrium pressure p, the equilibrium constant K is correctly given by:

1. K = (alpha^(1/2) * p^(3/2)) / ((1 + 3/2 alpha)^(1/2) * (1 - alpha))
2. K = (alpha^(3/2) * p^(1/2)) / ((2 + alpha)^(1/2) * (1 - alpha))
3. K = ((alpha*p)^(3/2)) / ((1 + 3/2 alpha)^(1/2) * (1 - alpha))
4. K = ((alpha*p)^(3/2)) / ((1 + alpha)(1 - alpha)^(1/2))

Correct answer: K = (alpha^(3/2) * p^(1/2)) / ((2 + alpha)^(1/2) * (1 - alpha))

Solution

With total moles 1 + alpha/2 = (2+alpha)/2, the mole fractions give Kp = (alpha)*(alpha/2)^(1/2) / [(1-alpha)] * p^(1/2) / (total moles)^(1/2). Simplifying yields K = alpha^(3/2) p^(1/2) / [(2+alpha)^(1/2)(1-alpha)].

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