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For the gas-phase dissociation N2O4 (g) <-> 2 NO2 (g), starting from 1 mole of N2O4 at total pressure P and equilibrium constant Kp, which expression gives the degree of dissociation alpha?

1. alpha = sqrt(Kp/(Kp + 4P))
2. alpha = sqrt(Kp/(4P))
3. alpha = sqrt(4P/(Kp + 4P))
4. alpha = Kp/(Kp + 4P)

Correct answer: alpha = sqrt(Kp/(Kp + 4P))

Solution

Substituting partial pressures into Kp gives Kp = 4*alpha²*P/(1 - alpha²), which rearranges to alpha = sqrt(Kp/(Kp + 4P)).

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