Consider the following chemical equilibrium of the gas phase reaction at a constant temperature: If being the total pressure, is the pressure equilibrium constant and is the degree of dissociation, then which of the following is true at equilibrium?

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Solution

Q.
Consider the following chemical equilibrium of the gas phase reaction at a constant temperature:

$A (g) ⇌ B (g) + C (g)$

If $p$ being the total pressure, $K_{p}$ is the pressure equilibrium constant and $α$ is the degree of dissociation, then which of the following is true at equilibrium [2025]

1 If $p$ value is extremely high compared to $K_{p}, α \approx 1$

2 When $p$ increases $α$ decreases

3 If $K_{p}$ value is extremely high compared to $p, α$ becomes much less than unity

4 When $p$ increases $α$ increases

Ans.
(2)

$\begin{matrix} A (g) & ⇌ & B (g) & + & C (g) \\ t=0 (moles) & a & 0 & 0 \\ t =∞ (moles) & a (1 - α) & a α & a α \\ t =∞ (mole fraction) & \frac{1 - α}{1 + α} & \frac{α}{1 + α} & \frac{α}{1 + α} \\ t =∞ (partial pressure) & (\frac{1 - α}{1 + α}) P & (\frac{α}{1 + α}) P & (\frac{α}{1 + α}) P \end{matrix} \begin{matrix} Total = a (1 + α) \end{matrix}$

$K_{p} = \frac{P_{B} \times P_{C}}{P_{A}} = \frac{(\frac{α}{1 + α}) P \times (\frac{α}{1 + α}) P}{(\frac{1 - α}{1 + α}) P} = \frac{α^{2} P}{1 - α^{2}}$

As $K_{p}$ is constant for a constant temperature, as P increases, $α$ decreases.

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