The correct relationship between and equilibrium pressure P is

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Q.
$A_{(g)} ⇌ B_{(g)} + \frac{C}{2} (g)$ The correct relationship between $K_{p},$ $α$ and equilibrium pressure P is [2024]

1 $K_{P} = \frac{α^{1 / 2} P^{1 / 2}}{{(2 + α)}^{3 / 2}}$

2 $K_{P} = \frac{α^{1 / 2} P^{3 / 2}}{{(2 + α)}^{3 / 2}}$

3 $K_{P} = \frac{α^{3 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2} (1 - α)}$

4 $K_{P} = \frac{α^{1 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2}}$

Ans.
(3)

$K_{p} = \frac{P_{C}^{1 / 2} \times P_{B}}{P_{A}}$

$= \frac{{(\frac{α P}{2 + α})}^{1 / 2} \times (\frac{2 α}{2 + α}) P}{(\frac{2 - 2 α}{2 + α}) P} = \frac{α^{3 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2} (1 - α)}$

Solution

Q.
$A_{(g)} ⇌ B_{(g)} + \frac{C}{2} (g)$ The correct relationship between $K_{p},$ $α$ and equilibrium pressure P is [2024]

1 $K_{P} = \frac{α^{1 / 2} P^{1 / 2}}{{(2 + α)}^{3 / 2}}$

2 $K_{P} = \frac{α^{1 / 2} P^{3 / 2}}{{(2 + α)}^{3 / 2}}$

3 $K_{P} = \frac{α^{3 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2} (1 - α)}$

4 $K_{P} = \frac{α^{1 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2}}$

Ans.
(3)

$K_{p} = \frac{P_{C}^{1 / 2} \times P_{B}}{P_{A}}$

$= \frac{{(\frac{α P}{2 + α})}^{1 / 2} \times (\frac{2 α}{2 + α}) P}{(\frac{2 - 2 α}{2 + α}) P} = \frac{α^{3 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2} (1 - α)}$

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Solution

Q. A(g)⇌B(g)+C2(g) The correct relationship between Kp, α and equilibrium pressure P is [2024]

1 KP=α1/2P1/2(2+α)3/2

2 KP=α1/2P3/2(2+α)3/2

3 KP=α3/2P1/2(2+α)1/2(1-α)

4 KP=α1/2P1/2(2+α)1/2

Ans. (3) Kp=PC1/2×PBPA = (αP2+α)1/2×(2α2+α)P(2-2α2+α)P=α3/2P1/2(2+α)1/2(1-α)

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Q.
$A_{(g)} ⇌ B_{(g)} + \frac{C}{2} (g)$ The correct relationship between $K_{p},$ $α$ and equilibrium pressure P is [2024]

1 $K_{P} = \frac{α^{1 / 2} P^{1 / 2}}{{(2 + α)}^{3 / 2}}$

2 $K_{P} = \frac{α^{1 / 2} P^{3 / 2}}{{(2 + α)}^{3 / 2}}$

3 $K_{P} = \frac{α^{3 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2} (1 - α)}$

4 $K_{P} = \frac{α^{1 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2}}$

Ans.
(3)

$K_{p} = \frac{P_{C}^{1 / 2} \times P_{B}}{P_{A}}$

$= \frac{{(\frac{α P}{2 + α})}^{1 / 2} \times (\frac{2 α}{2 + α}) P}{(\frac{2 - 2 α}{2 + α}) P} = \frac{α^{3 / 2} P^{1 / 2}}{{(2 + α)}^{1 / 2} (1 - α)}$