Degree of Dissociation Using Equilibrium Constant

❓ Question

For decomposition of steam:

$$H_2O(g)\rightleftharpoons H_2(g)+\frac12 O_2(g)$$
$$K_p=8.0\times10^{-3}$$

at:

$$2300\text{ K}$$

Total pressure at equilibrium:

$$1\text{ bar}$$

Degree of dissociation of water is:

$$\alpha=\_\_\_\_\times10^{-2}$$

(Nearest integer value)

Assume:

$$\alpha \ll 1$$

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🖼 Question Image

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✍️ Short Explanation

This problem is based on:

👉 Degree of dissociation
👉 Equilibrium constant $K_p$
👉 Partial pressures.

Main idea:

For decomposition:

$$H_2O(g)\rightleftharpoons H_2(g)+\frac12 O_2(g)$$

if initial moles of water are 1:

$$\boxed{ K_p= \frac{P_{H_2}\cdot P_{O_2}^{1/2}} {P_{H_2O}} }$$

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🔷 Step 1 — Assume Initial Moles 💯

Take initially:

$$1\text{ mole } H_2O$$

Let degree of dissociation be:

$$\alpha$$

Reaction:

$$H_2O \rightleftharpoons H_2+\frac12 O_2$$

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Equilibrium Moles

Species	Initial	Change	Equilibrium
$H_2O$	1	$-\alpha$	$1-\alpha$
$H_2$	0	$+\alpha$	$\alpha$
$O_2$	0	$+\frac{\alpha}{2}$	$\frac{\alpha}{2}$

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🔷 Step 2 — Total Moles at Equilibrium

$$n_{total} = 1-\alpha+\alpha+\frac{\alpha}{2}$$
$$= 1+\frac{\alpha}{2}$$

Given:

$$\alpha\ll1$$

So:

$$n_{total}\approx1$$

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🔷 Step 3 — Partial Pressures

Total pressure:

$$P=1\text{ bar}$$

Thus:

$$P_{H_2}\approx\alpha$$
$$P_{O_2}\approx\frac{\alpha}{2}$$
$$P_{H_2O}\approx1$$

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🔷 Step 4 — Apply $K_p$ Expression

$$K_p= \frac{P_{H_2}\cdot P_{O_2}^{1/2}} {P_{H_2O}}$$

Substitute:

$$8\times10^{-3} = \alpha\left(\frac{\alpha}{2}\right)^{1/2}$$
$$= \frac{\alpha^{3/2}}{\sqrt2}$$

Thus:

$$\alpha^{3/2} = 8\times10^{-3}\times\sqrt2$$
$$\approx1.13\times10^{-2}$$

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🔷 Step 5 — Solve for $\alpha$

$$\alpha = (1.13\times10^{-2})^{2/3}$$
$$\approx0.050$$

Thus:

$$\alpha\approx5.0\times10^{-2}$$

Nearest integer:

$$\boxed{5}$$

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🔷 Step 6 — JEE Trap Alert 🚨

❌ Total moles calculate karte time:

$$\frac{\alpha}{2}$$

bhool jaana

❌ Partial pressure directly mole maan lena without total pressure

❌ $K_p$ expression galat likh dena

Remember:

$$\boxed{ P_i= \frac{n_i}{n_{total}}P_{total} }$$

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✅ Final Answer

$$\boxed{5}$$

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📚 Related Topics

• MOI of Combined Bodies Using Parallel Axis
• Van’t Hoff Factor Shortcut for Percentage Dissociation
• Quadratic Equation Roots Reciprocal Relation Trick