Water decomposes at 2300 K The percent of water decomposing at 2300 K and 1 bar is __________ (Nearest integer). Equilibrium constant for the reaction is at 2300 K. [2023]

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Solution

Q.
Water decomposes at 2300 K

$H_{2} O (g) ⇌ H_{2} (g) + \frac{1}{2} O_{2} (g)$

The percent of water decomposing at 2300 K and 1 bar is __________ (Nearest integer).

Equilibrium constant for the reaction is $2 \times 10^{- 3}$ at 2300 K. [2023]

Ans.
(2)

$\begin{matrix} H_{2} O (g) & ⇌ & H_{2} (g) & + & \frac{1}{2} O_{2} (g) \\ 1 - α & α & α / 2 \end{matrix}$

$K_{p} = \frac{α {(\frac{α}{2})}^{1 / 2}}{1 - α} = 2 \times 10^{- 3}$

$= \frac{{(α)}^{3 / 2}}{\sqrt{2} (1 - α)} = 2 \times 10^{- 3}$

$= {(α)}^{3 / 2} = 2 \sqrt{2} \times 10^{- 3} (α ≪ 1)$

${(α)}^{3 / 2} = \sqrt{8} \times 10^{- 3}$

$α = 2 \times 10^{- 2}$

$% α = 2 \times 10^{- 2} \times 100 = 2$

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