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Q.

Water decomposes at 2300K
$H_{2} O (g) \to H_{2} (g) + \frac{1}{2} O_{2} (g)$
The percent of water decomposing at 2300K and 1 bar is _______ (Nearest integer). Equilibrium constant for the reaction is 2 x 10^-3 at 2300K.

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answer is 2.

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Detailed Solution

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$H_{2} O \to H_{2} + 1_{2} O_{2} 1 0 0 1 - x x \frac{x}{2}$
$\begin{array}{l} k_{P} = 2 \times 10^{- 3} = \frac{x \times {(\frac{x}{2})}^{\frac{1}{2}}}{1 - x} \\ 2 \times 10^{- 3} = \frac{x \times x^{1 / 2}}{\sqrt{2}} (1 - x = 1) \\ 2 \sqrt{2} \times 10^{- 3} = x^{3 / 2} \\ 2^{\frac{3}{2} \times 10^{- 3} = x^{3 / 2}} \\ 2^{3} \times 10^{- 6} = x^{3} \\ x = 2 \times 10^{- 2} \\ % x = 2 \end{array}$

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