QJEEM23Ch2ffd: JEE Main 2023 Chemistry - Class 11 JEEM23Ch2ffd Solution: Water decomposes at 2300 K H 2 O ( g ) → H 2 ( g ) + 1 2 O 2 (…

Question

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Water decomposes at 2300 K

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

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.

Accepted Answer

\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2}

\begin{aligned} K_{p} = \frac{P_{T}^{\frac{3}{2}} (1 + \frac{α}{2}) α^{\frac{3}{2}}}{2^{\frac{1}{2}} P_{T} {(1 + \frac{α}{2})}^{\frac{3}{2}} (1 - α)} \\ 2 \times 10^{- 3} = \frac{α^{\frac{3}{2}}}{2^{\frac{1}{2}}} [as α << 1 and let P_{T} = 1] \end{aligned}

\begin{aligned} α^{\frac{3}{2}} = 2^{\frac{3}{2}} \times 10^{- 3} \\ \approx 2 \times 10^{- 2} \end{aligned}

\therefore \%

of water decomposition

=2 \%

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