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Question

The equilibrium constant for the reaction $$\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})=2\mathrm{N}\mathrm{O}(\mathrm{g})
$$at temperature $$\mathrm{T}$$ is $$4\times 10^{-4}$$. The value of $$\mathrm{K}_{\mathrm{c}}$$ for the reaction:

$$NO(g)$$ $$=\displaystyle \frac{1}{2}\mathrm{N}_{2}(\mathrm{g})+\frac{1}{2}\mathrm{O}_{2}(\mathrm{g})$$ at the same temperature is :


A
2.5×102
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B
50
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C
4×104
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D
0.02
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Solution

The correct option is A $$50$$
The equilibrium constant for the reaction $$\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})= 2\mathrm{N}\mathrm{O}(\mathrm{g})
$$at temperature $$\mathrm{T}$$ is $$4\times 10^{-4}$$. The value of $$\mathrm{K}_{\mathrm{c}}$$ for the reaction:
NO(g) $$=\displaystyle \frac{1}{2}\mathrm{N}_{2}(\mathrm{g})+\frac{1}{2}\mathrm{O}_{2}(\mathrm{g})$$ at the same temperature is $$\displaystyle \frac {1}{\sqrt {K_c}} = \frac {1}{\sqrt {4 \times 10^{-4}}} = 50$$
Note: The second reaction is obtained when the first reaction is reversed and divided by 2.

Chemistry

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