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Characteristics of Equilibrium Constant

At a particul...

Question

At a particular temperature, the equilibrium constant for
$2 {N O}_{2} (g) ⇌ N_{2} O_{4} (g)$ is one. The same reaction is carried out in a container of volume just half of the former. Will the value of $[N_{2} O_{4}] / {[{N O}_{2}]}^{2}$ be equal to $1$ if no reaction occurred? Will the equilibrium constant change by this change in volume?

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Solution

${2 N O}_{2} ⇌ N_{2} O_{4} K = 1$
If we half the volume of container partial pressure or concentration of species double.
Hence $\frac{[N_{2} O_{4}]}{{[{N O}_{2}]}^{2}}$ value will be $1 / 2$ not equal to $1$
$K$ of reaction doesn't depend on volume changes.
Hence $K = 1$
$K$ only changes with the temperature.

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