Question
A certain gas ‘A’ polymerizes to a very small extent at a given temperature as nA(g)$\rightleftharpoons$ An(g). The reaction is started with one mole of ‘A’ in a container of capacity V. Which of the following is the correct value of $\frac{PV}{RT}$, at equilibrium?
Options
Solution
nA(g) $\rightleftharpoons$ An(g)
Initial moles 1 0
Equilibrium moles 1 – x $\frac{x}{n}$
Now, $K_{C} = \frac{\left( \frac{x/n}{V} \right)}{\left( \frac{1 - x}{V} \right)^{n}} = \frac{x.V^{n - 1}}{(1 - x)^{n}.n} \approx \frac{x.V^{n - 1}}{n}\left( \text{as }x < < 1 \right)$
Now, total moles = $(1 - x) + \frac{x}{n} = 1 + x.\left( \frac{1}{n} - 1 \right)$
$= 1 + \frac{n.KC}{V^{n - 1}}\left( \frac{1 - n}{n} \right) = 1 + \frac{(1 - n)K_{C}}{V^{n - 1}}$
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