The equilibrium constant $\left(K_C\right)$ for the following equilibrium $2…

The equilibrium constant $\left(K_C\right)$ for the following equilibrium $2 \mathrm{SO}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{SO}_3(g)$ at $563 \mathrm{~K}$ is 100 . At equilibrium, the number of moles of $\mathrm{SO}_3$ in the 10 litre flask is twice the number of moles of $\mathrm{SO}_2$, then the number of moles of oxygen is
  1. 0.4
  2. 0.3
  3. 0.2
  4. 0.1

Solution

Let, number of moles of $\mathrm{SO}_2=x$ moles of $\mathrm{SO}_3=2 x$ $2 \mathrm{SO}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{SO}_3(g)$ At equilibrium, $\begin{aligned} K_c & =\frac{\left[\mathrm{SO}_3\right]^2}{\left[\mathrm{SO}_2\right]^2\left[\mathrm{O}_2\right]} \\ 100 & =\frac{\left[\frac{2 x}{10}\right]^2}{\left[\frac{x}{10}\right]^2\left[\frac{n_{\mathrm{O}_2}}{10}\right]} \\ 100 & =\frac{40}{n_{\mathrm{O}_2}} n_{\mathrm{O}_2}=\frac{40}{100}=0.4 \end{aligned}$ Hence, number of moles of oxygen $=0.4$

Asked in: AP EAMCET 2017 (26 Apr Shift 1)

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