Chemical And Ionic Equilibrium

Chemical And Ionic Equilibrium Result Question 49 — JEE PYQ Chapterwise

49. The equilibrium constant $K_p$ of the reaction,

$2 \mathrm{SO}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{SO}_3(g)$

is $900$ atm at $800$ K . A mixture containing $\mathrm{SO}_3$ and $\mathrm{O}_2$ having initial pressure of $1$ and $2$ atm respectively is heated at constant volume to equilibrate. Calculate the partial pressure of each gas at $800$ K .

(1988, 4M)

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Solution:

$\quad \quad \quad 2 \mathrm{SO}_2(g)+\mathrm{O}_2(g) \rightleftharpoons \mathrm{SO}_3(g)$

$\begin{array}{lccc} \text { lnitial } p_i: & 0 && 2 && 1 \\ \text { Equilibrium } p_i: & 2 p && 2+p && 1-2 p \end{array}$

$K_p=900=\frac{(1-2 p)^2}{(2+p)(2 p)^2} \quad$ [Ignoring $p$ in comparison to 2$]$

$ p=\frac{1}{87} \mathrm{~atm} $

Partial pressure of $\mathrm{SO}_2=2 p=\frac{2}{87} \mathrm{~atm}$

Partial pressure of $\mathrm{O}_2=2+p=2+\frac{1}{87}=\frac{175}{87} \mathrm{~atm}$

Partial pressure of $\mathrm{SO}_3=1-2 p=1-2\left(\frac{1}{87}\right)=\frac{85}{87} \mathrm{~atm}$