Question

In the equilibrium $2S{O}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2S{O}_3\left(g\right)$, the partial pressure of $S{O}_2,O_2$ and $S{O}_3$ are $0.662,0.10$ and $0.331$ atm respectively. What should be the partial pressure of oxygen so that the equilibrium concentrations of $S{O}_2$ and $S{O}_3$ are equal?

• A. $0.4$ atm
• B. $1.0$ atm
• C. $0.04$ atm
• D. $0.25$ atm

Answer 1

The correct option is A $0.4$ atm

$2{SO}_2+O_2\rightleftharpoons {2SO}_3$

$P_{{SO}_2}=0.662$atm

$P_{O_2}=0.10$ atm

$P_{{SO}_3}=0.331$ atm

$K_p=\frac{{\left[P_{{SO}_3}\right]}^2}{{\left[P_{{SO}_2}\right]}^2\left[P_{O_2}\right]}=\frac{{\left(0.331\right)}^2}{{\left(0.662\right)}^2\left(0.10\right)}=2.5$

now, given $P_{{SO}_2}=P_{{SO}_3}$

$K_p=\frac{{\left[P_{{SO}_3}\right]}^2}{{\left[P_{{SO}_2}\right]}^2\left[P_{O_2}\right]}$

$\left[P_{O_2}\right]=\frac{1}{K_P}=\frac{1}{2.5}=4.0\times {10}^{-1}=0.4$ atm

$\Rightarrow$ $0.4$ atm should be partial pressure of oxygen for equal equilibrium concentrations of ${SO}_3$ and ${SO}_2$.