Chemical and Ionic Equilibrium - Result Question 49
####49. The equilibrium constant $K _p$ of the reaction,
$$ 2 SO _2(g)+O _2(g) \rightleftharpoons 2 SO _3(g) $$
is $900 atm$ at $800 K$. A mixture containing $SO _3$ and $O _2$ having initial pressure of 1 and $2 atm$ respectively is heated at constant volume to equilibrate. Calculate the partial pressure of each gas at $800 K$.
$(1989,3 M)$
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Solution:
$$ \begin{array}{lccc} & 2 SO _2(g)+O _2(g) & \rightleftharpoons SO _3(g) \ \text { Initial } p _i: & 0 & 2 & 1 \ \text { Equilibrium } p _i: 2 p & 2+p & & 1-2 p \end{array} $$
$$ K _p=900=\frac{(1-2 p)^{2}}{(2+p)(2 p)^{2}} \quad[\text { Ignoring } p \text { in comparison to 2] } $$
$$ p=\frac{1}{87} \text { atm } $$
Partial pressure of $SO _2=2 p=\frac{2}{87}$ atm
$$ \text { Partial pressure of } O _2=2+p=2+\frac{1}{87}=\frac{175}{87} atm $$
Partial pressure of $SO _3=1-2 p=1-2\left(\frac{1}{87}\right)=\frac{85}{87} atm$
