Question

At ${727}^o$C and $1.23$ atm of total equilibrium pressure, $S{O}_3$ is partially dissociated into $S{O}_2$ and $O_2$ according to $S{O}_3\left(g\right)\rightleftharpoons S{O}_2\left(g\right)+1/2O_2\left(g\right)$. The density of equilibrium mixture is $0.9$ g/litre. The degree of dissociation is (assuming ideal behaviour of gases):

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{2}{3}$

$\begin{array}{c}P{M}_0=dRT\\ 1.2\times M_0=0.9\times 0.08\times 1000\\ M_0=60gmol\end{array}$

$\frac{n_0}{n_{min}}=\frac{{\left(M_0\right)}_{\text{min},f}}{{\left(M_0\right)}_{mix,i}}$

$\begin{array}{cc}{\mathrm{SO}}_3\text{molecular weight}& =32+3\times 16\\ & =80\end{array}$

$\begin{array}{cc}\frac{a\times 1}{a(1+\frac{\alpha }{2})}& =\frac{60}{80}\\ \frac{4}{3}& =1+\frac{\alpha }{2}\end{array}$

$\begin{array}{c}\frac{1}{3}=\frac{\alpha }{2}\\ \alpha =\frac{2}{3}\end{array}$