Question

$S{O}_3$ decomposes at a temperature of 1000 K and at a total pressure of 1.642 atm. At equilibrium, the density of mixture is found to be 1.28 g/L in a vessel of 90 litres. Find the degree of dissociation of $S{O}_3$ for $S{O}_3\rightleftharpoons S{O}_2+1/2O_2$ :

• A. $\alpha =0.5$
• B. $\alpha =1$
• C. $\alpha =2$
• D. None of these

Answer 1

The correct option is A $\alpha =0.5$

$S{O}_3\rightleftharpoons S{O}_2+\frac{1}{2}{O}_2$

Initially 1 0 0

Equilibrium $\begin{array}{cc}-\alpha & +\alpha +0.5\alpha \end{array}$

__________________

$\begin{array}{ccc}1-\alpha & \alpha & 0.5\alpha \end{array}$

$\rho =1\cdot 28$

$\rho =\frac{PM}{RT}$

$M=\frac{\rho RI}{P}=\frac{1.28\times 0.0821\times 1000}{1.642}=64mol/l$

$\text{Average molecular mass}=64$

$\frac{80(1-\alpha )+64\alpha +32\times 0.5\alpha }{1-\alpha +\alpha +0.5\alpha }=64$

$80-80\alpha +64\alpha +16\alpha =64(1+0.5\alpha )$

$\alpha =0.5$