Question

For the reaction, $S{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\rightleftharpoons S{O}_3\left(g\right)$ if $K_c=K_p(RT{)}^x$ where, the symbols have their usual meaning, then the value of $x$ is: (assuming ideality)

• A. $-1$
• B. $-\frac{1}{2}$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

The correct option is C $\frac{1}{2}$

For the given reaction,
$\Delta n_g=n_{P\left(g\right)}-n_{R\left(g\right)}$
$K_p=K_c(RT{)}^{\Delta n_g}$
$\therefore \Delta n_g=-\frac{1}{2}$
where, $n_g$ = gaseous moles of products - gaseous moles of reactants
$K_c=K_p(RT{)}^{-\Delta n_g},x=-\Delta n_g=\frac{1}{2}$