For a general gaseous dissociation reaction , which of the following mathematical relationships is/a — Chemical Equilibrium Chemistry Question
Question
For a general gaseous dissociation reaction $A(g) \rightleftharpoons nB(g)$, which of the following mathematical relationships is/are universally correct? (where $D$ = theoretical vapour density, $d$ = observed vapour density, $M_{th}$ = theoretical molar mass, $M_{obs}$ = observed molar mass, $\alpha$ = degree of dissociation)
💡 Solution & Explanation
Formulas A and B are standard textbook derivations for $\alpha$ based on conservation of mass. For $PCl_5$, $n = 2$, so substituting $n=2$ into $d = \frac{D}{1 + (n-1)\alpha}$ yields $d = \frac{D}{1 + \alpha}$ (C is correct). For $2HI \rightleftharpoons H_2 + I_2$, $\Delta n_g = 0$ (so $n=1$), which makes the denominator $(n-1) = 0$. Thus, $D=d$ at all times, making it impossible to find $\alpha$ via vapour density (D is false).