For the dissociation reaction , the degree of dissociation is small () and varies inversely as the s — Chemical Equilibrium Chemistry Question
Question
For the dissociation reaction $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$, the degree of dissociation $\alpha$ is small ($\alpha \ll 1$) and varies inversely as the square root of the total system pressure. Suppose at constant temperature, the volume of the system is slowly increased to exactly $16$ times its initial volume. By what integer factor will the degree of dissociation $\alpha$ increase?
💡 Solution & Explanation
Since $\alpha \propto 1/\sqrt{P}$ and pressure is inversely proportional to volume at constant temperature ($P \propto 1/V$), we have $\alpha \propto \sqrt{V}$. If the new volume $V_{new} = 16 V_{initial}$, then the new degree of dissociation $\alpha_{new} = \sqrt{16} \alpha_{initial} = 4 \alpha_{initial}$. Thus, it increases by a factor of 4.