Practicing Success
At \(250^oC\) and 1 atmospheric pressure, the vapour density pf \(PCl_5\)is \(57.9\). Calculate: (i) \(K_p\) for the reaction, \(PCl_5(g) ⇌ PCl_3 (g) + Cl_2(g)\), at \(250^oC\) (ii) the percentage dissociation when pressure is doubled. |
1.78 and 68.6% 1.78 and 58.6% 1.58 and 68.6% 1.58 and 58.6% |
1.78 and 68.6% |
The correct answer is option 1. 1.78 and 68.6%. Molar mass of \(PCl_5\) \(= 208.5\) Vapour density, \(D = \frac{208.5}{2} = 104.25\) Observed vapour density, \(d = 57.9\) Degree of dissociation, \(\alpha = \frac{D - d}{d} = \frac{104.25 - 57.9}{57.9} = 0.80\)
Total number of mole \(= (1 - \alpha ) + \alpha + \alpha = 1 + \alpha = 1 + 0.80 = 1.80\) Partial Pressure of \(PCl_5\) \(= \frac{0.2}{1.8} \times 1 = \frac{1}{9}\) Partial Pressure of \(PCl_3\) \(= \frac{0.8}{1.8} \times 1 = \frac{4}{9}\) Partial Pressure of \(Cl_2\) \(= \frac{0.8}{1.8} \times 1 = \frac{4}{9}\) So, \(K_p = \frac{p_{PCl_3} \times p_{Cl_2}}{p_{PCl_5}}\) \(⇒ K_p = \frac{\frac{4}{9} \times \frac{4}{9}}{\frac{1}{9}}\) \(⇒ K_p = \frac{16}{9} = 1.78\) Let the degree of dissociation be \(\alpha \) when pressure is \(2\) atmosphere. At equilibrium, \(p_{PCl_5} = \frac{1 - \alpha }{1 + \alpha }P = \frac{1 - \alpha }{1 + \alpha } \times 2\) \(p_{PCl_3} = \frac{\alpha }{1 + \alpha }P = \frac{\alpha }{1 + \alpha } \times 2\) \(p_{Cl_2} = \frac{\alpha }{1 + \alpha }P = \frac{\alpha }{1 + \alpha } \times 2\) \(K_p = \frac{\frac{\alpha }{1 + \alpha } \times 2 \times \frac{\alpha }{1 + \alpha } \times 2}{\frac{1 - \alpha }{1 + \alpha } \times 2}\) or, \(\frac{\alpha ^2}{1 - \alpha ^2} \times 2 = 1.78 \) or, \(\frac{\alpha ^2}{1 - \alpha ^2} = 0.89\) or, \(\alpha ^2 = 0.89 - 0.89\alpha ^2\) or, \(1.89\alpha ^2 = 0.89\) or, \(\alpha ^2 = \frac{0.89}{1.89}\) or, \(\alpha = 0.686\) |