Related Formula
KP = PB · (PC)(1)/(2)PA$$K_P = \frac{P_B \cdot (P_C)^{\frac{1}{2}}}{P_A}$$
where Pᵢ$P_i$ is the partial pressure of component i$i$.
Step 1: Setting up the ICE Table
For the reaction A(g) leftharpoons B(g) + (1)/(2) C(g)$A_{(g)} \rightleftharpoons B_{(g)} + \frac{1}{2} C_{(g)}$
Let initial moles of A = 1$A = 1$.
At equilibrium:
Moles of A = 1 - α$A = 1 - \alpha$
Moles of B = α$B = \alpha$
Moles of C = (α)/(2)$C = \frac{\alpha}{2}$
Total moles at equilibrium = (1 - α) + α + (α)/(2) = 1 + (α)/(2) = (2 + α)/(2)$(1 - \alpha) + \alpha + \frac{\alpha}{2} = 1 + \frac{\alpha}{2} = \frac{2 + \alpha}{2}$
Step 2: Calculating Partial Pressures
Using mole fraction ×$\times$ Total Pressure (P$P$):
PA = (1 - α)/(1 + (α)/(2)) · P$P_A = \frac{1 - \alpha}{1 + \frac{\alpha}{2}} \cdot P$
PB = (α)/(1 + (α)/(2)) · P$P_B = \frac{\alpha}{1 + \frac{\alpha}{2}} \cdot P$
PC = ((α)/(2))/(1 + (α)/(2)) · P$P_C = \frac{\frac{\alpha}{2}}{1 + \frac{\alpha}{2}} \cdot P$
Step 3: Calculating Kp
KP = PB · (PC)(1)/(2)PA$$K_P = \frac{P_B \cdot (P_C)^{\frac{1}{2}}}{P_A}$$
KP = ( (α)/(1 + α/2) P ) · ( (α/2)/(1 + α/2) P )1/2(1 - α)/(1 + α/2) P$$K_P = \frac{\left( \frac{\alpha}{1 + \alpha/2} P \right) \cdot \left( \frac{\alpha/2}{1 + \alpha/2} P \right)^{1/2}}{\frac{1 - \alpha}{1 + \alpha/2} P}$$
KP = α · (α/2)1/2 · P3/2(1 + α/2)3/2 · (1 + α/2)/((1 - α) P)$$K_P = \frac{\alpha \cdot (\alpha/2)^{1/2} \cdot P^{3/2}}{(1 + \alpha/2)^{3/2}} \cdot \frac{1 + \alpha/2}{(1 - \alpha) P}$$
KP = α3/2 · P1/2√(2) · (1 + α/2)1/2 · (1 - α)$$K_P = \frac{\alpha^{3/2} \cdot P^{1/2}}{\sqrt{2} \cdot (1 + \alpha/2)^{1/2} \cdot (1 - \alpha)}$$
Since 1 + α/2 = (2+α)/(2)$1 + \alpha/2 = \frac{2+\alpha}{2}$, the √(2)$\sqrt{2}$ in denominator cancels out perfectly leaving:
KP = α(3)/(2) P(1)/(2)(2 + α)(1)/(2)(1 - α)$$K_P = \frac{\alpha^{\frac{3}{2}} P^{\frac{1}{2}}}{(2 + \alpha)^{\frac{1}{2}}(1 - \alpha)}$$
Chapter Mix
Class 11 Chemistry: Equilibrium