Question #44719

Due to significant ion-pair formation, a $0.05 \text{ M}$ aqueous solution of the coordination complex pentaamminechloridocobalt(III) chloride exhibits incomplete dissociation at $300 \text{ K}$. The solution is placed in a reverse osmosis chamber separated from pure water by a semipermeable membrane. The resistance of this solution, measured in a conductivity cell with a cell constant of $1.2 \text{ cm}^{-1}$, is $200 \Omega$. Given the limiting molar conductivities: $\lambda^\infty(\ce{[Co(NH_3)_5Cl]^{2+}}) = 160 \text{ S cm}^2 \text{ mol}^{-1}$ and $\lambda^\infty(\ce{Cl^-}) = 70 \text{ S cm}^2 \text{ mol}^{-1}$. Assuming the Arrhenius theory of electrolytic dissociation is valid for the apparent degree of dissociation, what is the minimum external pressure that must be applied to the solution to initiate reverse osmosis? (Use $R = 0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}$)