Question #44294

The first ionization energies ($IE_1$) of the elements $\ce{K}$, $\ce{Rb}$, $\ce{Cu}$, and $\ce{Ag}$ are $403$, $419$, $731$, and $745 \text{ kJ/mol}$, listed in random order.

Consider the formation and subsequent dissolution of silver chloride, $\ce{AgCl(s)}$, at $300 \text{ K}$.

Given the following thermodynamic data at $300 \text{ K}$: $\Delta H_{sub}(\ce{Ag, s}) = 284 \text{ kJ/mol}$ $\Delta H_{diss}(\ce{Cl2, g}) = 242 \text{ kJ/mol}$ $EA_1(\ce{Cl, g}) = -349 \text{ kJ/mol}$ Lattice enthalpy ($\Delta H_{lattice}$) for $\ce{Ag+(g) + Cl-(g) -> AgCl(s)}$ is $-916 \text{ kJ/mol}$ Standard entropy of formation, $\Delta S_f^\circ(\ce{AgCl, s}) = -58 \text{ J K}^{-1} \text{ mol}^{-1}$ $\Delta G_f^\circ(\ce{Ag+, aq}) = 77.0 \text{ kJ/mol}$ $\Delta G_f^\circ(\ce{Cl-, aq}) = -131.6 \text{ kJ/mol}$

Use $R = \frac{25}{3} \text{ J K}^{-1} \text{ mol}^{-1}$.

Calculate the natural logarithm of the solubility product ($\ln K_{sp}$) of $\ce{AgCl(s)}$ at $300 \text{ K}$.