Chapter 18, Problem 18.52QP

Interpretation Introduction

Interpretation:

$Ksp$ of $AgCl$ at $60°C$ has to be calculated.

Concept Information:

Enthalpy$\left(H\right)$: It is the total amount of heat in a particular system.

The value of heat formed in a reaction $\text{ΔH}$ is calculated by the formula,

$\text{ΔH=}{{\displaystyle \sum \left(BondDissociationEnergy\right)}}_{\left(\text{reactants}\right)}-{{\displaystyle \sum \left(BondDissociationEnergy\right)}}_{\left(\text{products}\right)}$

Free energy change$\left(\Delta G\right)$: Change in the free energy takes place while reactants convert to product.

The free energy $\Delta G$ can be determined by

$\Delta G=\Delta H-T\Delta S$

Change in the free energy can be determined by solubility product as follows:

$\begin{array}{c}\text{ΔG}°\text{=}-\text{RTln}{\text{K}}_{sp}\\ \\ \text{where,}\\ \text{ΔG}°=\text{Standard free energy}\\ \text{R}\text{=}\text{Gas}\text{Constant}(\text{8}\text{.314 J/K mol})\\ T=\text{Temperature}\\ {\text{K}}_{sp}\text{=}\text{Solubility}\text{product}\end{array}$

Solubility product constant ${\text{K}}_{\text{sp}}$ refers to the level in which the solute gets dissolved in a solution. It explains the equilibrium of a solid with its corresponding ions in a solution.

It is the product of concentration of ions that are dissolved raised to power of their corresponding coefficient of stoichiometry.

$\begin{array}{l}{\text{A}}_{\text{c}}{\text{B}}_{\text{d}}\stackrel{}{\rightleftarrows }{\text{cA}}^{\text{+}}\text{+}{\text{dB}}^{-}\\ \text{Therefore,}\\ {\text{K}}_{\text{sp}}\text{=}{\left[{\text{A}}^{\text{+}}\right]}^{\text{c}}{\left[{\text{B}}^{-}\right]}^{\text{d}}\end{array}$