Chapter 6, Problem 6.143QP

From the following data, calculate the heat of solution for KI:

Interpretation Introduction

Interpretation:

The heat of solution for $\text{KI}$ has to be calculated.

Concept Introduction:

Heat of hydration can be defined as the change in enthalpy associated with the process of hydration.  Applying Hess’s law, it is possible to estimate ${\text{ΔH}}_{\text{soln}}$ is the sum of two related quantities, lattice energy and the heat of hydration.  The heat of hydration is given by the equation,

${\text{ΔH}}_{\text{soln}}\text{=}{\text{U+ΔH}}_{\text{hydration}}$

Answer to Problem 6.143QP

The heat of solution for $\text{KI}$ is $\text{43}\text{kJ/mole}\text{.}$

Explanation of Solution

The ${\text{ΔH}}_{\text{hydr}}$ of $\text{KI}$ is calculated below,

$\begin{array}{l}\left(\text{1}\right){\text{Na}}^{\text{+}}{}_{\left(\text{g}\right)}{\text{+Cl}}^{\text{-}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{Na}}^{\text{+}}{}_{\left(\text{aq}\right)}{\text{+Cl}}^{\text{-}}{}_{\left(\text{aq}\right)}{\text{ΔH}}_{\text{hydr}}\text{=}\left(\text{4}\text{.0-788}\right)\text{kJ/mole}\text{=}\text{-784}\text{.0}\text{kJ/mole}\\ \\ \left(\text{2}\right){\text{Na}}^{\text{+}}{}_{\left(\text{g}\right)}{\text{+I}}^{\text{-}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{Na}}^{\text{+}}{}_{\left(\text{aq}\right)}{\text{+I}}^{\text{-}}{}_{\left(\text{aq}\right)}{\text{ΔH}}_{\text{hydr}}\text{=}\left(\text{-5}\text{.1-686}\right)\text{kJ/mole}\text{=}\text{-691}\text{.1}\text{kJ/mole}\\ \\ \left(\text{3}\right){\text{K}}^{\text{+}}{}_{\left(\text{g}\right)}{\text{+Cl}}^{\text{-}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{K}}^{\text{+}}{}_{\left(\text{aq}\right)}{\text{+Cl}}^{\text{-}}{}_{\left(\text{aq}\right)}{\text{ΔH}}_{\text{hydr}}\text{=}\left(\text{17}\text{.2-699}\right)\text{kJ/mole}\text{=}\text{-681}\text{.8}\text{kJ/mole}\end{array}$

The equation $\left(\text{2}\right)\text{and}\left(\text{3}\right)$ are added together and then subtracted from the first equation.  The heat of hydration of $\text{KI}$ is given as,

$\begin{array}{l}\underset{\_}{\begin{array}{l}\left(\text{2}\right)\cancel{{\text{Na}}^{\text{+}}{}_{\left(\text{g}\right)}}{\text{+I}}^{\text{-}}{}_{\left(\text{g}\right)}\stackrel{}{\to }\cancel{{\text{Na}}^{\text{+}}{}_{\left(\text{aq}\right)}}{\text{+I}}^{\text{-}}{}_{\left(\text{aq}\right)}\text{ΔH=-691}\text{.1}\text{kJ/mole}\\ \\ \left(\text{3}\right){\text{K}}^{\text{+}}{}_{\left(\text{g}\right)}\text{+}\cancel{{\text{Cl}}^{\text{-}}{}_{\left(\text{g}\right)}}\stackrel{}{\to }{\text{K}}^{\text{+}}{}_{\left(\text{aq}\right)}\text{+}\cancel{{\text{Cl}}^{\text{-}}{}_{\left(\text{aq}\right)}}\text{ΔH=-681}\text{.8}\text{kJ/mole}\\ \\ \left(\text{1}\right)\cancel{{\text{Na}}^{\text{+}}{}_{\left(\text{aq}\right)}}\text{+}\cancel{{\text{Cl}}^{\text{-}}{}_{\left(\text{aq}\right)}}\stackrel{}{\to }\cancel{{\text{Na}}^{\text{+}}{}_{\left(\text{g}\right)}}\text{+}\cancel{{\text{Cl}}^{\text{-}}{}_{\left(\text{g}\right)}}\text{ΔH=+784}\text{.0}\text{kJ/mole}\end{array}}\\ {\text{K}}^{\text{+}}{}_{\left(\text{g}\right)}{\text{+I}}^{\text{-}}{}_{\left(\text{g}\right)}\stackrel{}{\to }{\text{K}}^{\text{+}}{}_{\left(\text{aq}\right)}{\text{+I}}^{\text{-}}{}_{\left(\text{aq}\right)}\text{ΔH=-588}\text{.9}\text{kJ/mole}\end{array}$

The heat of solution is calculated as,

$\begin{array}{l}{\text{ΔH}}_{\text{soln}}\text{=}{\text{U+ΔH}}_{\text{hydr}}\\ \\ {\text{ΔH}}_{\text{soln}}\text{=}\left(\text{632}\text{kJ/mole-588}\text{.9}\text{kJ/mole}\right)\\ \\ {\text{ΔH}}_{\text{soln}}\text{=}\text{43}\text{kJ/mole}\end{array}$

The heat of solution for $\text{KI}$ is $\text{43}\text{kJ/mole}\text{.}$

Conclusion

The heat of solution for $\text{KI}$ was calculated as $\text{43}\text{kJ/mole}\text{.}$