Chapter 13, Problem 142CP

Interpretation Introduction

Interpretation: The possible structures and enthalpy for ${\text{M}}_{\text{a}}{\text{X}}_{\text{b}}$ should be determined.

Concept Introduction:

The enthalpy is defined as the product of pressure and volume added up with the system’s internal energy. The change in enthalpy is defined as the heat absorbed or released. The bond energy is also known as the mean bond enthalpy or the average bond enthalpy. It is the measure of the bond strength depends on the chemical bond.

Answer to Problem 142CP

  ${\text{M}}_{\text{2}}\text{X}$ has the more negative enthalpy formation. The charges of the ions in ${\text{M}}_{\text{2}}\text{X}$ are ${\text{M}}^{\text{+}}$ and ${\text{X}}^{\text{2-}}$

Explanation of Solution

Given information:

Successive ionization energies of M: 480, 4750

Successive electron affinity values for X: -175, 920.

Enthalpy of sublimation for M(s) —> M (g): 110.

Bond energy of ${\text{X}}_{\text{2}}\text{:250}$

Lattice energies are $\text{MX}\text{=}\text{-1200}\text{kJ/mol;}{\text{MX}}_{\text{2}}\text{=}\text{-3500}\text{kJ/mol;}{\text{M}}_{\text{2}}\text{X}\text{=}\text{-3600}\text{kJ/mol}$

To determine all the possible structures. There are four possible structures for the compound ${\text{M}}_{\text{a}}{\text{X}}_{\text{b}}$ . The compound is MX that can be formed by two different ways ${\text{M}}_{\text{2}}\text{X}$ and ${\text{MX}}_{\text{2}}$ . To determine $\Delta H$ of formation of all the compounds is given below,

The equation is formed as,

  $\begin{array}{l}\text{M}\left(\text{s}\right)\to \text{M}\left(\text{g}\right)\text{ΔH=110}\text{kJ}\\ \text{M}\left(\text{g}\right)\to {\text{M}}^{\text{+}}\left(\text{g}\right){\text{+e}}^{\text{-}}\text{ΔH=480}\text{kJ}\\ {\text{M}}^{\text{+}}\left(\text{g}\right)\to {\text{M}}^{\text{2+}}\left(\text{g}\right){\text{+e}}^{\text{-}}\text{ΔH=4750}\text{kJ}\\ \frac{\text{1}}{\text{2}}{\text{X}}_{\text{2}}\left(\text{g}\right)\to \text{X}\left(\text{g}\right)\text{ΔH=}\frac{\text{1}}{\text{2}}\left(\text{250}\text{kJ}\right)\\ \text{X}\left(\text{g}\right){\text{+e}}^{\text{-}}\to {\text{X}}^{\text{-}}\left(\text{g}\right)\text{ΔH=-175}\text{kJ}\\ {\text{X}}^{\text{-}}\left(\text{g}\right){\text{+e}}^{\text{-}}\to {\text{X}}^{\text{2-}}\left(\text{g}\right)\text{ΔH=920}\text{kJ}\\ {\text{M}}^{\text{2+}}\left(\text{g}\right){\text{+X}}^{\text{2-}}\left(\text{g}\right)\to \text{MX}\left(\text{g}\right)\text{ΔH=-4800}\text{kJ}\end{array}$

For MX composed of ${\text{M}}^{\text{2+}}\text{and}{\text{X}}^{\text{2-}}\text{,}{\text{M}}^{\text{2+}}\left(\text{s}\right){\text{+X}}^{\text{2+}}\left(\text{g}\right)\to \text{MX}\left(\text{s}\right)\text{:}$

  $\begin{array}{l}\Delta H_f^{\circ }=110+480+4750+\frac{1}{2}\left(250\right)-175-1200-920\\ \Delta H_f^{\circ }=1410\text{kJ}\end{array}$

For MX composed of ${\text{M}}^{\text{+}}\text{and}{\text{X}}^{\text{-}}\text{,}2\text{M}\left(\text{s}\right)\text{+}\frac{\text{1}}{2}{\text{X}}_2\left(\text{g}\right)\to \text{MX}\left(\text{s}\right)\text{:}$

  $\begin{array}{l}\Delta H_f^{\circ }=110+480+\frac{1}{2}\left(250\right)-175-1200\\ \Delta H_f^{\circ }=-660\text{kJ}\end{array}$

For MX composed of ${\text{M}}^{\text{+}}\text{and}{\text{X}}^{\text{2-}}\text{,}2\text{M}\left(\text{s}\right)\text{+}\frac{\text{1}}{2}{\text{X}}_2\left(\text{g}\right)\to {\text{M}}_2\text{X}\left(\text{s}\right)\text{:}$

  $\begin{array}{l}\Delta H_f^{\circ }=2\left(110\right)+2\left(480\right)+\frac{1}{2}\left(250\right)-175-920-3600\\ \Delta H_f^{\circ }=-1550\text{kJ}\end{array}$

For MX composed of ${\text{M}}^{\text{2+}}\text{and}{\text{X}}^{\text{-}}\text{,}\text{M}\left(\text{s}\right){\text{+X}}_2\left(\text{g}\right)\to {\text{M}}_2\text{X}\left(\text{s}\right)\text{:}$

  $\begin{array}{l}\Delta H_f^{\circ }=110+480++4750+250+2\left(-17\right)5-3500\\ \Delta H_f^{\circ }=1740\text{kJ}\end{array}$

The compound with the most negative enthalpy values are most likely to form. Only ${\text{M}}^{\text{+}}{\text{X}}^{\text{-}}\text{and}{\left({\text{M}}^{\text{+}}\right)}_{\text{2}}{\text{X}}^{\text{2-}}$ are possible because they have negative enthalpies of formation. Since ${\text{M}}_{\text{2}}\text{X}$ has the more negative enthalpy op formation, it is most likely to form. Thus, the charges of the ions in ${\text{M}}_{\text{2}}\text{X}$ are ${\text{M}}^{\text{+}}$ and ${\text{X}}^{\text{2-}}$

Conclusion

  ${\text{M}}_{\text{2}}\text{X}$ has the more negative enthalpy formation. The charges of the ions in ${\text{M}}_{\text{2}}\text{X}$ are ${\text{M}}^{\text{+}}$ and ${\text{X}}^{\text{2-}}$