Q80 E - Chemistry (OpenStax)

Question

Which compound in each of the following pairs has the larger lattice energy? Note: \({\rm{M}}{{\rm{g}}^{{\rm{2 + }}}}\) and \({\rm{L}}{{\rm{i}}^{\rm{ + }}}\) have similar radii; \({{\rm{O}}^{{\rm{2 - }}}}\) and \({{\rm{F}}^{\rm{ - }}}\) have similar radii. Explain your choices. 

(a) \({\rm{MgO}}\) or \({\rm{MgSe}}\) 

(b) \({\rm{LiF}}\) or \({\rm{MgO}}\) 

(c) \({\rm{L}}{{\rm{i}}_{\rm{2}}}{\rm{O}}\) or \({\rm{LiCl}}\) 

(d) \({\rm{L}}{{\rm{i}}_{\rm{2}}}{\rm{Se}}\) or \({\rm{MgO}}\)

Step-by-Step Solution

Answer

1. \({\rm{MgO}}\) has greater lattice energy.
2. \({\rm{MgO}}\) has greater lattice energy.
3. \(Li{}_2O\) has greater lattice energy.
4. \({\rm{MgO}}\) has greater lattice energy.

Step 1: Concept Introduction

The lattice energy is the change in energy that occurs when a crystalline ionic compound is formed from its constituent ions

Step 2: Larger Lattice Energy between \({\rm{MgO}}\) and \({\rm{MgSe}}\)

(a)

Selenium has larger radius than oxygen. The larger radius results in a larger interionic distance. 

 

Therefore, \({\rm{MgO}}\) has lattice energy than \({\rm{MgSe}}\).

 

Step 3: Larger Lattice Energy between \({\rm{LiF}}\) and \({\rm{MgO}}\)

(b)

Since there are higher charges on \({\rm{Mg}}\) and \({\rm{O}}\), whereas radii of the ions are almost similar. 

 

Therefore, \({\rm{MgO}}\) has larger lattice energy than \({\rm{LiF}}\).

Step 4: Larger Lattice Energy between \({\rm{L}}{{\rm{i}}_{\rm{2}}}{\rm{O}}\) and \({\rm{LiCl}}\)

(c)

The higher charge on \({{\rm{O}}^{{\rm{2 - }}}}\) leads to a larger energy; additionally, \({\rm{C}}{{\rm{l}}^{\rm{ - }}}\) is larger than \({{\rm{O}}^{{\rm{2 - }}}}\); this leads to a larger interionic distance in \(LiCl\) and a lower lattice energy.

 

Therefore, \(Li{}_2O\) has higher lattice energy.

Step 5: Larger Lattice Energy between \({\rm{L}}{{\rm{i}}_{\rm{2}}}{\rm{Se}}\) and \({\rm{MgO}}\)

(d)

Since there are higher charges on \({\rm{Mg}}\) and \({\rm{O}}\), whereas radii of the ions are almost similar. 

 

Therefore, \({\rm{MgO}}\) has larger lattice energy than \(Li{}_2Se\).