Q79 E
Question
The lattice energy of \({\rm{LiF}}\) is \({\rm{1023 kJ/mol}}\), and the \({\rm{Li - F}}\) distance is \({\rm{201 pm}}\). \({\rm{MgO}}\) crystallizes in the same structure as \({\rm{LiF}}\) but with a \({\rm{Mg - O}}\) distance of \({\rm{205 pm}}\). Which of the following values most closely approximates the lattice energy of \({\rm{MgO}}\): \({\rm{256 kJ/mol, 512 kJ/mol, 1023 kJ/mol, 2046 kJ/mol,}}\) or \({\rm{4008 kJ/mol}}\)? Explain your choice.
Step-by-Step Solution
VerifiedThe value for lattice energy for \({\rm{MgO}}\) is \({\rm{4008 kJmo}}{{\rm{l}}^{{\rm{ - 1}}}}\) and \({\rm{4008 kJmo}}{{\rm{l}}^{{\rm{ - 1}}}}\) closely approximates to the result.
The lattice energy is the change in energy that occurs when one mole of a crystalline ionic compound is formed from its constituent ions.
Formula to calculate lattice energy is –
\({\rm{U = C}}\left( {\frac{{{{\rm{Z}}^{\rm{ + }}}{{\rm{Z}}^{\rm{ - }}}}}{{{{\rm{R}}_{\rm{o}}}}}} \right)......(1)\)
Where \({{\rm{R}}_{\rm{o}}}\), is the interatomic distance.
Charges are \({\rm{4}}\) times in case of \({\rm{MgO}}\) than \({\rm{LiF}}\), however bond distances are almost similar i.e., \({\rm{2}}{\rm{.01}}\mathop {\rm{A}}\limits^{\rm{o}} \) vs \({\rm{2}}{\rm{.05}}\mathop {\rm{A}}\limits^{\rm{o}} \).
From the data for \({\rm{LiF}}\), with \({{\rm{Z}}^{\rm{ + }}}{{\rm{Z}}^{\rm{ - }}}{\rm{ = - 1}}\),
\(\begin{align}{\rm{C = }}\frac{{{\rm{U}}{{\rm{R}}_{\rm{o}}}}}{{{{\rm{Z}}^{\rm{ + }}}{{\rm{Z}}^{\rm{ - }}}}}\\{\rm{ = }}\frac{{{\rm{1023 \times 2}}{\rm{.01}}}}{{{\rm{ - 1}}}}\\{\rm{ = - 2056 kJ}}\mathop {\rm{A}}\limits^{\rm{o}} {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\end{align}\)
Then, it is obtained that –
\(\begin{align}{{\rm{U}}_{{\rm{NaF}}}}{\rm{ = }}\frac{{{\rm{ - 2056 \times - 4}}}}{{{\rm{2}}{\rm{.05}}\mathop {\rm{A}}\limits^{\rm{o}} }}\\{\rm{ = 4008 kJmo}}{{\rm{l}}^{{\rm{ - 1}}}}\end{align}\)
Therefore, value for lattice energy is obtained as \({\rm{4008 kJmo}}{{\rm{l}}^{{\rm{ - 1}}}}\).