${}_c$ Consider an ionic compound, $M{x}_3,$ composed of generic metal $M$ and generic gaseous halogen $x.$

The enthalpy of formation of $M{x}_3$ is $H_f=-661k\frac{J}{m}ol.$

The enthalpy of sublimation of $M$ is $H_{\text{s}\text{u}\text{b}}=143k\frac{J}{m}ol.$

The first, second, and third ionization energies of $M$ are $I{E}_1=637k\frac{J}{m}ol,I{E}_2=1739k\frac{J}{m}ol,$ and $I{E}_3=2523k\frac{J}{m}ol.$

The electron affinity of $x$ is $H_{EA}=-325k\frac{J}{m}ol.($Refer to the hint$).$

The bond energy of $x_2$ is $BE=201k\frac{J}{m}ol.$

Determine the lattice energy of $M{x}_3.$