Calculate the lattice enthalpy of `MgBr_(2)` from the given date:
`{:(Mg(s)+Br_(2)(l)rarrMgBr_(2)(s),,Delta_(f)H^(@)=-524 kJ mol^(-1)),(Mg(s)rarrMg(g),,Delta_(1)H^(@)=+148 kJ mol^(-1)),(Mg(g)rarrMg^(2+)(g)+2e^(-),,Delta_(2)H^(@)=+2187 kJ mol^(-1)),(Br_(2)(l)rarrBr_(2)(g),,Delta_(3)H^(@)=+31 kJ mol^(-1)),(Br_(2)(g)rarr2Br(g),,Delta_(4)H^(@)=+193 kJ mol^(-1)),(2Br(g)+2e^(-)rarr2Br^(-)(g),,Delta_(5)H^(@)=-662 kJ mol^(-1)):}`
Strategy : The thermochemical equation corresponding to lattice enthalpy of `MgBr_(2)` is
`{:(Mg^(2+)(g)+2Br^(-)(g)rarrMgBr_(2)(s),,,Delta_("Lattice")H^(@)=?):}`
Add the last five thermochemical equations to the thermochemical equation corresponding to lattice enthalpy to get the thermochemical equation for the formation of `MgBr_(2) (s)` from its constituent element. Finally, calculate `Delta_(Lattice) H^(@)`, using the concept of Hess's law.

Explanation

To calculate the lattice enthalpy of `MgBr_(2)`, we will use Hess's law and the provided thermochemical equations. Here’s a step-by-step solution:

### Step 1: Write down the thermochemical equations
We have the following thermochemical equations:

1. Formation of `MgBr_(2)(s)` from its elements:
\[
Mg(s) + Br_2(l) \rightarrow MgBr_2(s), \quad \Delta_f H^\circ = -524 \, \text{kJ/mol}
...