Lithium iodide has a lattice energy of −7.3×102kj/mol and a heat of hydration of −793kj/mol. find the heat of solution for lithium iodide. determine how much heat is evolved or absorbed when 10.0g of lithium iodide completely dissolves in water.

First you have construct a cycle
  
                        heat of solution
           Li I (s) > Li I (aq)
heat of lattice                           heat of hydration
                           Li + I + aq 
heat of solution + heat of lattice = heat of hydration
(you take one direction as positive and the other negative)

Therefore,
Heat of solution = heat of hydration - heat of lattice = -793 + 7.3 * 10^2 = E

For one mole of Lithium iodide E amount of energy is release, then for 10 g how much.

1 = E
10/Molar mass of LiI = x
E * 10/molar mass of LI I = x