a 4.50 sample of LiCl at 25.0*C dissolves in 25.0 mL of water also at 25.0*C. The final equilibrium temperature of resulting solution is 60.8*C. What is the enthalpy of solution, of LiCL expressed in kilojoules per mole?

I would do this.

q = mass H2O x specific heat H2O x (Tfnial-Tinitial).
mass H2O = 25.0,
specific heat water = 4.184 j/g*C
Tfinal = 60.8 C
Tinitial = 25.0 C.
Then q/4.50 give you J/g.
Divide by 1000 to convert to kJ and multiply by molar mass LiCl to convert to moles. Check my thinking.