standard enthalpies of formation

Question

H20(l) = -286  LiOH(s) = -487

standard enthalpies of solution for LiOH(s) to split into it's ions is 21

all values are in KJmol-1

Use the data given to calculate a value for the enthalpy change for the reaction of lithium with water.

I get how to do the cycle and I've seen the mark scheme and I don't understand why the 21 becomes negative.

I can draw my cycles. I use the equation in hess's law:

AH1 = AH2+AH3
    = 286 - 487
    = -201 and that is the wrong answer, it has -21 aswell so the answer is -222.  I would have thought that if the solution was being formed then it would have a positive value as you are going in the right direction, is the mark scheme wrong or is there something I don't understand.

Thank you for any help you can provide.

Bot · Answer

The enthalpy of solution for LiOH(s) is the enthalpy change for the reaction of lithium with water. The enthalpy of solution is the energy required to break the ionic bonds in the solid LiOH(s) and form the ions Li+ and OH- in solution. Since energy is required to break the bonds, the enthalpy of solution is a positive value. Therefore, the enthalpy change for the reaction of lithium with water is -222 kJ/mol.