enthalpy change of solution

i know that if the enthalpy change of hydration is larger, you get a more exothermic value but i don't understand why that is accroding to the formula:

enthalpy change sol= sum of hydration enthalpies- lattice enthalpy.

does this formula not suggest that if the sum of hydration enthalpies is larger then you get a more positive value (since you are taking away from a larger number) and that is the LE is larger then you get a more exothermic value (which is wrong)

Reply 1

isla21!

your formula is correct, remember stronger/larger hydration enthalpy means more exothermic and that means more negative (as hydration enthalpy is always exothermic)

Lets try it with both an exo enthalpy of solution and an endo.

Exo:
Lets say sol = -100.
If you set up your energy profile/born haber, you have gaseous ions at the top, ionic lattice halfway down and aqueous ions at the bottom (as your enthalpy of solution is exo, your lattice enthalpy is exo and your hydration enthalpy is exo.) Remember that going from gaseous ions to aqueous ions (hydration enthalpy), lets call this A, is the same as going from gaseous ions to ionic lattice (B) and then dissolving the ionic lattice in water (C) (lattice enthalpy + enthalpy of solution).
Therefore to figure out enthalpy of solution, (C), it would be going backwards round the cycle, starting from the same place from the ionic lattice, gaseous ions to aqueous ions, which is the same as backwards B so -B and forwards A so +A. Therefore it is A-B, hydration - lattice.
If we use numbers, our hydration (A) is -2300 and our lattice enthalpy is -2200 (B)
so hydration - lattice is -2300 - -2200, so -2300+2200 = -100 enthalpy of solution.
If our hydration gets larger, (more exothermic), lets say -2500, and our lattice stays the same, its -2500 - -2200, so -2500+2200 = -300. This gives us an enthalpy of solution MORE exothermic than before. I think the main thing to remember is that hydration enthalpies are always exothermic, so are alway negative numbers. Therefore a larger/stronger hydration enthalpy = more exothermic = technically a smaller number

I think thats the issue but we will go through endo anyway
Lets say our enthalpy of solution is +100.
We still have an exothermic lattice enthalpy and an exothermic hydration enthalpy, so these 2 arrows need to point downwards. This means that overall our cycle has gaseous ions at the top (like in an exo solution profile) BUT instead, the aqueous ions are in the middle and the ionic lattice is at the bottom in terms of energy. (This sets up the profile so that the solution arrow points up as it is endothermic, and it also makes it clear that the lattice enthalpy in this situation is going to have to be MORE exothermic than the hydration enthalpy). (Top of the cycle means highest amount of energy, so downwards arrows release energy so are exothermic. There should be lots of profiles like this in your textbook but just in case)
Therefore if we want to calculate solution enthalpy, we would have to start at the same place (ionic lattice) and end up at aqueous ions… so we need to go backwards along the lattice enthalpy line (-B) and forwards along the hydration line (+A) so again it is A-B.
If hydration (A) is -800 and B lattice is -900, A-B is -800 - -900, so -800+900 = +100. (endo! yay)
If you then made hydration bigger, so stronger, so more exothermic, so lets say -1000, and kept lattice the same, it would be -1000 - -900, so -1000+900 = -100. This is MORE exothermic enthalpy of solution.

Let me know if u dont understand anything