How to derive the energy of solvation equation?

The work done as a ion is solvated is given by: $-z^2e^2/8\pi\epsilon r$ but since the top line can be written $Q^2$, for simplicity I will say the equation is $-Q^2/8\pi\epsilon r$. Is this derived from integrating potential with respect to charge $Q$?


i.e $$w=\int\_Q^0 VdQ$$ where $$V=Q/4 \pi \epsilon r$$


I believe this would give the correct units and equation but is this an acceptable derivation?


Also, as a, sort of, side question why can't I write: 


$$\triangle w=\int\_Q^0 VdQ$$.


I understand that work is an inexact differential but I fail to understand the argument regarding paths - surely if you change the charge of a particle from one value to another, you must be doing the same amount of work no matter how you do it. This argument must be wrong but I don't know why and why does this mean I cant write $\triangle w$? I know you can do this for things like entropy and enthalpy because they are state functions - I just don't understand the difference. Thanks.


