# How to calculate the energy to dissociate a bond into neutral atoms?

I am self studying chemistry through MiT ocw 5.111 . On practice exam 2 problem 2 there is a question which states the following

    element           ionization energy          electron   affinity
Potassium(K)      418 kJ/mol                 48 kJ/mol
Fluorine(F)       1680 kJ/mol                328 kJ/mol
Chlorine(Cl)      1255 kJ/mol                349 kJ/mol


(a) (12 points) The ionic bond length for KF is 0.217 nm. Calculate the energy (in units of kJ/mol required to dissociate a single molecule of KF into the neutral atoms K and F, using information provided above. For this calculation, assume that the potassium and fluorine ions are point charges.

I proceeded to calculate the bond dissociation energy using the following formula $$U(r)=\frac{z_1z_2e^2}{4\pi\varepsilon_0r}$$ from which I obtained a dissociation energy of $$-640$$ kJ/mol. Then left with two ions F$$^{-1}$$ and K$$^{+1}$$. I went on to determine their ionization energies and electron affinities respectively.

To make F$$^{-1}\to$$ F + $$e^{-}$$ an electron must be lost thus warranting an ionization energy of $$-1680$$ kJ/mol and. To make K$$^{+1}$$+ $$e^{-} \to$$ K and electron must be gained thus referring to the election affinity of K of $$18$$ kJ/mol. When equated as (Energy Required - Energy Released) I arrive at

 (Dissociation Energy + Ionization Energy) - Electron Affinity = (-640 kJ/ mol - 1680 kJ/mol) + 48 kJ/mol = -2272 kJ/mol required


However I see in the answer key this is incorrect could someone guide me as to where I am going wrong here thank you.

Your $$\pu{640 kJ mol^-1}$$ value is correct, so the next step is to neutralize the ions. First add an electron to a potassium ion to get a potassium atom. This releases $$\pu{418 kJ mol^-1}$$ because it is the reverse of the potassium atom ionization. Then take away an electron from fluoride ion to get a fluorine atom. This requires an input of $$\pu{328 kJ mol^-1}$$ because it is the reverse of the fluorine electron affinity. So the result is $$\pu{550 kJ mol^-1}$$, i.e., $$\pu{640 kJ mol^-1}$$ - $$\pu{418 kJ mol^-1}$$ + $$\pu{328 kJ mol^-1}$$.