Search for Answers to Your Chemistry Questions

Madelung constant for NaCl, lattice energy and enthalpy of solution

Needing some help with an inorganic assignment...

2 questions that I have no idea how to do and are not explained in our text (Descriptive Inorganic Chemistry 4ed - Rayner).

1.  Calculate the first three terms of the series for the Madelung constant for the sodium chloride lattice.  How does this compare with the limiting value?  (Apparently none of my classmates are familiar with this either).

2.  For an ionic compound, MX, the lattice energy is 1205kJ/mol and the enthalpy of solution is -90kJ/mol.  If the enthalpy of hydration of the cation is 1.5 times that of the anion, what are the enthalpies of hydration of the ions?

These have frustrated me for a longer amount of time than I care to volunteer.

Help please -- anything!  Thanks. :'(

The Madelung constant is used in determining the energy of a single ion in a crystal. Because the anions and cations in an ionic solid are attracted to each other by virtue of their opposing charges, separating the ions requires a certain amount of energy. This energy must be given to the system in order to break the anion-cation bonds. The energy required to break these bonds for one mole of an ionic solid under standard conditions is the lattice energy.

Since charges in ions are based on the electric energy of an electron, we can use the energy of the electron and then modify it to see how close the other electrons are.

E = -\frac{z^2 e^2 M}{4 \pi \epsilon_o r_0}

    \, z = charge of ions
    \,e = 1.6022×10?19 C
    \,4\pi \epsilon_o = 1.112×10?10 C²/(J m)
    \, M = Madelung's constant, which is a relationship of the distance of the ions from one another due to a specific type of crystal.

for the ionic crystal:-
M = \sum_{i,j,k=-\infty}^{\infty}\prime {{(-1)^{i+j+k}} \over { (i^2 + j^2 + k^2)^{1/2}}}

If you find this answer useful please share it with other students.