## coulomb potential energy and Madelung constant, as well as lattice energy

EvaLi_3J
Posts: 53
Joined: Wed Oct 02, 2019 12:16 am

### coulomb potential energy and Madelung constant, as well as lattice energy

Are we supposed to know these concepts and equations for midterms and finals?

If yes, can someone explain how the lattice energy works please?

KeyaV1C
Posts: 103
Joined: Sat Aug 17, 2019 12:17 am
Been upvoted: 1 time

### Re: coulomb potential energy and Madelung constant, as well as lattice energy

I don’t think we went over these concepts in class

Yiyang Jen Wang 4G
Posts: 76
Joined: Wed Nov 21, 2018 12:18 am

### Re: coulomb potential energy and Madelung constant, as well as lattice energy

I hope these will not be on the test or I would definitely fail.:(

EmilyJoo_1G
Posts: 50
Joined: Thu Jul 25, 2019 12:16 am

### Re: coulomb potential energy and Madelung constant, as well as lattice energy

The midterm will only cover up concepts up to 2D in the Chemical Bonds unit, so you don't need to worry about lattice energy

Sean Cheah 1E
Posts: 105
Joined: Wed Sep 18, 2019 12:20 am

### Re: coulomb potential energy and Madelung constant, as well as lattice energy

Lattice energy represents the change in energy that occurs when separated gaseous ions are packed together to form the ionic solid, which is always negative due to the process being exothermic.

This kinda gets into the realm of physics but essentially the negative derivative of the electrostatic forces between two ions (as given by Coulomb's Law) gives you their electric potential (aka Coulombic energy).

The Madelung constant is a scalar that depends on the geometric structure of the ion in question. While the formula for Coulombic energy only takes the interaction between two ions into account, since an ionic solid consists entirely of these two ions, one can focus on an arbitrary single ion and derive a very messy infinite sum that totals up all the electric potentials resulting from the forces between the chosen ion and each of the other ions in the lattice. Dividing the value of that infinite sum by the electric potential between two ions yields the Madelung constant for that ionic solid.

Putting that all together, lattice energy is equal to the electric potential of a single ion in the lattice (which is given by the sum of all the electric potentials between that ion and each of the other ions in the lattice) combined with the repulsive energy experienced by that ion due to electron repulsion. Most sources list lattice energies with the unit kJ/mol by multiplying this value by Avogadro's number and dividing by 1000.