Ionic Bonding

Coulomb's Law

A fundamental science concept here: positive charge is attracted to negative charge. This is called electrostatic attraction. It is also true that like charges repulse one another but that is not what ionic bonding is all about. Ionic bonding and the compounds that form because of it (ionic compounds) are there because of full blown electrostatic attractions between oppositely charged ions. There is even a physical "law" that mathematically describes this force of attraction between two ions - Coulomb's Law:

\[{q_1q_2\over r^2} \propto {\rm force}\]

Where \(q_1\) and \(q_2\) are the charges on particle 1 and particle 2 and \(r\) is the distance between the centers of the two charges. So for atoms the \(r\) is measured from the center of each nucleus of the two atoms. So a bond length is really the combination of two atomic radii. This is illustrated below.

This means that r₁ + r₂ would be the length for r in the equation up above. Now if we wanted to change the "is proportional to" symbol of \(\propto\) to an equal sign =, we'd have to insert coulomb's constant, \(k_{\rm e}\). That's nice for a physics class, but for chemistry class we just want to know the relative forces of attraction. Also note that based on coulombs law, if the force is a negative number, that is a force of attraction between the two particles (1 and 2) meaning one must be positive (+) and the other negative (–). If the force is positive then the two charges repulse one another (+ to +, and – to –).

Chemist prefer ENERGY more than Force

Forces are nice - always fun to measure and talk about newtons (N) which is a unit for force. We chemists prefer to deal in energy units though - joule (J). We like energy of reaction, energy of fusion, energy of vaporization, energy of ionization... the list goes on. If you do some math (take an integral) you can rewrite Coulomb's Law in terms of energy of the bond formed between ions.

\[{q_1q_2\over r} \propto {\rm energy}\]

Not much of a change at all - actually, its even easier than the force one because the r in the denominator isn't even squared. So we now say that the energy of a bond of attraction between two ions (ionic bond) is inversely proportional to the bond distance, r. Easier to think about it this way. And, for what it's worth, we chemists will scale up all those teeny tiny energies of one ion and another ion to a mole of ions. Once we do that, we get much bigger numbers ranging from like 400 to 800 kJ/mol for +1 to –1 salts all the way up to 15000 kJ/mol for +3 to –3 salts. That is crazy big. What does that mean to you and me? Ionic compounds are really stable and have very very high melting points. It takes a LOT of heat energy to overcome those big ionic bond energies.

Lattice Energy

Remember that ionic compounds are a massive cluster of cations and anions all held tight by coulombic attractions. Think about it, if there is a mole of salt, then there is a mole of cations and anions and even more than a mole of ion-ion interaction. Adding up all those attractions is a math nightmare but is totally doable. If you add up ALL the holding power of a salt crystal you will arrive at an energy that we call the lattice energy. Ionic compounds are just great big lattices of ions. The lattice energy is the energy required to completely pull every ion OUT of the lattice an infinite distance apart which would be zero energy at that point. Here is the full equation for doing this with NaCl, including the actual amount of energy needed to do it (the lattice energy).

NaCl(s)   +   786 kJ   →   Na⁺(g)   +   Cl^–(g)

This is effectively blowing up and obliterating the NaCl crystal such that ever single ion is infinitely separated... to do that, you need 786 kJ of energy - that's the lattice energy. You can still think of lattice energies the way you think about ion-ion interaction and coulomb's law... the smaller the ions and the bigger the charge, the bigger the lattice energy. Calcium carbonate (CaCO₃) has a lattice energy of about 2800 kJ/mol... which is close to 4× that of NaCl. Why? Because it's a 2+ to 2– interaction which gets you 4× more lattice energy. Heck let's try another one, how about Al₂O₃? That's aluminum oxide (aka: alumina).. two very small ions at 3+ and 2–. Should be about 6× bigger right? Alumina comes in at around 15500 kJ/mol. That's about 20× more. Why so much? Well Al³⁺ is much smaller than Na⁺ and O^2– is considerably smaller than Cl^–... So not only the charges are bigger, but the radius (r) is almost 4× smaller - that is why alumina has such a huge lattice energy.

What should YOU know about lattice energies? You should be able to rank various salts in order of lattice energies by using what you know about trends in the periodic table and coulomb's law. In general, the charge differences are the most important, but size does matter as they say when the ions are considerably different in radii.