![]() In general, the charge differences are the most important, but size does matter as they say when the ions are considerably different in radii. 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. 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. Why so much? Well Al 3+ is much smaller than Na + and O 2– is considerably smaller than Cl –. Should be about 6× bigger right? Alumina comes in at around 15500 kJ/mol. Heck let's try another one, how about Al 2O 3? That's aluminum oxide (aka: alumina). Why? Because it's a 2+ to 2– interaction which gets you 4× more lattice energy. Calcium carbonate (CaCO 3) has a lattice energy of about 2800 kJ/mol. the smaller the ions and the bigger the charge, the bigger the lattice energy. You can still think of lattice energies the way you think about ion-ion interaction and coulomb's law. to do that, you need 786 kJ of energy - that's the lattice energy. This is effectively blowing up and obliterating the NaCl crystal such that ever single ion is infinitely separated. Here is the full equation for doing this with NaCl, including the actual amount of energy needed to do it (the lattice energy). 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. Ionic compounds are just great big lattices of ions. If you add up ALL the holding power of a salt crystal you will arrive at an energy that we call the lattice energy. Adding up all those attractions is a math nightmare but is totally doable. 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. Remember that ionic compounds are a massive cluster of cations and anions all held tight by coulombic attractions. It takes a LOT of heat energy to overcome those big ionic bond energies. What does that mean to you and me? Ionic compounds are really stable and have very very high melting points. 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. 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. 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. 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. ![]() If you do some math (take an integral) you can rewrite Coulomb's Law in terms of energy of the bond formed between ions. We like energy of reaction, energy of fusion, energy of vaporization, energy of ionization. We chemists prefer to deal in energy units though - joule (J). Chemist prefer ENERGY more than Forceįorces are nice - always fun to measure and talk about newtons (N) which is a unit for force. If the force is positive then the two charges repulse one another (+ to +, and – to –). 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 (–). That's nice for a physics class, but for chemistry class we just want to know the relative forces of attraction. ![]() 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, \(k_\). This means that r 1 + r 2 would be the length for r in the equation up above. ![]()
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