Charles Collingwood walks through the Born-Haber cycle for magnesium oxide, breaking down each thermochemical step from elements to solid MgO. The cycle sums atomization energy, ionization energies, electron affinities, and lattice enthalpy to calculate the enthalpy of formation.
The Born Arbor cycle for magnesium oxide. Born Arbor cycle can be constructed for any ionic compound. We see here that the full cycle is shown. We start off with magnesium down here plus half oxygen molecules. That means we get the required elements for mgo. In fact, the enthalpy of formation is shown here. Delta HF, it goes all the way from MG solid plus a half O2 gas. Delta HF will give us MGO solid. Okay, so we can get to Mgo solid by looking at all of the possible energy changes that need to take place here. Half o2 gas. First of all, we change the magnesium solid into magnesium gas. This is the enthalpy of atomization. This enthalpy of atomization requires that we break up all the magnesium atoms. They're all bonded together in the metallic structure and make gaseous magnesium. Well, that process then will give us magnesium gas plus a half O2 gas. We next need to ionize the magnesium. Now, our magnesium's got two ionization energies. It needs to lose two electrons per atom or two moles of electrons or per. Well per mole of atoms. However, it needs to lose one electron first to make magnesium plus and then one electron to make magnesium two plus. So we go back. The second ionization energy here is magnesium plus to magnesium two plus. So it's a different energy requirement in this case. The second ionization requires 1451 kilojoules per mole. So at this stage we've got magnesium 2 plus plus a half O2 gas. Now, to turn a half O2 gas into O gas, this is equal to the enthalpy of atomization, or 1/2 the bond enthalpy, because there's a half a mole of bonds. In this particular case, we're going to look at it from the point of view of the bond enthalpy. So one mole of bonds will produce two, two moles of atoms. We only need one mole of atoms. So therefore we need half a mole of bonds. So it's 1/2 the bond enthalpy term at this stage. Then we've got our oxygen in gaseous form. We've got magnesium in gaseous ions. However, the oxygen needs to be turned into oxide ions. And this is a two stage process. Again, the first step is exothermic. The oxygen gains an electron. It's the first electron affinity where the electron releases energy as it bonds to the electronegative oxygen. The second ionization, sorry, the second electron affinity is actually an endothermic process because you're forcing an electron onto a negative particle. So to bring two negative particles together requires energy. So this step, the second electron affinity, is endothermic. And at this stage, we have magnesium ions, gaseous ions, plus oxide, gaseous ions. And the last step is the reverse of the endothermic lattice enthalpy. So, in other words, this is an exothermic process where we're bringing together all of the ions into their positions in the lattice, and this releases a massive amount of energy. Alright, so mathematically, it's very simple. We can calculate the. I'm sorry, I'm getting confused by all these particles coming in here. And in fact, I haven't put a back button on this particular part. But it doesn't matter, because we've seen the construction of the Born Haber cycle for magnesium oxide. And as it says here, in order to calculate the enthalpy of formation, we simply add up all of the energetic steps to go the other way around the circle.
