![]() ![]() Energies of this magnitude can be decisive in determining the chemistry of the elements. Representative values for calculated lattice energies, which range from about 600 to 10,000 kJ/mol, are listed in Table 4.2.1. The value of the constant k′ depends on the specific arrangement of ions in the solid lattice and their valence electron configurations, topics that will be discussed in more detail in the second semester. We see from Equation 4.4 that lattice energy is directly related to the product of the ion charges and inversely related to the internuclear distance. As before, Q 1 and Q 2 are the charges on the ions and r 0 is the internuclear distance. ![]() U, which is always a positive number, represents the amount of energy required to dissociate 1 mol of an ionic solid into the gaseous ions. The cause of this effect is less efficient stacking of ions within the lattice, resulting in more empty space.\) ![]() Note, that while the increase in r + + r − r^++r^- r + + r − in the electronic repulsion term actually increases the lattice energy, the other r + + r − r^++r^- r + + r − has a much greater effect on the overall equation, and so the lattice energy decreases. As elements further down the period table have larger atomic radii due to an increasing number of filled electronic orbitals (if you need to dust your atomic models, head to our quantum numbers calculator), the factor r + + r − r^++r^- r + + r − increases, which lowers the overall lattice energy. The other trend that can be observed is that, as you move down a group in the periodic table, the lattice energy decreases. For example, we can find the lattice energy of CaO \text 3430 kJ / mol. This kind of construction is known as a Born-Haber cycle. If we then add together all of the various enthalpies (if you don't remember the concept, visit our enthalpy calculator), the result must be the energy gap between the lattice and the ions. So, how to calculate lattice energy experimentally, then? The trick is to chart a path through the different states of the compound and its constituent elements, starting at the lattice and ending at the gaseous ions. These additional reactions change the total energy in the system, making finding what is the lattice energy directly difficult. This is because ions are generally unstable, and so when they inevitably collide as they diffuse (which will happen quite a lot considering there are over 600 sextillion atoms in just one mole of substance - as you can discover with our Avogadro's number calculator) they are going to react to form more stable products. While you will end up with all of the lattice's constituent atoms in a gaseous state, they are unlikely to still be in the same form as they were in the lattice. After this, the amount of energy you put in should be the lattice energy, right? Experimental methods and the Born-Haber cycleĪs one might expect, the best way of finding the energy of a lattice is to take an amount of the substance, seal it in an insulated vessel (to prevent energy exchange with the surroundings), and then heat the vessel until all of the substance is gas. You can calculate the last four using this lattice energy calculator. We will discuss one briefly, and we will explain the remaining four, which are all slight variations on each other, in more detail. Perhaps surprisingly, there are several ways of finding the lattice energy of a compound. ![]()
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