so how can we tell which ionic compound has the highest lattice energy so we're comparing magnesium oxide and sodium fluoride which one has the highest lattice energy before we can answer that question we need to know what is lattice energy now lattice energy is the energy change that occurs when gaseous ions react to form a solid ionic compound so let's take sodium chloride for example so if we have the sodium cation in its gaseous state reacting with the chloride ion and together they're producing sodium chloride as a solid the energy that is released in this reaction is known as the lattice energy now lattice energy depends on the charge q1 q2 that's the charges of the ions and it's also dependent on the distance between the ions so as you increase the charge of the ion the lattice energy will increase and as you increase the distance between the ions the lattice energy will decrease so what does this mean ions with larger charge values have greater lattice energy values and ionic compounds that contain ions that are large will have small lattice energy values whereas compounds that contain ions that are small will have large lattice energy values so to summarize what i've just said if you want to increase the lattice energy you need to increase the charge and decrease the size of the ions so let's look at our first example let's compare magnesium oxide with sodium fluoride so which one do you think is going to have the highest lattice energy well let's look at the ions that are found in this compound magnesium carries a plus two charge and oxygen carries a minus two charge sodium has a plus one charge and fluoride has a minus one charge now there's two things that we can consider the charge and the sizes of the ions the first thing i like to give priority is the charges so let's see which compound has a higher product of q1 times q2 so q1 the charge of the first ion is positive two and q2 the charge of the second ion is negative two so this gives us a value of negative four now for the second compound if we multiply q1 and q2 it's going to be positive one times negative one so it's negative one so notice that the product of the charges in magnesium is four times as large than in sodium fluoride so we should expect that magnesium oxide should have a much higher lattice energy than sodium fluoride in fact the magnesium oxide lattice energy value is negative 3 800 kilojoules per mole and for sodium fluoride it's about negative 923 kilojoules per mole notice what happens if we divide these two numbers so if we take 3 800 and divided by 923 you should get 4.12 so the lattice energy of magnesium oxide is more than four times greater than sodium fluoride so why is it a little bit more than four times larger well for one thing the magnesium plus two ion is smaller than the sodium plus ion now oxide is a little bit bigger than fluoride but magnesium is a lot smaller than sodium compared to oxide and fluoride to put that in perspective magnesium is 65 picometers that's the mg plus 2 ion and the size of the sodium cation is 95 picometers so magnesium is a lot smaller than sodium whereas the oxide ion it's about 140 picometers and fluoride is 136. so as you can see these two they don't really differ much in terms of size but these two they are significantly different so because magnesium oxide has very high ionic charges and also magnesium is a lot smaller than sodium that's why the lattice energy of mgo is significantly larger than sodium fluoride now let's move on to our next example part b which one is going to have a higher lattice energy sodium fluoride or potassium chloride now sodium and potassium both have a plus one charge fluoride and chloride both contain a minus one charge so the charges are the same for these two compounds therefore the lattice energy of these two compounds should be very similar now the sizes of the ions are different potassium is a lot bigger than sodium as an ion we said that the sodium ion was about 95 picometers and the potassium ion is 133 so sodium is smaller than potassium if you decrease the size of the ions the lattice energy will increase now fluoride is also smaller than chloride fluoride is 136 picometers and the ionic radius of chloride is a lot larger 181 so because sodium fluoride contains smaller ions than potassium chloride we should expect that sodium fluoride is going to have a higher lattice energy than potassium chloride we said that sodium fluoride was negative 923 kilojoules per mole potassium chloride on the other hand is less it's 715 kilojoules per mole so as you can see you need to look at two factors when determining which compound has a higher lattice energy you need to look at the charge and also the ionic radius you should look at the charge first always give the charge more priority than the sizes of the ions if the charges are different the one with the greatest lattice energy will be the one with the highest charges now if the charges are the same then look at the sizes of the ions as the ionic radii increases the lattice energy will decrease so if you're looking for the one with the greatest lattice energy you need to look for the compound that contains the ions with the smallest radius so you're looking for the ions with the highest charge and the smallest ionic radius and that's how you can determine which compound has the highest lattice energy now let's work on this problem rank the following in order of increasing lattice energy that is from least to most exothermic so the first thing we should look at are the charges aluminum has a positive three charge and oxygen has a minus two charge so just by looking at that we know that aluminum oxide should have the highest lattice energy so i'm going to put that one last because that's going to be the greatest it's the one that's most exothermic next we have calcium and beryllium those two they have a positive two charge so now because the charges between those two are the same we need to see which ion is smaller beryllium is above calcium on a periodic table the ionic size of calcium is 99 picometers and the ionic radius of beryllium is 31. so calcium is significantly larger than beryllium so therefore we should expect that beryllium oxide should have a more exothermic lattice energy than calcium oxide because beryllium is a lot smaller so i'm just going to write the numbers here this is 99 this is 31. we'll talk about that later now let's consider the last two potassium iodide and lithium fluoride both potassium and lithium has a plus one charge iodide in fluoride has a minus one charge so the charges are the same between those two however lithium is a lot smaller than potassium the ionic radius of lithium is 60 and for potassium it's 133 iodide is a lot bigger than fluoride for fluoride the ionic radius is things like 136 and for iodide i don't know what that value is but i'm pretty sure it's a lot larger than 136 ionic radius increases as you go down the group and iodide is well below fluoride so we should expect that lithium fluoride should have a higher lattice energy than potassium iodide because lithium fluoride contains smaller ions than potassium iodide now let's write the numbers associated with these values the lattice energy for potassium iodide is 649. now it's negative because once these gaseous ions get together to form this ionic compound a lot of energy is released lithium fluoride is 1036 calcium oxide is 3400 beryllium oxide is 4443 and aluminum oxide is almost 16 000. so the reason why this is significantly higher is because aluminum has a plus three charge and plus aluminum is very very small i believe it's like 50 picometers in terms of ionic radius beryllium is a lot smaller than calcium as we can see calcium is almost three times as big as beryllium so that's why there's a significant difference in the lattice energy between these two valves even though they have the same charge plus two now lithium fluoride is a lot more exothermic than potassium iodide because as you said before lithium is a lot smaller than potassium and fluoride is significantly smaller than iodide so now you know how to determine which compound has the greatest lattice energy you're looking for the one with the highest charge and the smallest ionic radius you