Which of the following trends in lattice energy is due to differences in ionic radii? (a) LiF NaF CsF, (b) CaO KCl, (c) PbS Li2O.

Question

Which of the following trends in lattice energy is due to differences in ionic radii? (a) LiF > NaF > CsF, (b) CaO > KCl, (c) PbS > Li2O.

Accepted Answer

Welcome back everyone in this example, we need to choose the lattice energy arrangement that can be attributed to the variation in ionic radius. So we want to recall that lattice energy is represented by this symbol here. And it is calculated by taking the charge of our carry on Q. One, which is multiplied by the charge of our an ion Q two. And then divided by our period number of our Catalan which is then added to the period number on the periodic table. And sorry, let's make this red Of our an eye on Q two. So we can see from this relationship that we have an inverse relationship of lattice energy and our period number of our ions because they're in the denominator. Whereas lattice energy is in the numerator on the other side of the equation. And what this is saying is that all the trend on our periodic table where ionic radius. So this is our periodic table. Ionic radius we want to recognize is increasing towards the bottom left of our periodic table. So this is the trend. And if we understand that the lower or sorry, the higher our period number of our ions will correspond to a larger ionic radius. And sorry just so everything is visible. Yeah, So the larger ionic rhetta is attributed to a higher period number. And understanding that it would make sense as to why our lattice energy has an inverse relationship with the period number of our charges of our ions. And that is because if we have a larger ionic radi I that means that there is an therefore an increase an increased distance between our ion and its charge. Which will therefore correspond, we can say thus the lattice energy will be lower. So this is just one of the ways that lattice energy is affected which is by the ready of our ions. But we also want to recognize that lattice energy can also be affected by the charges of our ions. Which is why we have that in the numerator there, Q one and Q. Two. So charges of our ions also affect the lattice energy. But we can see that because lattice energy and the charges of our ions are in the numerator, they have a direct relationship meaning as our charges are increasing our lattice energy increases. So noting these things down, we have two factors so far and our third factor we want to recognize is going to be also the arrangement other ions in the lattice. And what that is saying is that that's really based on how our opposite lee charged ions are bonded. So for this factor affecting lattice energy, we want to recall that the smaller the radi of our opposite lee charged ions corresponds to a stronger bonds. So we can say the stronger the bond between them. And so because they have a stronger bond. Their lattice arrangement is going to be packed much tighter with an alternating arrangement of our cattle onto our an ion. So these are all the factors affecting lattice energy. So let's just write that out factors affecting with an A lattice energy. So now that we have these listed out, let's consider our options. Now, according to the prompt, we need to focus on the option that is attributed by variation and ionic radius for our lattice energy arrangement. So looking at example A. We have magnesium oxide versus potassium fluoride. So let's begin with comparing them based on their charges we recognize or magnesium is located in Group two A. On our periodic table corresponding to a two plus county in charge. Whereas oxygen we recall is in group six A. Of the periodic table corresponding to a two minus an ion charge. And let's use the color red. Now potassium we recognize is in group one A. On the periodic table corresponding to a plus one charge. Whereas florian is located in group seven A. On the periodic table, which we recall means that corresponds to a minus one an ion charge. And we can see we have differing ion charges where we have the higher ion charges associated with our magnesium oxide ionic compound, which is why this ordering or this arrangement of lattice energy where magnesium magnesium oxide has the greater lattice energy is attributed to ion charge. So because it's attributed to ion charge, we're going to rule out choice A. Because we want again the one that is attributed to variation in atomic or ionic radius. So moving on to example B. We have zinc sulfide, which is said to have the greatest letters, a greater lattice energy than sodium oxide. So beginning with our carry on in sync sulfide recall that zinc is located in a transition metal D. Block. But it's one of the only exception or few exceptions, which only has one charge because I recognize that any atoms in the transition metal D. Block will have multiple charges, but zinc will always be ZN two plus as a caddy on. Whereas sulfur we recognize is located group six A. Of our periodic table, which like oxygen means it forms a two minus an ion sodium we recognize is in Group one A. On our product table, forming a plus one catalon and oxygen, as we stated earlier forms a two minus an eye on being in group six A. So yet again, we can see we have higher ionic charges associated with zinc sulfide are ionic compound, meaning it's going to be the main factor affecting our arrangement here according to lattice energy. So this is also attributed two ion charge. And that leaves us with ruling out choice B. And focusing on choice see where we are told that calcium oxide has a greatest greater lattice energy than strontium oxide, which has a greatest greater lattice energy than barium oxide. Where barium oxide has the smallest lattice energy. And so we want to first begin by analyzing our ions. So calcium located in Group two A of our periodic table will form a two plus carry on oxygen as we stated, forms a two minus an ion strontium also located in Group Two A. Of the periodic table forms a two plus carry an oxygen will form a two minus an ion. Barium. Also located in Group two A. Of our periodic table will form a two plus carry on. And yet again we have oxygen as two minus in charge. And here we can see that ion charge is not the main factor affecting our arrangement according to lattice energy. So we're going to keep going and now we want to look at ionic radius. So as we stated, ionic radius on our periodic table increases as we go towards the bottom left of our periodic table. And we said that the larger the ionic great I the increased distance between the ion and charge. Because we know our charge comes from the electrons surrounding our ion, meaning that if there is an increased distance between the charge and our ion, those electrons are definitely far out from our ion. And so the lattice energy will be lower. So we want to find the adam between calcium strontium and barium since they're all in the same group that has the smallest ionic great I to have the largest lattice energy. Whereas according to choice, see it should be calcium oxide. And so we're going to look at which period these Catalans fallen on our periodic tables. So we want to recognize that calcium is located in period four of our periodic table. Strontium is located in period five of our periodic table in Group two A. And barium is located in period six. So even though barium oxide has the smallest lattice energy, barium is located in period six, meaning it has the largest radius, Which makes sense as to why it has the smallest lattice energy because it has a large distance between the charge and the ion. So barium is very far away from its electrons, whereas calcium is much closer to its electrons, so it's closer to its charge and therefore will have the largest lattice energy. And so we can confirm that the arrangement and choice E. Is attributed two ionic radius. And so that is why Choice C. Is going to be the correct choice to complete this example because it's the only arrangement of lattice energy that is based upon our ionic radius trend of our periodic table for these ions. So, I hope everything I reviewed was clear. If you have any questions, leave them down below and I'll see everyone in the next practice video

Which of the following trends in lattice energy is due to differences in ionic radii? (a) LiF > NaF > CsF, (b) CaO > KCl, (c) PbS > Li2O.

Verified Solution

Key Concepts

Lattice Energy

Ionic Radii

Trends in Lattice Energy