Illustrated are four ions — A, B, X, and Y— showing their relative ionic radii. The ions shown in red carry positive charges: a 2+ charge for A and a 1+ charge for B. Ions shown in blue carry negative charges: a 1- charge for X and a 2- charge for Y. (b) Among the combinations in part (a), which leads to the ionic compound having the largest lattice energy?

Video transcript

hey everyone were given six ions below and were asked which 1 to 1 ion combination has the lowest lattice energy. Now we've learned that lattice energy is going to be equal to negative Q. One times Q two Q. Being our charge divided by our radius. And when we're looking at 1 to 1 ion combinations, we want to choose combinations that will have the opposite charge but the same magnitude. And also we want small ions to be paired with large ions. So are ready. Difference will cancel out. So for example, we will pair up our ion A. With ion X. And the reason why is because we have that plus one charge and a negative one charge. And as we can see right here, we have our small ion which is A. And we want to pair it with the larger ion which is X. So looking at A X. We're going to plug in our values into our lattice energy formula. So we're going to take the negative of our plus one times our negative one. And since our radar difference canceled out, we don't have to show it in our formula. So this will get us to a lattice energy of one. Now let's go ahead and pair up B and Y. Because of that plus two and minus two. So looking at our B. Y, we're going to take the negative of our plus two times negative two. This will get us to a lattice energy of four. And lastly we're going to pair up our C. N. Z. Looking at season, we're going to take the negative of our three times our negative three. This will get us to a lattice energy of nine. As we can see from our values, the ion combination with the lowest lattice energy is going to be a. X. And this is going to be our final answer. Now, I hope that made sense and let us know if you have any questions.