#### Determine Lattice Energy From Kapustinski Approximation

• 22-Mar-2022

Alright, so in the previous video, we talked about the Bourne lambda equation in the Bourne Meyer equation. And we talked about how to calculate lattice energy using that now we're going to cover something called the kaput Minsky approximation. Okay.

So for the Kappa Stanley approximation, this is just an approximation. Okay. It has more error than the board land equation. And part of the reason for that is you use this only when the lattice structure type is unknown. So definitely if you know, the lattice. Structure type you're going to want to use the ports lambda equation. Okay, because if we know the lattice structure type, we can get the Madeleine constant.

Notice, the capacitance key approximation, doesn't use the Madeleine constant. It actually doesn't use the born exponent, either, which makes this equation, a little simpler to use. Because you don't have to you don't have to determine a Madeleine constant. You don't have to determine a born exponent. But that makes this equation.

More error-prone. And you only use this when the lattice structure type is unknown, but it's going to have more air generally from the born lambda or born Meyer equations. But this is the equation that you'll use all right. So we are going to ultimately look at a problem and see how you use the Kappa students get approximation all right, so it's, an approximation, that's, all it is.

So what we're going to do is do the same issue. We want to assume a rock salt structure for rubidium bromide. This is what we did in the. Previous video, we want to use the Kappa students key approximation and see if we get something relatively similar all right. So let me go to the paintbrush, and I'm going to go ahead and do this I'm going to erase this part erase that part.

This was by the way, the lattice energy that we got in the previous video using the Bowland equation. So what I'm going to do here is I'm going to actually going to leave that right there. So let me do that all right this down here is the Kappa students key. Equation or approximation, I should say because it is an approximation, and you don't see it over here. But this is U naught. This is the lattice energy.

So let's, go ahead and calculate the lattice energy. And one of the nice things about this is that we actually technically already have the entire optic distance calculated because it's the same problem. So rubidium bromide, we calculated that in the previous video, and I'll show you again in this video, how to do it just so it's clear.

Now notice there's a. Few differences here we don't have the made lung constant. We don't have a born exponent.

But what we do have is V and the two charges let's, go ahead and calculate in tyrannic distance again. So the inter manic distance is approximated as the radius of the cation, plus the radius of the anion in the lattice and for rubidium bromide. Now, this is something I looked up in a table, but I found that the radius of rubidium was 265 picometers. We add on to that the radius of bromide, the anion, which is about 94. Picometers, and when we sum of those together, we got about 359 picometers, and I'm going to do it again, even though it's a little redundant I'm going to show you how to convert picometers to angstroms.

You can either memorize the conversion factor, which I don't recommend, because you can get them mixed up pretty easily. But you should understand where the conversion factor comes from 359 picometers, I want to convert that to angstroms. And the reason I want to do that is because for both the boron. Lambda equation and the capacitance key approximation you have to put the distance in an angstrom for that equation to work out, so I'm going to say, well, remember that mill is 10 to the third micros 10 to the 6 Janos 10 to the ninth Pecos 10 to the 12th. So I know, there are 10 to the 12 PICO meters in 1 meter I also know that 1 meter is 10 to the 10th angstroms. So that ultimately means I'm going to divide the number of picometers by a hundred, and I get that this is going to be about three point.

Five nine, angstroms and that's exactly what I got here. That's. My D, naught okay, that's the D naught I'm going to use in the capacitance key approximation. Alright. So what I'm going to get is my U naught is equal to 1202 I'm going to multiply that times V. What fee is, it is the number of ions in a unit formula, all right, so we're dealing with rubidium bromide there's, just one of each because they both have a charge with magnitude one, plus one and minus one. So the number of ions is going to be two.

All right charge on one is plus one. The charge on the other is minus one, and we're going to divide that by three point, five, nine, angstroms, then we're going to multiply that times the quantity. One minus zero point, three, four, five, divided again by D, naught, which is going to be three point, five, nine all right. So let's, go ahead and calculate that I'm going to take first one minus the quantity point, three, four, five, divided by three point, five, nine, all right, and then I'm going to multiply by 1200 and.Two times minus one divided by three point, five nine, and let me write down the answer over here.

All right, so I got that the lattice energy from the Kappa snails approximation is about negative, six hundred and five point, three and that's going to give it to me in units of kilojoules per mole. Let me get the toolbox out, and I'm going to box that let me do it in a slightly different color. Let me do light blue. This is the lattice energy. But this is from the Kappas tin. Ski approximation.

All right? So notice, when I did a born land equation, I got negative. Six, oh, nine point, four and with Kappa students key approximation, negative, six, oh, five point. Three, those are pretty close. So the Kappas into the approximation does have more air in it.

But it's, still, if you don't know, the lattice type, it's, a good approximation, okay and that's how you use the capacity equation ultimately to calculate is how you calculate the lattice energy and like I mentioned in one of the previous videos, a lot of. Times what we don't, we don't just want to calculate lattice energy using this. What we want to calculate is the thermodynamic radius and that's going to be the topic of the next video. So it turns out that thermodynamic radii are perfect to calculate because sometimes that's, actually what we don't know, we don't know that there was a Mir Dias.

Okay. And the reason sometimes we don't know, the thermodynamic radius is we don't have simple compounds like rubidium bromide. Sometimes we have something. In here like in this equation, or this problem size me, we have an anion that's C - 2 - what is that. I mean, can you really look up the radius of that with respect to calcium, no, you can't.

So sometimes just if we had simple cation in the Sybil, and we could just add them together and get a good approximation. But sometimes we actually just want to calculate the inter ionic radius, not the lattice energy, because we can determine the lattice energy from a born-haber cycle. And then we can use that. To calculate D naught, okay, so we're going to we're going to ultimately calculate we're going to calculate the equilibrium in ionic distance in the next video. So join us. Next time make sure to like this video and subscribe to the channel for future videos and notifications. Thank you.