All right, welcome to Brmmoil green equilibrium systems. I chose the picture because there's a lot of green and blue, which we're going to see both of this week. So, as you can see, there's a whole spectrum of colors that we're going to be going from. Um, an indicator is actually just a weak acid that partially dissociates and is an equilibrium. And what it'll do is it'll change colors depending on which side the equilibrium is leaning on. So in this case, we're going to have um a blue green color for the conjugate base side and then the acid um indicator side is going to be yellow. And you can see that in our little picture there for the substances and the spectrum of the of the um that we're going to see. So um one thing to note, you're going to get the uh indicator provided to you as a solution of sodium salt. It's a solution. So if you put a salt in solution, it's going to dissolve and you're going to have the two ions Na+ and ion minus. ion minus will then automatically be in equilibrium with the H+ making the indicator itself HIN. So that's why that equation actually is correct. So we're going to be calculating K. Um we're going to be doing um spectroscopy and using pH in order to fill in all three of those. So we can get the K for our bromocal green and check that our K is in in fact constant um as K would imply since it is the equilibrium constant that it should be constant. Then we're going to check what happens when you change the temperature with it. So we're going to see if we can make it not constant at some point. Okay. Okay, so like I said, we have this um this reaction equation um in equilibrium, which means we have an equilibrium constant K, which is going to equal to the concentration of the products over the concentration of the reactants. And we can measure these um using the absorption of those two different sides. Um one is blue, one is yellow. So we measure those two wavelengths and we can actually get the concentrations then at those two wavelengths to get those two values. And we can get the hydrogen ion concentration by looking at pH and then doing a little math to get the hydrogen ion concentration equal 10 pH. So, and from that we can calculate K. Strong suggestion here, set up an Excel spreadsheet. It'll make your life a lot easier when you're in the lab and you'll be able to easily go through all the calculations that you need to do in that Excel spreadsheet. So, spectroscopy, we're going to use um uh our little spectrophotometers in the lab. Um, but we're also going to use the beer Lambert law and look at the absorption equal to the molar absorptivity times the path length times the concentration. And that's how we can convert our absorbances into concentrations. Um, the path length is 1 cm cuz that's your little cuette. That's literally the diameter that the light is passing through. So since that's 1 cm, that term usually drops out. And then you can get molar absorptivity as just the ratio of absorption to concentration. So we use that to um to get molar absorbity and then make those conversions later in our calculations. So our solutions that are in equilibrium are going to be somewhere with both parts of that equilibrium in it. So the the total absorption is going to be the sum really of the two different wavelengths that we're looking at. So you can break that apart in a couple different ways using the beer Lambert law. And then when you're looking at at those two wavelengths, you're going to get the absorption for HIN in the yellow. And then that's going to you're going to be able to get to the concentration of HIN by um using the molar absorptivity at 442 in the yellow. Do the same thing with the conjugate base, the in minus also at 442. So you can get the molar absorptivity and relate concentration and absorption. And then you get this really interesting looking equation to interrelate both of those at one wavelength. So that's where we're going to get one equation with one wavelength. And remember though, we're actually measuring this at two wavelengths. So we're going to get two of these equations with two unknown concentrations. Two equations, two unknowns. If only we knew how to solve that. We do. So molar absorptivity, don't forget, um we're going to be able to drive this entirely to to one direction and know that it's all acidic. HIN and we can calculate the concentration of HIN at those two wavelengths that we're going to use and get our molar absorptivities at those two wavelengths for HIN. Then we're going to do the same thing with the basic side. We're going to push it all the way to the basic side. So we just have in minus and assume that we have no HIN. And then we're again going to be able to calculate at those two wavelengths what our molar absorptivities are. Once we know what those four molar absorivities are, then we're going to be able to use those in our calculations to figure out our concentrations of both pieces that are in there in equilibrium at all other times. As I said, that's the that's how we're going to do that. Our pH, we're going to use uh find the hydrogen concentration, finding pH, 10 the negative pH. Remember, if it's acidic, pH should be below 7. If it's neutral, it'll be at 7. And if it's basic, it should be above seven. Just so you remember how that all works. The higher the pH, the lower the hydronion concentration because it is the negative log of the hydrogen ion concentration. So just so you remember how that all works. As I said, you're actually going to prepare um in the first step, you're going to have eight solutions total. You're going to have um two standards that you know you're and those are what you're going to do to get those four molar absorptivity values. Um you're going to have five samples in between so that you can make a standard curve out of this. and then also your unknown that you're trying to solve exactly what that concentration is of your unknown. So, you're going to measure these two absorptions uh for all eight samples at those two wavelengths. Um you're going to measure the pH of all of those samples, the five samples and the the one unknown. And then you're going to do all your calculations. And this is where I'm telling you, you're going to want a um an Excel spreadsheet to set this up. So, I would actually start that earlier. You might as well. um you are going to have to show a calculation but um but otherwise for the rest of it you can do it in Excel to find it. So to get K for our equilibrium equation if you want to remember what K is actually equal to we're going to use a pH meter to find the hydrogenion concentration. We're use spectroscopy to find the other two using the beer Lambert law. We can figure out at these two wavelengths what our equations are at those two wavelengths. And then we're going to get two equations at two wavelengths to find our two unknown concentrations using those four molar absorptivity values. I know this seems really complicated. That's why I'm telling you set up an Excel spreadsheet. It will make your lives a lot easier. Okay. Um because you solve two equations with two unknowns using um using uh system of equations to make that solution. So you're actually going to want to do that. You're going to do that five times. um one more time for an unknown. So you're going to have six total calculations where you're doing this. You only need to show the calculation once, but you need to actually do it each time. So like I said, Excel spreadsheet, it will help you. So um rather than doing a demo, I'm actually going to walk you through some of the calculations so that I'm sure you know how to do this one pretty well. So in this case, we're um we're going to make a standard solution. So how many moles of NaN, so our salt are contained in 5 milliliters of that stock solution? So we know the volume, we know how many moles that we have of sodium indicator, our bromacel green. And then we just need to convert it to the right units and we can figure that out. That's actually the 7th 107th. So that just looks a little funky there. Make sure your units all cancel out like they should so that you're in the correct number of moles. And then the molar ratio is going to be 1 one based on the equation that's written above here. So um all your salt indicator N A I N is going to convert itself into H I N when you add it to HCl and then the total volume of the solution it's going to be the 5 milliliters of your stock solution plus 25 milliliters of your HCl give you a total volume of 30. So now you can go back and get the concentration of your HIN um that could should be a capital I H I N in solution A. So you have 6.25 * 7 moles and then it's a 1:1 molar ratio. you have total of 30 milliliters, convert it to liters and you've got your actual concentration. So hopefully you remember how to prepare a standard solution and do those calculations. I always like to double check and cross those things off and make sure. And then like I said, you can always convert um using the molar absorptivity you can um convert uh absorbance and concentration. That's how you get the molar absorptivity. And then from pH you can get the hydronion concentration just 10 the negative pH and that gives you your hydronion concentration. So, that's the mechanics of what we're going to be doing. Um, like I said, there's four different molar absorptivities you're going to be doing because you've got two wavelengths. You've got an acid side and a basic side. So, you're going to need all of this. And here's a sample how you're going to process your data. Notice this looks a lot like an Excel spreadsheet. Take the hint. Okay. So, you've got two equations with two variables. And um all you need to do then is take your data table and plug it into the appropriate columns. So if you see our absorption at 423 should be 442. I'm not sure why that says 423, but in any case at 442 it's 2225. So I plug that in. Um the molar absorptivity for your X at 442 you pull that over. That's actually 4320. So I plug that in. I don't know the concentration of X. That's why that stays as a variable. And I'm going to add to that the molar absorptivity of um of Y at 442. And so that's also in the table up above. It's at 170. So I've got one equation with actual numbers in it. I still have two variables, my concentration of X and my concentration of Y. So those are still there. I do the same thing at the other wavelength then with the numbers from this table. Now I've got a system of equations. I need to solve the system of equations. You actually will probably need more space than just this in order to answer this question. So I just copied these numbers back in over here. I'm solving the first equation. It doesn't matter which one you wanted to solve for. I just solved for the first one for X. Once I get x, I can put it into the second equation for that value of x. Plug that in and then solve for y. Now I know the concentration of y in this solution. Now I can go back and plug that in to find the concentration of x and I can actually find that actual answer. It is a total coincidence that these are the same numbers. They're not necessarily always going to be the same numbers, just so we're clear. So um that's how you do the calculations. Hopefully you follow this along. Please, I can't beg you enough to do an Excel spreadsheet. It will help you tremendously to set that up ahead of time. Okay, have a good life.