Hello, everyone. Thanks for joining me, Miss Hallstrom. As we discuss Celje Bility calculations today, we're going to focus on a problem that does that asks us to performance scalability calculation for a solution at two different temperatures. Before we get started, I'd like to you to take a quick look at this image I've included. This particular graph shows us the relationship of Celje bility to temperature, and this says it's for solids. But if you look right here, you'll see that solids are the solid lines. This one also includes some gases, which are beyond the scope of what we're going to take a look at today. But you'll solve lines or what we're going to consider. You'll notice that temperature is on our X axis and we're going from 0 to 100 which makes sense for water. And the substance we're going to be looking at today is potassium nitrate, which is the red line that goes from here to here from here to here. And if you take a look at this image, you'll see the potassium nitrate. Candle three is a substance most affected by a change in temperature on the Y axis were given selling Celje bility in terms of grams of Salyut per 100 grams of solvent. In this case, since these air all a quickest solutions, it's per 100 grams of water now on the line the quantities that we see on the line. For instance, if I'm looking right, I'm gonna try to pick something that sort of close to being right on the line so I can read it easily. This one's pretty close. Um, I can see that at 20 degrees C, about 29 grams of salt Salyut for both of these two, both K and 03 and any an a c L. That's the maximum amount of Salyut that can dissolve in 100 grams of water. That would be the amount to prepare a saturated solution. And a saturated solution contains the maximum amount of Salyut that can be dissolved. The problem were given today was gonna take me a moment to write down. We're going to be working with a solution of K and all three potassium nitrate, and we're starting with exactly and noticed, since we're given exactly a 100 grams l 1/4 sample of a solution at 75 degrees C and this solution is saturated. This is a saturated solution in 75 degrees C and were given to sell you abilities. First, we're given the soluble idiot 75 degrees Celsius were given that 155 grams potassium nitrate will dissolve to create a saturated solution in 100 grams water. Now we're gonna tow. We're told we're going to cool this solution to 25 degrees C and 25 degrees C were given The 38.0 grams of potassium nitrate will be present in a saturated solution at containing 100 grams of water. What we need to find out what we're as to find out is in the process of cooling down 100 grams of sample from 75 degrees to 25 degrees. How much Kono three is going to precipitate out of solution. How much is going to crystallize out of solution? So we're gonna make a plan to do this, and our plan is gonna have three steps. Our first part of our plan is we're going to find mass of Salyut and massive are solvent, which is water in 100 grams of a saturated can. All three solution at 75 degrees Celsius at Step one, our second step, we're going to find the massive Salyut of a saturated solution at 25 degrees Celsius. Given the mass of water from step one and last but not leave Super easy step, we're going to take the massive Salyut that could be contained at 75 degrees C minus the massive Salyut at 25 degrees C. To find out the mass of Salyut that will crystallize. So that's what we're going to do. Let's be again. And if you need Teoh, I'll try to jot all of our numbers back down again. Okay, so let's do our Step one again. I'm just going abbreviate here mass, Uh, Salyut and water in 100 grands saturated K and R three solution. Okay, In order to do that, this is actually going to be pretty good. And I'm going to give you again what we were given. 155 grams of Cano three will dissolve in 100 exactly 100 grams of water at 75 degrees C. Let's figure out what percentage k on all three. We have percentage of Kono three, I have 155 grams of candle three and to figure out the percentage of K and all three in the solution, I'm going to add this number and this number 1 55 grams plus 100 grams times 100 times 100. And my answer for this is going to be 60 0.8 percent. I knew I was gonna run out of room for my percent Here. We try to squeeze this in little bit. Times 100 equals 60.8 percent que on all three since we were given a 100 gram starting solution 60.8% of 100 grams. I'm sure you see where I'm going with This is 60.8 grams of K N 03 are initially present. This is the mass of Cannell three. It's initially present, since I have a 100 grams sample, 100 grams minus the 60.8 grams. That's K and all three gives me 39.2 grams of water initially present. And this is how much water we're gonna have present at both temperatures. The amount of water will not change for step two That's not a very nice too, but I think you can figure it out if I have. If we have 39.2 grams of water are solvent when we cool it to 25 degrees Celsius. How much Salyut for K Anil three. Can it contain? Okay, so this is a super simple calculation. Were given the following information. We know that 38.0 grams of K and all three will dissolve in 100 grams of water to give a saturated solution. So how many grams of Kono three will dissolve in 39.2 grams of water? Simple solve for the X and X gives us 14.9 grams of K and all three. I'll just switch pins for the last step here for Step three if you'll recall, and I'll just run back to the previous page. Here. Here is the amount of Kono three that was present. We started with 60.8 grams of candle three in a saturated solution. We're going to subtract 14.9 grams of candle three in our saturated solution. This one was at 75 degrees Celsius. The sun's at 25 and 45.9 grams of Cannell three will crystallize out of solution and that is our final answer. So this problem really doesn't have any really tough math in it. Um I think that the biggest problem that I see in a problem like this is that I'm going to go back to this page when I'm given 100 grams of saturated Enel three I see that people often forget that this is not Ah 100 grams saturated anal three solution. People forget that this is not 100 grams of water. It's 100 grams of solution. So make sure to read your questions carefully. Thanks so much for joining me. See you soon.