 ## General Chemistry

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Associated with any ionic compound is the solubility product constant, which measures how soluble the compound will be in a solvent.

Molar Solubility
1
concept

## Understanding the Solubility Product Constant 1m
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Hey, guys, In this new video, we're gonna take a look at a new concept. The side ability product constant. So we're used to so many K's up to now we've seen K A. We've seen K B, but now we're gonna be dealing with K S P, which we're gonna refer to as our soluble ity product Constant. And we're gonna say here that saw you bility was the maximum amount of salute that could successfully be dissolved in a solvent. Remember, another name for soluble iti is mole arat e Another name from polarity is concentration. So solid ability, molar ity, concentration, all three different words. But all mean the same exact thing. How much saw you can I get to dissolve in my give and solve it? Now we're gonna say, in this section, we learn about associated with any type of solid. Any solid is the K S P value. We're gonna say the KS piece value stands for what we've been saying. The soluble ity product constant. Now we're gonna say the larger RKS p value is than the mawr soluble. The solid is in its given solvent. We're gonna say the smaller RKs p value than the less soluble. The solid isn't it's given solvent. Okay, so K s P is just the measurement of soluble ity. How soluble is your solid? And if you ever given K sp for a compound, you should know automatically. Since this compound is given a K S P value, the compound has to be a solid.

The general rule is that the greater the solubility product constant for a compound then the more soluble the compound.

2
example

## Consider the following compounds 1m
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Now we're gonna say example. One. Consider the following compounds, which has the highest concentration off O. H minus ions. What we should realize here is that all of them have to O H minus is involved and because they all have the same number of O H minus is that means that is not a deciding factor. So just ignore that. That means just look at the K S P value. We're going to say the one that has the highest K S P value would be the most soluble, which means it breaks up into the most ions. And the one that breaks up into the most ions would have the highest concentration off O. H minus ions. So all we gotta do here is look to see which GSP is the biggest. Here we have two that are to the negative 15. And but this one is 4.1 and this one is just 1.3 so d would be are correct. Answer Now, another way your professor could have worded this is remember, associated with O H minus ions is V acidity. Right? So the Maura O H minus is you have the more basic you are. I could've ordered this as which is the most basic, and you should have read into that and said Okay, he means most basic. So that means who has the highest amount of O. H minus? I could have also said least acidic. Which of the following is least acidic, which would have mean who has the lowest amount of H 30 plus ions or who has the highest concentration off O. H minus ions, different ways. Three different ways to ask the same exact question. And remember, because all of them had 20 H minus is we didn't have to look at the number of ions. We only looked at the K SP. If they had different number of O. H minus ions, then we'd have to do calculations in order to find their Moeller Moeller Sawyer bility, which is X on. We'll learn how to do that a little bit later on
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example

## The solubility of silver sulfate, Ag2SO4, is 0.025 M at 25oC 5m
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So let's look at the next example. And because we're gonna need some room guys for this, I'm gonna remove myself from the image so we have more room to work with. All right. So for this one, it says the Moller sigh ability or its liability actually off silver sulfate is 0.25 Moeller at degrees Celsius. Calculate its saw liability product constant. All right, so they're telling us this compound has a K S P value. Remember we said earlier, if it has a K S P value associated with it, we assume that it is a solid because Onley solids have k S P values. So we're gonna say here a G two s 04 solid, and we have to show how it breaks up into ions. So we say that the medal will break off by itself. Remember, eggy is a transition metal, but a G is always plus one, and it's breaking up in pure water, and we just assume it's breaking up in pure water. If it wasn't, they would tell us. And that's why we have a quiz here. But here there are two eggs and over on the right side. There's only one. So we're gonna put it to here plus eso four. Where did this to come from? Over here In reacting side. It came from the S 04 s 04 to minus is our sulfate ion. So their goals are equation showing how the K SP is related to this solid, how it breaks up into ions. And guess what? Anytime we're dealing with K sp, we're also dealing with a nice chart. I remember in a nice chart, what two phases do we ignore? We ignore solids and we ignore liquids. So any time we're dealing with K SP, we're always going to ignore our reacted because I reacting will always be a solid. Now let's fill this out. I don't tell you anything initially about the ion, so they're both zero and their products. So we're making them. This has a two in front of it. So this is plus two X. This has a one in front of it. So it's just plus X plus two x plus X. Now what we're gonna do here is we're gonna say K SP is just like all the other case in equals products overreacting. It's but remember are reacting. Section got canceled out because it's a solid. So when it comes to K S P, it will Onley equal products because the reacting will always be a solid so equals a g positive. Remember, the coefficient makes it squared Times Essel four to minus plug in what we have at equilibrium for them. So plug this in here, plug this in here. So we're gonna have this is two x squared times X Now what is two X squared means Well, that means that the two will be squared and in the X will be squared. So two squared is what it's four and X squared is just X squared. So we're gonna have four x squared times x and there's a one here we don't see. I remember when we're multiplying things together, their powers will add up. So there's two will add up with this one. So that will give us four x cubed. Okay, so we're gonna work over here, gonna say K s P equals four x cubed. We're looking for K SP. So the last thing we need to realize here is if they tell you the sala bility of something you have to realize Sigh ability or Mueller. Solid ability is X So what they just told us here is what X equals. So just plug it in for X. And when we do that, what you have to do first is you're going Thio Cube 0.25 So do 0.25 to the three. Get that answer. Once you have that answer, then you multiply times four. So remember first cubit, then multiplied by four. Don't multiply by four, then cubit because if the order, you do it and we'll give you a correct answer or wrong answer. So order of operations Cuba first, then multiplied by four. When we do that, we're gonna get 6.3 times 10 to the negative five. So K s P is a little bit different from what we're used to. But some of the steps are similar toe what we've seen in the past, So just remember the fundamentals when it comes to K S P. We're dealing with a solid solid are ignored slow in a k SP ice chart. We always ignore the react inside. So only really focused on the product side. Since we're talking about K sp of, ah compound, we assume that compound is a solid and we showed Hy breaks up into ions. They're not telling us what type of solvent it's breaking up into, so we assume it's pure water. This is important. So since it's breaking up into pure water, we have zero amounts for both of our initial products. Set up everything we find out that chaos P equals four X Cubed Saudi ability always equals X. So take that X value and plug it in. When we find out what r. K s P s. So just remember the fundamentals, you'll be able to do questions like this in a breeze.

Whenever the question refers to the solubility then that value represents our “x” variable.

4
example

## Find the solubility of CoCl3 (Ksp = 2.8 x 10-13) in 5m
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Hey, guys, In this new video, we're gonna take a look at our Sala Bility product Constant, also called K SP. So here it says, find a sigh ability of cobalt three chloride, The soluble ity product constant or K sp that I give to you is 2.8 times 10 to the negative 13 and here we're gonna have to find it in pure water and also in a solution that is not pure water. Now, when we asked to find the solid ability, all I'm really asking you is to find X So we need to find the X here of our compound. So if we're dealing with K S P, that means that the compound itself is a solid and we have to have to. We have to show how that solid breaks up in solution. It breaks up into Cobalt three plus ion. That's where that little three came from. And since it has a charge, it's acquis. Plus, there are three chlorine, so it's three cl negative three chloride ions now. And since we're dealing with K SP, we're gonna use our favorite friend the ice chart. Now, remember what's not included in our ice chart, solids and liquids. If they give you a K S p for a compound, that compound must be a solid, so we ignore it. So with chaos P, we're always going to ignore the reactive. Now, products were breaking them up. So initially there zero, they're breaking up in pure water. And remember, we lose reactant to make product, So this is gonna be plus X. This has a three here. So this is gonna be plus three x plus X plus three X now K s P is just like all the other case and equals products overreacting. It's But remember, we said that our reactant are always gonna be solid, so we're always going to ignore them. So K s P will always equal just products. Now, since we're gonna need some room to work this out, guys, I'm going to remove myself from the image so we have more room to work with. So K s P equals products. Okay. S P equals cobalt three. I on times cl negative. I remember because the coefficient is a three. It's gonna be due to the third power. Next we plug in. What we know what equilibrium at equilibrium. Cobalt equals three chloride equals three X. So this is gonna be X times we're gonna cube three. So that's three times three times three, which is 27 and X to the third Now x to the third times X equals X to the fourth. So 27 x to the fourth equals R K sp from the very beginning 2.8 times 10 to the negative 13. So we're gonna bring this math over here we need to solve for X. So we're gonna do now is we're gonna divide by 27 on both sides here, so x to the fourth equals 1.4 times 10 to the negative 14. Now, we need to take the fourth route in order to just find X on your calculator. Some of you may see this button. You see a little X and then a square root sign. For those of you who see that button, we need to take the fourth root. So just do four. Hit the button number four and then hit this button that looks like this plug in 1.4 times 10 to the negative. 14 close brackets that should give you 3.19 times 10 to the negative four. And here the units will be polarity. Some of you may not see that button. For those of you who don't see that button, you're going to do this number in brackets in your calculator. You may see this button. Why do the X so hit? Why did the X open brackets one divided by four close brackets? And that should give you the same answer. Some of you may not even see this button and say you might see this button carrot pointing up. So substitute that that in hit that button brackets one of the fourth close brackets, you all should get that answer 3.19 times 10 to the four negative four. So that is the sigh ability of this compound. Now, let's say they weren't asking for the side ability of the compound if they were asking for chlorine chloride ion. If they were asking for one of the ions, you will come back to the ice chart and look to see what they equal at equilibrium at equilibrium. Chloride ion equals three x. So this sensor we got here you would take it and plug it into that three X to find the side ability of that ion. So again, when you're looking for the sorry ability of the compound as a whole, it's always equal to just X. If they want us to find a side ability of an eye on, you have to take that extra just found and plug it into the equilibrium line in our ice chart to get the correct answer.

Whenever we deal with the solubility product constant we use an ICE Chart and since the reactant will always be a solid then we can ignore it. If our compound dissolves in a solution with similar ions then the Common Ion Effect takes place. 5
example

## Find the solubility of CoCl3 (Ksp = 2.8 x 10-13) in 4m
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So we did this one in pure water. But now we're gonna dissolve that same compound, no longer impure water. But in a solution that is 0.20 Mueller and a C l. The beginning is still the same. It's still cocoa. Three solid breaks up into cobalt three plus acquis plus three c l minus a quiz. So that part doesn't change. Now, what's gonna be different is this here is Ionic is well and it breaks up into and a positive and see all negative and notice Here we have a C o negative and here we have a c All negative did the same exact ion. We call this type of problem a common iron effect. And here, we're going to say, is that this mole Arat e is the morality of the n a plus the c l minus. They each have that same polarity. We don't care about DNA because DNA is not found in our equation. But we do care about the C l minus. And since the same ion, if the molar ity of this chloride ion is 20 Mueller than the initial polarity of this clarity on is also 20 Mueller that's a big difference. Cobalt. We don't see any of its common ion. So this is zero. This is a solid. So we ignored. We're making products. So this is gonna be plus X plus three acts because of the coefficient plus x 20 plus three X here. We're gonna say K SP equals just products again because are reacting is a solid Now, here's the thing. Anytime we're dealing with K sp, we're gonna say that any time we have k S P, we can ignore a number in its variable as long as it follows a real number. So here this is an actual number. And because it's an actual number, we could ignore this plus three x. So our calculation just becomes X Times 0. Cute. So again for K S P, As long as there's a number in front of that X variable, we could always ignore that X variable here. This plus X here doesn't have a number in front of it, so we can't ignore. That's why we keep it around. Okay, Now this kid, it's still equals r k s P, which is 2.8 times 10 to the negative 13 which we saw earlier. All we gotta do now is solve for X, so divide both sides by 0.20. Cute. What you should get as your answer is X equals 3.5 times 10 to the negative. 11 Moeller. Now, what you should realize here is common in effect. Look at what are X was before we had the common ion. It was to the negative four. Now, because of the common I, in effect, it becomes to the negative 11. You're gonna say the common I in effect decreases soluble ity. So that's the biggest thing you need to take away from this. Not only how to solve a question like this, but the theory behind it. Kalmunai an effect decreases soluble ity because think about it. This thing gets dropped into a bucket and it wants to break up in tow ions. It's gonna try to break up into a much cobalt three plus and as much CEO minuses as it can. But even before it even starts toe break apart, there's already some C l minus initially, which would mean that this thing does not need to break up as much. That's why it's sigh ability is so much smaller because there was already some chloride ions present before it even began to break apart. And that's the key to this type of question. So remember how to solve a regular K SP question in pure water versus solving a K SP question that's not impure water and has a common iron involved.
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example

## What is the molar solubility of Fe(OH)3 (s) in a solution that is buffered at pH 3.50 at 25 oC 4m
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in this example of states. What is the Moller soluble ity of iron three hydroxide in a solution that is buffered at Ph 3.50 at 25 degrees Celsius. Here they also tell us that our K S P, which is R Saudi ability product constant, is equal to 6.3 times 10 to the negative 38 at 25 degrees Celsius. All right, so they tell us k sp. So that means we're dealing with an ionic compound in in solid form. And we're talking about how it breaks up into its ions when dropped into solution. So this breaks up in tow. Iron three ion and there are three hydroxide ions. So remember, we're dealing with K sp. We do a nice chart in a nice chart. We ignore solids and liquids. And if something has a K S P value, it will be an ionic solid. So here my reacted as an X through it. Now here's the thing. This is being thrown into solution that is at a ph of 3. But remember, since it's a metal with an O. H group, this represents a base bases don't deal with pH. They deal with P o H. So how do we figure out p o h? Remember P O. H will equal 14 minus pH. And why? That's because ph plus p o H together gives us 14. So it's 14 minus 3.50 which means our p O. H is 10.50. Now, if we know our p o h, that means that we know what our O. H minus concentration will be. Remember, our next formula is o h minus equals 10 to the negative p o. H. So plugging the 10.50 that we just got So we do that it gives me 3. times 10 to the negative 11 Moeller. So that's the concentration of our hydroxide. Um solution now realize that we're taking this ionic compound and we're dumping it in a solution that has a concentration of 3.16 times 10 to the negative Mueller hydroxide ion realize that our solution is made up of this ion. But our ionic compound that's breaking up also has the same exact ion. We're going to stay here that since both of these ions are the same. We call this the common ion effect. So that would mean that this is also 3.16 times 10 to the negative 11. So this is a common I, in effect question just phrased in a different way. We don't have any iron three initially, so that zero So this is plus X plus three x plus x and then bring down everything 3. times 10 to the negative, 11 plus three X Now remember, K SP just equals products here because are reacting is a solid, so we're going to ignore it. So here K s P equals F E three plus times O h minus. Remember, the coefficient here is going to become a power. So this is to the third power now K SP here is 6.3 times 10 to the negative 38 at equilibrium. I am three equals x And remember, if we have actual numbers in front of our X variable, that means we can ignore our ex variables. All of this is ignored, so that will be 3.16 times 10 to the negative 11. Cute. So we divide both sides by 3.16 times 10 to the negative cube. Okay, so we divide them by that. So we do that we're going to get as our answer for X X equals 2.0 times 10 to the negative. Six. Mueller. Now we're looking for the Mueller saw the ability of our Ionic compound and any time we're looking for the suitability of the Ionic compound, that's always just equal to X. So this would be our final answer. This would represent the concentration or Mueller Sigh ability off iron three hydroxide.
7
example

## Ksp and pH 5m
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8
example

## The Reaction Quotient & Ksp 7m
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9
example

## Q vs Ksp 6m
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10
example

## Ksp Determination 3m
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here. It states that a saturated solution of Lumen chloride contains 5.15 times 10 to negative for Mueller chloride ions. What is the salt ability product Constant or what's K SP? Since we're dealing with CSP here, we're dealing with aluminum chloride. We're dealing with its solid form. It breaks up into its eye on, so it breaks up into aluminum ion plus three Cloyd islands. We're dealing with a nice chart. So initial change equilibrium. Remember, in a nice chart, we ignore solids and liquids here. This is being broken down in pure water. So initially these two or zero their products or making them so this would be plus X. There's a three year so this would be plus three x plus X plus three X Now remember, K SP is just like all other cases equals products overreacting but are reacting will be a solid so ignore our reacted. So k spes equals products, therefore equals aluminum ion times chloride ion And again this three here means that this is to the third power here We're looking for K sp. So this is X times three X cube three cubed is three times three times three, which is 27. And this will be 27 x cubed and this will be 27 x to the fourth. So we know that K s P equals 27 x to the fourth. What are they telling me here when they say 5.15 times 10 to the negative for Mueller chloride ions. What? We're gonna see any equilibrium e chloride ion equals three X. And when they tell us this, that's also telling us that chloride ion equals 5. times tension Negative four. So Florida, I am equals this and equals this. So that must mean that they equal each other. And this is important because when we make them equal to each other, that means that we can find out what X is. So we divide both sides by three. So now we're gonna have X X equals 1.72 times to the negative four Moeller. And now that I have acts, I can plug it in to this X right here. So Caspi equals 27 times 1.72 times 10 to the negative, four to the fourth power. Now, remember your order of operations. You would do this number to the fourth power first, then multiplied by 27. So that'll be 27. And when I take this number to the fourth, it comes out as 8.68 times 10 to the negative 16. Now I multiply that number times 27. So here my ks ps 2.34 times 10 to the negative 14. So that would be the K S P of aluminum chloride in this situation. So just remember, the key here was realizing that at equilibrium chloride ion equals three X but also equally, Librium equals 5.15 times 10 to the negative four. Because chloride equals both those numbers, they must be equal to each other knowing this allows us to isolate X and in turn, help us figure out K sp at the end.
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example

## Molar Solubility of Ions 4m
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so an example to they tell us that calcium phosphate has a K S p up 5.8 times 10 to the negative 32. Or ask what is the Moller Saudi ability of calcium ions in a saturated solution off calcium phosphate? Since we're dealing with K SP, we're talking about the ionic solid form of this and how it breaks up into its ions. So breaks up into calcium ions and there are three calcium ions. Remember, Cal seems a group two ways, so that's why it's plus two. Then it breaks up into two phosphate ions, which is a poly atomic ion. Since we're dealing with K SP, we're dealing with a nice chart. Okay? And remember, in a nice chart, we ignore solids and liquids. Here. This is breaking up in pure water. So these two are initially zero Here there are three calcium. So this is three X. There are two phosphates. So this is two X So this is plus three x plus two x Remember, k SP will equal products here. So it's calcium ion. Remember, the coefficients become powers phosphate ion here. So now we plug in what we know. So K s P here is 58 times 10 to the negative 32. So this is three X cubed. This is two X squared. So three cubed is three times three times three, which is 27 and two squared is four. So now we have 27 times four, which is 108 and then X to the third times X to the second you add the exponents. So that's X to the fifth and this equals my K sp, which is still 5.8 times 10 to the negative. 32. We need toe isolate X. So we're gonna divide both sides here by So X to the fifth equals 5. times 10 to the negative 34. Now you may see this bun on your calculator. So you do five. You hit this button, then put 537 times 10 to the negative, 34 in parentheses. If not, you might see this button or this fun instead. So you would do this number in parentheses and then it also in parentheses. After you hit this number, this butter this button you put in parentheses one to the fifth to help you take the fifth root. So when we do that, that would give me my ex. Which comes out to 222 times 10 to the negative seven Moeller. But this X represents the Saudi ability of the entire Ionic compound, but we don't want the Saudi ability, the entire Ionic compound. We want the Mueller Saudi ability of calcium ions. So we look on the equilibrium line for calcium and we see that of equals three x. So we take this X and plug it in here so you multiply it by three. So that comes out to 6.7 times 10 to the negative seven Mueller. So this will be the concentration or Moeller Salyer bility of calcium ions. Remember, if we want the Mueller saw ability of the entire compound, it's just X. But if we want the Mueller Saudi ability of a particular ion, we look at the equilibrium line and we plug in the answer for X that we got in for that ion. If we wanted phosphate, then we plug that X into here to find the Mueller saw the ability of phosphate ions
12
example

## Ksp and solubility 3m
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Hey guys. So here in this example, we're told that the Sala bility of calcium fluoride is 53. g per milliliter at 25 degrees Celsius and then were asked to just calculate its Sala Bility product Constant or K sp. Since we're dealing with CSP, we're dealing with the Ionic solid form of this compound and we're talking about how it breaks up into its ions. It breaks up into calcium ion and then there are two fluoride islands. Remember, with K S P. That means we're dealing with a nice chart and in a nice chart we ignore solids and liquids the reactions of solid. So we ignored here It's breaking up in pure water. So initially, both our products are zero. Their products are making them. So this is plus X. There's a two here, so this is plus two x plus X plus two x. Remember, K SP will just equal products here because we ignore the reacted because again, it's a solid. So this is calcium ion times fluoride ion The coefficient becomes the power. Alright, so here this would be X times two x squared so that the x Times four X squared, which will come out to four X to the third. So for us to be able to find what are K. S P is we need to figure out what X will be here. They could be the Cy ability off calcium fluoride. Sigh ability here represents X. But remember, this is a nice chart. So we need the units to be in polarity, not grams per milliliter. So we're gonna take the 53 0.2 g of calcium fluoride per one middle leader, and we have to convert it to polarity, which is moles per liter. So we're going to stay here for every one mole of calcium fluoride. What's the massive calcium fluoride? While calcium Florida has calcium in it. One calcium, which, according to the periodic table, is 40.0 Gramps. And then we have two florins which, according to the periodic table, each one is 19 grams. So that's 40.8 g. Plus. Here are 38 g, so the mass you would be 78.8 g. So grants cancel out. Now we have moles over milliliters. We have to get rid of middle leaders here. It's on the bottom. So we're gonna put metal leaders on the top. So it's 1000 mL is one leader. So again, we have moles over leaders. So this is 6 81.35 to Mueller. So that represents my ex. So now I'm gonna plug that in here. Remember your orders of operation. You have to keep this number now before you multiply by four. So it's like Cube 6. 81.352 That gives me 3.16 times 10 to the eight. Now we can multiply that times four. That comes out to 1.26 times 10 to the ninth. So this would represent the K S P off calcium fluoride. So again, here I just made up. That's a liability value here. We're focusing on how exactly what I figure out gsp from the information given doing the steps would give us our final answer here
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example

## Selective Precipitation 3m
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