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For which of the following sparingly soluble salt, the solubility (S) and solubility produce (Ksp) are related by the expressions $mathrm{S}=(mathrm{Ksp} / 4)^{13}$...

Question

For which of the following sparingly soluble salt, the solubility (S) and solubility produce (Ksp) are related by the expressions $mathrm{S}=(mathrm{Ksp} / 4)^{13}$ ?(a) $mathrm{BaSO}_{4}$(b) $mathrm{Ca}_{3}left(mathrm{PO}_{4}ight)_{2}$(c) $mathrm{Hg}_{2} mathrm{Cl}_{2}$(d) $mathrm{Ag}_{2} mathrm{PO}_{4}$

For which of the following sparingly soluble salt, the solubility (S) and solubility produce (Ksp) are related by the expressions $mathrm{S}=(mathrm{Ksp} / 4)^{13}$ ? (a) $mathrm{BaSO}_{4}$ (b) $mathrm{Ca}_{3}left(mathrm{PO}_{4} ight)_{2}$ (c) $mathrm{Hg}_{2} mathrm{Cl}_{2}$ (d) $mathrm{Ag}_{2} mathrm{PO}_{4}$



Answers

Write the solubility product expressions for
the following slightly soluble salts: AgI,
$\mathrm{SrSO}_{4}, \mathrm{Ag}_{2} \mathrm{CO}_{3}, \mathrm{Ag}_{2} \mathrm{S}, \mathrm{PbI}_{2}, \mathrm{AgIO}_{3}$
$\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2},$ and $\mathrm{Hg}_{2} \mathrm{Cl}_{2}$

So we have a number of ionic solids slightly or so insoluble Aaron soluble salts. In order to write the, uh, sally ability product equilibrium, constant expression, we need to have the reaction. And in writing the reaction, we always want the insoluble salt to solid on the left. And then we want to write the ions that it is composed of on the right and that will give us the K S P expression, the equilibrium, constant expression saw. The ability product in this case always comes from the balanced equation. And so similarly, now you want to recognize those ions that you've become familiar with. This is not strong IAM and sulfur and oxygen. It's the strong IAM two plus ion and the sulfate ion. And so you don't want to take those occean ions apart. You want to keep them as individual units. So these two that we've done, or both, uh, 1 to 1 one cat eye on as hard to plus in this case, when and I on sulfate Ah, but here we've got two silvers. That's not a G two, that is, to a G's. That is crucial because it makes the difference of whether we have a square in the equilibrium, constant expression or not, and especially if you're going to do any calculations, you've got to be sure you've got the right expression in the equilibrium. Constant. So again, that's not a G two. That's to a G plus. And that gives us the square on the silver ion concentration because of the two as the coefficient in the balanced equation. So to silver and one carbonate. Ah, and likewise for all three This the soap eight, the carbonate, the Iot date. Keep the that Oxy and I on intact don't separate the oxygen's. That's just one I o date I on. And so the corresponding K s P. Now we've got three. Magnesium is here and of course, magnesium is a two plus ion and to phosphates, which is a triple minus. And so our k s P here is going to be the concentration member. Square brackets represent Moeller concentration or mill arat e the cube of the magnesium ion concentration and the square of the, uh, phosphate cube for magnesium square for phosphate. Now, I emphasized here that this is to a G's and not a G two this is the only example that I know of the so called silver one eye on where the eye on ah is Polly Atomic while only having one element it namely to magnesium Adams in the eye on with a total charge of plus two. And so this is the only case where that, too, as a coefficient, uh, doesn't become I'm sorry to, as a sub script doesn't become, too as a coefficient in every other case as we see here for the silver. If you've got a two, then that becomes to silver ions, not a G two, but with the Mercury I on the Mercury, one eye on it is an exception. And that is the H G 22 plus ion. And so it's just one of those again. This is the only one that you will ever see that works that way. That's not sealed. Two. That's two chloride ions. This is the big exception

Option e. Okay, so let us continue with the definition. First, the amount off given substance which is dissolved in a given quantity off a solvent at a particular temperature is called us solid ability. Auction is magnesium Ra might mdbr too. Generally all brew mites except a G b r edgy toe. Br to Andi B B B R two are soluble in water. Therefore, MGB are to a soluble What should be It's lead iodide generally all IOD ites except a G I ex G to I two and Phoebe I too soluble in water. Therefore, lead iodide is insoluble auction. See and Mitch four in each. Full mourning box elite generally all carbon needs except this one on carbon. It's off. Alkali metal are insoluble in water. Therefore, this is soluble auction D. This one is so lovable. The last one is Option E. It is Zaidan s o for so generally all sulfates except s R s. So full bso four edgy to s 04 and let s 04 are so liberally water. Therefore the given substance is soluble

So when you have assault that has the conjugal base of a weak acid, as it's an eye on, you end up getting a solid ability greater than that you that you would calculate. And so we're looking for assaults to contain the conjugal basis of weak acids. So this one here has cell fight. That's the congregate base of the weak acid H two s 03 Here we have the an eye on my minus. That's the congregate base of the strong acid H I for lead to carbon E you have C 03 to minus. That is the cognac, it base of the weak acid H two C 03 for lead to chloride. You have, um c l minus. That is tthe e con jacket base of hcl, which is a strong acid for thallium. One sulphide you have s to minus that is the conjugal base of the weak acid H two s. And for a potassium perk. Laurie, you have Cielo four minus. That is tthe e congregate base of the strong acid hcl 04 And the reason for this The reason why when you have let's look at this one, the conjugal base of a weak acid. You get a greater Sally ability than you would predict. So if you put this in solution you're gonna have C. O s 03 gives you hope All two plus plus cell fight. And so, if you use ke SP, you could calculate the Moler Sally ability. Bye. What happens in solution is because you have water interacting with this congregate base. You're gonna have 8 to 0 plus s +03 to minus gives you hydroxide plus h s +03 minus. And so this is going to react away. Some of the s 03 to money's gonna react away some of the cell fight. And what is that going to do? According to Lisette Lee's principle to this equation? Well, because you're lowering the concentration of this, it's going to push the equation to the right and that will lower. I'm sorry. That will increase the scalability of the salt

So the key here is that we're looking for an ions that are conjugated bases of weak acids, and so we want to identify the an eye on in all of these species. And if the an ion is the conjugal base of a weak acid, that means it's soluble ity is going to be higher than what's calculated, and I'll do one out so you can see exactly what's going on. The an ion in this 1st 1 is s 03 to minus. It's congregate. Acid is H two s 03 That is a weak acid. So it is going to have our higher sally ability than what you would calculate from chaos. P. Let's just look at the mechanism behind that here. So if we have C. O s 03 that dissolves into Kobol, it could be equilibrium because it's slightly soluble cobalt, and so fight. Now, this cell fight is a weak base, so it will interact with water. So you're gonna have sole fight. Plus water gives you H two s 03 plus hydroxide. And so what that's going to do is it's going to react away. Some of the S 03 to form a TSH to s 03 So when you lower the concentration of s 03 what does that do to this first equation? It's gonna push it to the right according to the Chatelet as principal. And in doing so, more of the, um, cobalt cell fight is going to dissolve than what would be calculated. If you have the an eye on that is not basic or it's the conjugal base of a strong acid, that's not gonna happen. So you're Sally. Ability is going to be what's calculated. So that would be the case for copper. One iodide the an eye on his eye minus its conjugate acid is each eye. So it's not gonna have a higher sally ability than calculated. Um, this is gonna be carbonate. The contra get acid is a weak acid, so it will be a higher sally ability than predicted. Fluoride is not basic would be the conjugal base of a strong acid. Sulphide is tthe e congregate base of the weak acid H two s so that we'll have a higher sally ability than calculated. And then for glory is, um, it's kinda get acid is per cleric acid, which is strong, so it will not have a higher sally ability than calculated


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