The solubility of PbSO₄ in water at 25 °C is 7.9 × ...

Question

The solubility of PbSO₄ in water at 25 °C is 7.9 × 10^-4 M. What is K_sp for PbSO₄₄?

Accepted Answer

Hey folks, welcome back. So we have silver to assassinate this compound. Right here it is sparingly soluble salt with KsB value of one times 10 to the negative 12. So we know that this is going to be a solid here. Right? So for the first part we need to calculate the volume bility of the salt and most per liter or polarity um in pure water. Right? And then for part B we need to calculate the scalability of that same compound but now we actually have a common iron effect here because we already are going to have a certain initial concentration Of the Diocesan eight iron. Okay from this solution. So let's go ahead and do the first one First. Alright, so obviously we're going to go ahead and write the equation here, the reaction for um silver 1008. So it's a solid and since we are dealing with equilibrium here and it's going to have double arrows and we're going to break this up into its eye on so we're going to have silver one. So silver here is going to have a positive one charge and of course this is going to be Equus right because it's in a solution of water plus I assign it is going to be S. C. And minus and also Aquarius. Alright, so first to calculate the scalability, what is scalability? It is going to be our ex um at equilibrium in our rice table. Okay so usually in most per liter that is the solar cell, the ability of that compound which is going to equal to X. So here we're going to be solving for X twice but of course for the first one, we're not going to have any initial concentration um for the products. Alright, so because the solid here is in the solid phase, we're always going to ignore the react inside and we only care about the product side. So initially there is nothing here, right? Because it's just pure water. That was changed. We're going to gain um products lose reactant and here we have only one mole of silver and one mole of finance. So it's just going to be plus one X for both. And then at equilibrium is just going to be what we gained. So X. And X. So here we're going to be using the K. S. P. Value that is given to us in order to find X. Right? And here we're looking for X. Which is going to be in polarity or most per liter. Same units. So KsB here equals to 1.0 Times 10 to the -12. Okay. And we know that K spain is always going to equal to just products multiply together because reactant is a is a salad. So we ignore that. Okay, so it's just going to be X times X, which is just X squared. Okay, now we just want X by itself. So we're gonna go ahead and just square root both sides, Right? And we're going to Find X just X. is going to equal to 1.00 times 10 to the negative six and moles in polarity or moles per liter. Okay, so that is going to be the scalability of this solid here in pure water. So we've answered part A. Now let's go ahead and answer part B for part B is going to look a little bit different. I'm going to go ahead and rewrite the equation really quick. The equation itself is obviously the same. It's just the initial concentrations that are going to differ. Alright, so we have silver plus one and thanks, I need iron and Equus now realize that case B is going to equal to, let's say it's going to equal to the same thing. Right. This is just case p value for that for this silver. So it's going to be the same. We're going to be able to use the same value here. Alright, so stable again, we're going to ignore the solid. So um initially for silver, do we have any silver initially um in the solution of potassium to assassinate? No, there's actually no silver in the solution. So for silver is still going to be zero but potassium to assassinate, breaks up into potassium plus one and then assign it I am Right, so we actually have point 150 moller of potassium to sign it. So this is a common iron effect and we do know that common iron effect is going to decrease the scalability of that solid of that salt. So for initially we're going to have 0.1 Mueller of the 1008 ions. But then for everything else is the same, we're going to gain X because there is only one mole of each. And then at equilibrium we're going to have X for silver. But here we're going to have 10.1 50 plus X. Right? What we started with plus what we gained. Now when we're dealing with KsB, remember when there is an actual number that we're adding to the X. We can actually go ahead and just ignore X in our case the expression and that makes it so much easier to find the other X. Alright, so KSB here, Okay, you speak is going to equal to the same thing. It's still 1.00 time stands with the negative too. But now we're going to have X. Right this product times that product. Remember we're ignoring the sex. So it's just going to be x times um . 0.1 50 of course this will just be 500.1 50 X. So to find X here, because again, X here is going to be our solar cell ability. We're just going to divide both sides by 500.50 and X here is going to be So we're going to get an answer of 6.67 times 10 to the negative again, Mueller or moles per liter. Okay, so that is going to be the scalability of that solid when we already have an initial concentration of assigning um iron. So notice that negative six is actually a larger number than negative 12. So scalability of this solid is actually greater without the common iron. But then when we do have a common iron effect here, when we actually already have initial concentration of one of the ions, that decreases the scalability and that's why our X here is smaller. Alright folks, we're all done here. Please let us know if you have any questions and we'll see you in the next problem.

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