A solution is 0.010 M in Ba²⁺ and 0.020 M in Ca²⁺. a. If sodium sulfate is used to selectively precipitate one of the cations while leaving the other cation in solution, which cation will precipitate first? What minimum concentration of Na₂SO₄ will trigger the precipitation of the cation that precipitates first?

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Hello everyone today we are being asked to determine the Cali on that will precipitate first. If potassium carbonate is used to precipitate one of the cal eons in a solution that contains 10.25 molar of manganese and 0.5 Mueller of sync. Were then asked to calculate the minimum concentration of this potassium carbonate that will start the precipitation of that carry on. So the first thing we wanna do is we want to draw our potassium carbonate being dis alluded In solutions. So we're going to say this is going to do this, is going to dissociate into two potassium plus ions as well as one carbonate to -1. And then we're also going to say that the concentration of our K two c 03 is going to equal the concentration of regular carbonate ions. And then we have to calculate that concentration of carbonate ions. So when we take our potassium carbonate and will react it with one of the ions, let's say we're gonna react it with meghan is first we're gonna say M two plus Mn two plus this is going to form manganese carbonate Solid as well as two potassium ions. We're then going to take this mega knees carbonate and we're going to dissociate to form our ice table. So we're going to say this solid is going to dissociate into mega knees two plus Aquarius as well as carbonate to minus Aquarius. And now we can set up our ice table here. So we have our rice table, we have our initial concentrations for the solid not mattering because it is a solid. But for mega needs we have 0.025. And for carbonate we have zero. We have a change in plus X because there's only one of each. And so our final is going to be 0.25 and X. And the reason why we don't say 0.25 plus X for magazines is because X here is negligible. So we don't it doesn't matter in the situation. The next thing we're going to do is we're gonna set up our K. S. P. Value. So R K S. P. Value for manganese Carbonate is going to be 2.24 times 10 to the -11. And when we set it up with our with our equation here, we're gonna see the concentration of manganese two plus it's going to be multiplied by the concentration of carbonate to minus. We plug in our values 2.24 times 10 to the -11 is going to equal our concentration of manganese which is .025. We're gonna multiply that by X, Dividing both sides by 0.025, we get that X. Is equal to 8.96 times 10 to the -10. In other words X. is equal to r carbonate concentration. And so we move on to our second portion where we have to react this potassium carbonate with zinc. And so we have potassium carbonate here in the form just as before, we're going to react it with zinc two plus Aquarius, we're going to form zinc carbonate, Aquarius or a solid. Excuse me and two potassium ions. We're going to take this solid that we formed this zinc carbonate and we're going to say that this is going to dissolve into one zinc two plus ion as well as a carbonate to minus ion. And then we're going to set up our ice table. So we're gonna have I. C. And E. Once again for solid, it doesn't matter. So we're going to just draw an X through their our initial concentration from that zinc was found in the question stem which is 0.50 moller for carbonated zero. Once again, our change is going to be plus X since we only have one of each of these ions. And so this is going to be 0.5 and X. And once again X is negligible here. R K S. P value for zinc carbonate is going to be equal to 1.46 times 10 to the negative 10. And so we set up our K sp table, we'll have concentrations of zinc two plus times our concentration of carbonate. We set up our equation furthermore, we have 1.46 times 10 to the negative 10 is equal to our concentration of zinc which is 0.5 times X X. is going to end up equaling 2.92 times 10 to the -9. And of course in a situation X is equal to carbonate. And so we have to find the minimum concentration, so we have to find the lowest number and so between our lowest numbers between reacting with manganese and zinc, we can confidently say that the manganese value is going to be the lowest concentration, so therefore we can say that manganese will precipitate or form a solid, so precipitate first. And so that is going to be how we reach our final answer. I hope this helped, and until next time.

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Key Concepts

Solubility Product Constant (Ksp)

Selective Precipitation

Concentration and Stoichiometry