A student needs 625 grams of zinc sulfide, a white pigment, for an art project. He can synthesize it using the reaction above. How many grams of zinc nitrate will he need if he can make the zinc sulfide in 85% yield? Assume that he as plenty of sodium sulfide. So in this problem, we've got lots of information that's given. And the first thing we want to do is kind of summarize that information. And so I'm going to start by seeing the amount of the product that we need, the 625 grams of the zinc sulfide, okay? He can synthesize it using the reaction above. And it's in an 85% yield. And we have plenty of sodium sulfide. So I'm just going to put an XS there to stand for excess. Okay? So we have plenty of that. So really we're only worried about how much zinc nitrate do we need? So, I've got a couple of things going on here. I've got to figure out how much zinc sulfide do I need to plan on making, if I know I'm only going to have 85% yield. And then I need to use stoichiometry to figure out how much zinc nitrate is going to be needed to make that amount of zinc sulfide. So let's first look at what we have for the zinc sulfide in that percent yield. Remember that percent yield equals the actual, or the experimental amount, over the theoretical, times 100. So I can use that equation to actually figure out how much I need to plan on making. So I know my percent yield is 85%. My actual yield needs to be 625, because this is what I actually need to end up with at the end of the experiment, and what I'm actually solving for here is the theoretical amount. How much do I need to plan on making so that I end up with 625 grams? So we know that x is going to be greater than 625. And when I do the calculation, I'm going to have to solve for that x. And I find that x is going to be equal to 735 grams. So that's how much I need to plan on making so that I end up with that 625, because my reaction is not going to go to completion. Now, a couple of things before we continue on with this problem that we want to take note of. One, we know the amount of zinc sulfide we need to plan on making. The other thing we need to notice is this ratio. For every one mole of zinc sulfide, I need to have actually reacted one mole of zinc nitrate. So we're going to bring over the information here that we're going to need to solve the rest of this problem. And we said we needed to plan on making 735 grams of the zinc sulfide. Remember that it was a one to one ratio between the zinc sulfide and the zinc nitrate. And that came from our balanced chemical equation. And I also know that I have molar masses for zinc sulfide, which is 97.47 grams per mole. And for zinc nitrate, the molar mass is 189.36 grams per mole. So with this information I can actually set up my stoichiometry calculation. Notice that the amount, the known amount is the 735 grams of zinc sulfide, and I'm going to have to get that to moles, because remember my ratio, that one to one ratio, is in terms of moles. So I use the molar mass, and I'm going to put the grams on the bottom because I need those grams to cancel with grams. Then I'm going to put in my mole ratio, that one mole of zinc sulfide to one mole of zinc nitrate. And even though it's a one to one ratio and it's not changing my actual calculation any, I'm still going to include it just to get in the habit and so that all my units cancel out correctly. Now I have one mole of zinc nitrate. Now I can use my molar mass of 189.36 grams per mole of zinc nitrate to get to the grams of zinc nitrate. Before I do the calculation, I'm going to cancel out grams and grams. Moles of zinc sulfide, moles of zinc sulfide, moles of zinc nitrate with moles of zinc nitrate. And what I'm left with are grams of zinc nitrate, which is what I'm actually trying to find in the problem. And when I do the calculation, I end up with 1428 grams of zinc nitrate, and to get that in the correct number of significant figures, I'm going to have to write that in scientific notation. So it would be 1.43 times ten to the third grams of zinc nitrate. So that's the amount of zinc nitrate I need to start with, so that in the end, I'm produce my 625 grams of the zinc sulfide.
