In this example, we'll solve a limiting reagent problem dealing with solutions. Our problem reads: a 25 milliliter sample of 2 molar sodium phosphate is mixed with 75 milliliters of 0.8 molar calcium chloride. When the precipitate is collected and dried, it is found to have a mass of 5.16 grams. Determine the percent yield. The first thing we need to do for this problem is to write out our balanced chemical equation. We're adding together sodium phosphate and calcium chloride. Our products will be calcium phosphate and sodium chloride. Calcium phosphate is insoluble, so that will be our precipitate. Next, we'll need to balance our equation. We can balance ions on each side. We'll begin by balancing phosphate. On the right, we have two moles of phosphate. To get two moles of phosphate on the left, we'll need two sodium phosphate. Now we have six moles of sodium on the left, so we'll need a six on the right. And now we have six moles of chloride on the right. So by adding a three to calcium chloride, we will balance chloride. We should also note that in the problem, we're given the actual yield. When we run the experiment, we produce 5.16 grams of our precipitate, which is calcium phosphate. Now we can solve this problem using a limiting reagent table. We'll begin by calculating the starting moles of each of our reactants. To calculate starting moles of sodium phosphate, we begin with 25 milliliters of our sodium phosphate solution. We can convert to liters of solution and then use the molarity of 2 molar to convert from liters of solution to moles of sodium phosphate. When we multiply this out, we get 0.05 moles of sodium phosphate. We can do the same thing with calcium chloride. We have 75 milliliters of calcium chloride solution. We can convert from milliliters to liters of solution, and then from liters of solution to moles using the molarity of calcium chloride. When we multiply this out, we get 0.06 moles of calcium chloride. Now we can calculate how many reactions we can perform with each of our reactants. We have 0.05 moles of sodium phosphate, and we need two moles for one reaction. So we can perform 0.025 reactions. We have 0.06 moles of calcium chloride, and we need three moles for every one reaction. So we can perform 0.02 reactions with our calcium chloride. Our limiting reagent is the one that runs out first. We can perform fewer reactions with calcium chloride, so that's our limiting reagent. Next, we can calculate the change in moles by using the number of reactions we can perform with our limiting reagent. We can perform 0.02 reactions. To calculate the change in sodium phosphate, one reaction will use up two moles of sodium phosphate, so we'll lose 0.04 moles of sodium phosphate. For calcium chloride, we'll still be able to perform 0.02 reactions, but one reaction uses up three moles of calcium chloride, so we'll use up a total of 0.06 moles of calcium chloride. We can also calculate the moles of calcium phosphate produced in our 0.02 reactions. One reaction only produces one mole of calcium phosphate, so we'll produce 0.02 moles of calcium phosphate. We don't need to calculate how much sodium chloride will be produced because in our problem we're only concerned about the precipitate. Next, we'll calculate the ending moles. We begin with 0.05 moles of sodium phosphate. We use up 0.04 moles of sodium phosphate, so we'll have 0.01 moles of sodium phosphate remaining. For the limiting reagent, calcium chloride, we begin with 0.06 moles of calcium chloride, and we use up all 0.06 moles of calcium chloride. So for the limiting reagent, we don't have any remaining. And for calcium phosphate, we begin with zero moles of calcium phosphate, and we've produced 0.02 moles, so we end with 0.02 moles of calcium phosphate. Next, we can calculate the theoretical yield for calcium phosphate, which is converting our 0.02 moles of calcium phosphate into grams of calcium phosphate. When we put the numbers into our calculator, we should get 6.2 grams of calcium phosphate. To calculate percent yield, we can use the equation percent yield equals actual yield divided by theoretical yield times 100 percent. We're given the actual yield in our problem, 5.16 grams, and we've calculated our theoretical yield, 6.20 grams. So when we put this in our calculator, we get 83.2 percent.