Equal volumes of 0.1-molar lithium phosphate and 0.1-molar calcium hydroxide are mixed and react according to the unbalanced reaction given. Blank Li3PO4 aqueous plus blank Ca(OH)2 aqueous react to form blank Ca3(Po4)2 solid plus blank LiOH aqueous. Which of the following statements is true about the reaction? (A) Once the reaction is complete, the concentration of lithium and calcium ions are essentially zero. (B) Lithium phosphate is the limiting reagent. (C) Calcium hydroxide is the limiting reagent. (D) The concentrations of phosphate ions in the final solution will be the same as the original lithium phosphate solution, as phosphate ions are considered spectator ions. Or (E) Li3PO4 and Ca(OH)2 react in the one-to-one ratio.
In this problem, we’re given the unbalanced chemical equation for the reaction between lithium phosphate and calcium hydroxide. So before we do anything else, let’s balance this equation. Since the polyatomic ions in this reaction, the phosphate ion and the hydroxide ion, stick together during the course of the reaction and don’t break up into their constituent elements, we can balance them as a group.
So let’s start off with the phosphate group. There is one phosphate group on the reactant side of the equation and two phosphate groups on the product side of the equation. So we can balance these phosphate groups by putting a two in front of the lithium phosphate in the reactant side.
Now let’s take a look at the lithiums. On the reactant side, we have three lithiums in lithium phosphate and we have two units of lithium phosphate, which gives us a total of six lithiums. But on the product side, we only have one lithium in lithium hydroxide. So to bring the lithiums into balance, we should put a six in front of the lithium hydroxide on the product side of the reaction. Now, let’s look at the hydroxide ions. On the reactant side, we currently have two hydroxide ions, but on the product side, we have six. So to balance the hydroxide ions, there needs to be a three in front of the calcium hydroxide on the reactant side.
Now, the only chemical species we haven’t looked at is calcium. On the product side, we have three calciums. And on the reactant side, we have three calciums. So the calciums are balanced. We didn’t have to put a number in front of the calcium phosphate on the product side to balance this reaction. So that means that there’s an implied one as the stoichiometric coefficient for calcium phosphate. Now that we have a balanced chemical equation, we can take a look at answer choice (E), which says that our two reactants, lithium phosphate and calcium hydroxide, react in a one-to-one ratio.
But as we can see from the stoichiometric coefficients from our balanced chemical equation, lithium phosphate and calcium hydroxide actually react in a two-to-three ratio, not a one-to-one ratio. So we can eliminate answer choice (E). Now let’s see if we can eliminate any additional answer choices. Let’s take a look at answer choice (D), which says that the concentration of phosphate ions in the final solution when the reaction is complete will be the same as the concentration of phosphate ions that we had in the original lithium phosphate solution. Specifically, this is because phosphate ions are spectator ions.
Spectator ions are ions that are present in both the reactants and the products, but they’re not involved in the chemical change. This usually occurs when you have a chemical species that’s present on both sides of the chemical equation in an aqueous form. Which is because when a chemical species is aqueous in solution, it will disassociate into its constituent ions. For example, on the reactant side of this equation, lithium phosphate, since it’s aqueous, would actually exist in solution as lithium ions and phosphate ions.
Similarly, on the product side, lithium hydroxide is also aqueous. So in solution, we wouldn’t have units of lithium hydroxide. It would dissociate into lithium ions and hydroxide ions. Since lithium ions are present on both sides of the chemical equation, lithium is a spectator ion in this reaction. But when we take a look at the phosphate group in this reaction, though it is an ion on the reactant side of the equation, it’s not an ion on the product side. Because calcium phosphate is a solid, so it wouldn’t dissociate into ions, which means that phosphate is not a spectator ion in this reaction.
So answer choice (D) is not correct. Phosphate ions are not spectator ions in this reaction. The concentration of phosphate ions in the final solution will be lower than the concentration of phosphate ions in the original lithium phosphate solution. Since the phosphate ions are being used to form solid calcium phosphate, which doesn’t form any phosphate ions.
If we look through our remaining answer choices, (B) and (C) have to do with determining which of our reactants will be the limiting reagent, which will involve some math. So before we tackle that, let’s see if we can eliminate or choose answer choice (A). Answer choice (A) says that once the reaction is complete, the concentration of lithium and calcium ions are essentially zero. To see if this statement is true, we can apply what we learned about spectator ions when we’re looking at answer choice (D).
As we discussed, lithium is a spectator ion in this reaction, which means lithium ions will be present in both the reactants and the products side of this reaction. Since lithium ions will be present in the product side of this reaction due to the presence of aqueous lithium hydroxide in the products. The concentration of lithium ions can’t be zero when the reaction is complete. So answer choice (A) is not correct.
So this leaves us with answer choices (B) and (C). So we’re going to need to calculate which one of our reactants is the limiting reagent, which simply means which one are we going to run out of first. One way to calculate the limiting reagent for a reaction is to determine how much of one of the products you can form given the amount of each reactant that you have and see which one is less.
The problem tells us that we mixed equal volumes of 0.1-molar concentration solutions for each of our reactants. To solve for the limiting reagent, we’ll need the amount of each of our reactants that we have in moles. Since molarity is defined as moles per liter, we’ll need to multiply this concentration by a volume in order to obtain the amount of moles of each of our reactants. So to make the math easy, let’s just assume that the equal volumes that we mixed of both of our reactants was one liter. So we can find the amount of each of our reactants that we have in moles by multiplying the concentration by one liter, which would give us 0.1 moles for both of them.
Our next step will be to determine how much of one of the products will be able to form given the fact that we have 0.1 moles of each of our reactants. To do this, we can pick either of the products. But I’m going to choose lithium hydroxide. According to our balanced chemical equation, there are six moles of lithium hydroxide for every two moles of lithium phosphate. So we can use this to convert from moles of lithium phosphate to moles of lithium hydroxide. If we multiply everything out, we’ll find that we can form 0.3 moles of lithium hydroxide if we have 0.1 moles of lithium phosphate.
Now let’s look at our other reactant, calcium hydroxide. We still have 0.1 moles of calcium hydroxide. But the stochiometric ratio for lithium hydroxide to calcium hydroxide is six to three now. This means that if we have 0.1 moles of calcium hydroxide to start off with, we’ll be able to form 0.2 moles of lithium hydroxide. Since we can form fewer moles of lithium hydroxide given the amount of calcium hydroxide that we have, that makes calcium hydroxide the limiting reagent. So answer choice (C) is correct.
Instead of doing this math, we could’ve also recognized that since we have the same amounts of both of our reactants, but the stochiometric coefficient in front of calcium hydroxide is larger, we’ll run out of that first. Either way, of the statements that we were given, the one that is true about this reaction is that calcium hydroxide is the limiting reagent.