2015 AP Chemistry free response 3b | Chemistry | Khan Academy

A total of 29.95 milliliters of 1.25 molar hydrochloric acid is required to reach the equivalence point. Calculate the concentration of potassium sorbate when you put the brackets; they're talking about concentration in the stock solution.

So, let's just remind ourselves what the equivalence point is. The equivalence point is the point at which all of the potassium sorbate has reacted with the acid, with the titrant.

We have just gotten to the right-hand side of this net ionic equation. So, another way to think about it is it's the point in which, because we are reacting, for every mole of the potassium sorbate that we want to turn into sorbic acid, we're adding a mole of the hydrochloric acid.

One way to think about the equivalence point is if I've added a certain number of moles of hydrochloric acid, that must be the exact number of moles of the potassium sorbate that we started out with. We've added the exact number of molecules of hydrochloric acid as there originally were of potassium sorbate, so they can completely cancel out with each other.

If we can figure out the number of moles of hydrochloric acid here, then we could say, "Well, at the equivalence point, if you needed that number of moles of hydrochloric acid to reach the equivalence point, then that means your original stock solution had that many moles of potassium sorbate," and then we can use that to calculate the actual concentration.

So, let's do the first part. Let's think about how many moles of hydrochloric acid this is right over here.

So, I'll just write HCl. If we have 29.95 milliliters, let's convert it into liters because if our concentration is given in terms of molarity, this is moles per liter. So, let's make sure we get our units right.

So, let's multiply this by, we want to convert this to liters. We want liters in the numerator and milliliters in the denominator, so these cancel out. So, 1 liter is equal to 1000 milliliters, and that makes sense.

If you want to go from milliliters to liters, you would multiply by one-thousandth or divide by a thousand. So, this will give us the total amount of hydrochloric acid solution we've added in liters.

Now let's figure out how many moles that will be. We multiply that by the molarity, times 1.25. Instead of writing molar (capital M), I'm going to write 1.25 moles per liter.

What is this going to give us? Well, let me get my calculator out. So, I'm going to have 29.95 divided by 1000, and that part right there, times 1.25.

1.25 is equal to, and let's see, I have three significant figures here, four over here, so the product I'm going to have three. So, 0.0374, and the units all work out. Milliliters cancel out with milliliters, liters cancel out with liters, and I have 0.00 moles.

Remember, this is moles of hydrochloric acid. So when they say that a total of 29.95 milliliters of 1.25 molar solution of hydrochloric acid is added, they really added this many moles of hydrochloric acid.

So, that means our original solution had that many moles of potassium sorbate. We can now figure out the original concentration of potassium sorbate.

So, the concentration of our potassium sorbate (C6H7O2) is going to be equal to the number of moles of potassium sorbate our stock solution starts off with. So, that's going to be the same number right over here, 0.0374 moles, divided by, well, what was our original volume of our original solution?

Let's see, a student titrates 45.00. So, we have four significant figures here; the student titrates 45 milliliters of the stock solution.

The stock solution originally has a volume of 45 milliliters. So, 45 milliliters, if we wanted to write that in terms of liters, remember the concentration, the molarity here we wanted it in terms of moles per liter.

So, 45 milliliters is the same thing as 0.045. I can write 0.0 there to show that I have four significant figures here, liters of solution.

What is this going to be equal to? I just divided this by a thousand; 45 milliliters is the same thing as 0.045 liters.

So what do we have? We could take that number we just had and then we divide it by 0.045. I could add two more zeros there, but from the calculator's point of view, it doesn't make a difference.

That's going to be equal to, 'All right, and how many significant figures do we have?' We have three significant figures, so 0.832, 0.832. Zero point eight three two moles per liter, or we could say zero point eight three two molar.

Did I write that right? Yeah, eight three two. And there you have it; that's the initial concentration of the potassium sorbate in our stock solution.