2015 AP Chemistry free response 3b

- [Voiceover] 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, we put the brackets, so we're talking about concentration, in the stock solution. So let's juts 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 titrate. So, 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. So, one way to think about the equivalence point is if I've added a certain number of moles of hydrochloric acid, that must 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 they originally were of potassium sorbate, so they can completely cancel out with each other. So if we can figure out the number of moles, if we can figure out the number of moles of hydrochloric acid here, then we could say, "Well, the equivalence point", or if you needed that number of moles of hydrochloric acid to reach the equivalent 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, and so, if we have 29.95 milliliters, and let's just convert it into liters, because if we have, 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 times, so we wanna convert this to liters, so we want liters in the numerator, and milliliters in the denominator, so these cancel out, so one liter's equal to 1000 milliliters, and that makes sense, if you wanna go from milliliters to liters, you would multiply by 1000, or divide by 1000. So this would give us the total amount of hydrochloric acid solution we've added in liters, and now let's figure out how many moles that will be. Well, we multiply that times the molarity, times 1.25, instead of writing molar capital M, I'm gonna write 1.25 moles per liter, and what is this going to give us? Well, let me get my calculator out, and so, I'm gonna have 29.95 divided by 1000, (mumbling) right there, times 1.25, times 1.25 is equal to, and let's see, I have three significant figures here, four over here, so the product, I'm gonna have three, so 0.0374, 0.0374, and the unit is all work out, milliliters cancels out with milliliters, liters cancel out with liters, and I have 0.0374 moles, and 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. So it had that many moles of potassium sorbate, we can now figure out the original concentration of potassium sorbate. 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 what was our original volume of our original solution? Let's see. A student titrates 45.00, so we have four significant figures here, a student titrates 45 milliliters of the stock solution. So 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 mole per liter, 45 milliliters is the same thing as 0.045, I can write zero there so that I have four significant figures here, liters of solution, and what is this going to be equal to, and I just divided this by 1000, 45 milliliters is the same thing as 45 thousands of a liter. And so, what do we have? We'll take that number we just had, and then we divided it by .045, and I can add two more zeros there, but form the calculator point of view it doesn't make a difference, and that's going to be equal to, all right, how many significant figures do we have? We have three significant figures, so 0.832, 0.832, 0.832 moles per liter, or we could say 0.832 molar, did I write that right? Yeah, 832, and there you have it, that's the initial concentration of the potassium sorbate in our stock solution.