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# 2015 AP Chemistry free response 3f

Analyzing concentrations when pH lower than half-equivalence point. From 2015 AP Chemistry free response 3f.

## Want to join the conversation?

• Shoudn't the conjugate base have a higher concentration, as most of the sorbic acid molecules has lost its acidic proton to lower the pH?
(7 votes)
• I can think of it the following way:
Initially, we had only sorbate ions, as potassium sorbate dissociates completely. Then some of sorbate ions picked hydrogen from HCl forming weak sorbic acid, small part of which dissociated again, this time making hydronium and actually lowering pH. Since at the half equivalence point we have the same amount of sorbic acid as sorbate ions (but not the hydronium, as sorbic acid is weak), then, as pH went down from equivalence point, more sorbic acid was made, leading to more - > more hydrogen ions were released.
It wouldn't be correct to assume that most of the sorbic acid lost its protons, as it's Ka is low: 1.7x10^-5, and for losing most of the protons it should be much higher than 1.
(4 votes)
• If you wanted to prove this mathematically, couldn't you simply use the Henderson-Hasselbalch formula as you have pKa for sorbic acid from the original question (shown in previous videos) and use the value of the log of ratio of concentrations to determine which is in higher concentration?
(5 votes)
• Yes, this gives you:`[sorbate] / [sorbic acid] = 0.040`.
(3 votes)
• Why is there equal concentrations of sorbate and sorbic acid at the half equivalence point and not the equivalence point?
(2 votes)
• At the equivalence point ALL the acid has been used up and so ALL of it has been converted into the conjugate base.

At the HALF equivalence point HALF the acid has been used up so HALF of it has been converted into the conjugate base.
(3 votes)
• The question is asking about a pH which is between the half equivalence point (pH=4.77) and the equivalence point (pH=2.7, approximated from the graph). The main reaction at this point is C6H7O2- and H+ reacting to form HC6H7O2. I was wondering if I can use the fact to justify that because the acid dissociation constant for HC6H7O2 (sorbic acid) is small, Ka=1.7x10^-5 (HC6H7O2 <--> C6H7O2- + H+), the reverse reaction is favored, meaning that there will be more HC6H7O2?
(2 votes)
• In the Above SET of Problems, Can we calculate pH at Equivalence Point? How? Will we consider Sorbic acid at Equivalence point as Weak Acid and then calculate its pH??
(1 vote)

## Video transcript

- The pH of the soft drink is 3.37 after the addition of the potassium sorbate. Which species, the sorbic acid or the sorbate ion, has a higher concentration in the soft drink. Justify your answer. So, this is related to the question we've been doing because the sorbate ion, this is what happens when you put potassium sorbate and it dis-associates in a solution. So the concentration of the sorbate ion is the same thing as the concentration. One way to think about it, is going to be the same as the concentration of your potassium sorbate. So if we're thinking about titrating potassium sorbate, which we've been doing in the last several parts of the problem. At what point do you have an equal concentration of potassium sorbate and sorbic acid. Well you have equal concentrations at the half-equivalence point. We marked that out when we figured it out in the last few parts of this problem. And the half-equivalence point happened at a pH of, we actually figured it out before, 4.77. So we could say... "half-equivalence point "of titration "of potassium sorbate "with hydrochloric acid "happens at a pH of," let me write that pH of, "4.77." And that's the point at which you have equal concentrations of, so we can put this in parentheses, "can be viewed as point "where we have equal "concentrations, "of C6H7O2 minus," and ascorbic acid, "HC6H7O2." "pH of 3.37 is lower and will thus," or we could say, "will happen beyond "half-equivalence point." Beyond half-equivalence point. So, concentration of the sorbic acid is higher. "So concentration "of sorbic acid, "HC6H7O2, is higher." When you're starting off, if you're doing a titration. Your concentration of potassium sorbate, it'll be higher then you keep titrating and it keeps reacting with the hydrochloric acid. You get to the half-equivalence point where these two things are going to have equal concentrations. Then if you keep titrating it, well then you're going to become more acidic and your going to have a higher concentration of the sorbic acid. So one way to think about, actually let me underline that whole part, "so concentration of sorbic acid is higher." That's the main thing that they're asking for. But the way to think about this soft drink is something it might not have, and obviously people are sitting there and titrating every soft drink. But you can kinda view this soft drink as well it got that point after a theoretical titration that got us past the... half-equivalence point. And so therefore, most of our things that we care about is in the form, is in the acid form versus the conjugate base. Most of the sorbic acid is in its acid form. Or I guess you could say it the other way. Most of the sorbate has become the conjugate acid.