pH of polyprotic acid and base solution

[Muzette]

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When 0.1 moles of NaH2PO4 and 0.2 moles Na2HPO4 are mixed in 100mL, what is the pH of the solution?
ANS: (pKa2+pKa3)/2 >pH>pKa2

Could someone please explane why pKa3 comes into the picture? I thought since it's not working with a phosphate that the answer would only include pKa1 and pKa2. Please help!

 

[wiloghby]

http://forums.studentdoctor.net/archive/index.php/t-729314.html

In short, if you draw a titration curve and assume that each equivalence point is the average of the half-equivalence point (pKa) above and below it you'll see that your pH must lie higher than pKa2 but before the next equivalence point (pKa2+pKa3)/2 based on the results you get from Henderson-Hasselbaching it out.

When 0.1 moles of NaH2PO4 and 0.2 moles Na2HPO4 are mixed in 100mL, what is the pH of the solution?
ANS: (pKa2+pKa3)/2 >pH>pKa2

Could someone please explane why pKa3 comes into the picture? I thought since it's not working with a phosphate that the answer would only include pKa1 and pKa2. Please help!

 

[circulus vitios]

I remember that question from TBR. It's absolutely ridiculous and will probably never show up on the MCAT.

 

[LaughingMan]

I remember that question from TBR. It's absolutely ridiculous and will probably never show up on the MCAT.

Thank God.

From my experiences with AAMC 3 and AAMC 4, they are pretty basic questions--nothing this advanced.

 

[Temperature101]

I remember that question from TBR. It's absolutely ridiculous and will probably never show up on the MCAT.

However after doing TBR these AAMC questions might look easy...

 

[BerkReviewTeach]

I remember that question from TBR. It's absolutely ridiculous and will probably never show up on the MCAT.

I generally hang on the sideline when comments like this get posted, but this is one of those times where I want to step in. Your word choice is such that some people may read your post and it's tone, and mistakenly think you are right.

The reality is that this is (a) an altered version of a simple question, (b) a common question, and (c) a question type that is found in the AAMC materials (although they generally have exact numbers for answer choices). The point of this question is to teach a great short cut to those willing to see how easy these things become when you look at them as points on a titration curve. You as a student have the choice to accept and use the tricks or disregard them and do traditional math, but it does a disservice to the forum on the whole when you opt to shoot down a very good technique that works well for many people.

You have a triprotic acid, H₃PO₄ that when treated with a strong base can be converted into three different species. A triprotic curve is really just three separate curves attached equivalence point to starting point. So in this question, you are given 0.1 moles of H₂PO₄^- and 0.2 moles HPO₄^2-. Those species are involved in the second titration curve, which starts at the first equivalence point and ends at the second equivalence point. If the two species were in equal concentration then pH would equal pK_a2. But, you have more of the conjugate base, so the pH is slightly higher than pK_a2 but not as high as the second equivalence point.

So let's make this question a number question and see how it goes.

Assuming pK_a1 = 1.8, pK_a2 = 7.2, and pK_a3 =12.0, then what will the pH be when 0.131 moles KH₂PO₄ is mixed with 0.083 moles K₂HPO₄?
a) 1.91
b) 4.64
c) 7.02
d) 7.88

The easiest way to get this within ten seconds or less is to visualize the titration curve and see that you are at a point slightly before the pH = pK_a2, which makes it just less than 7.2. To be safe, you know that the first equivalence point is an average of 1.8 and 7.2 = 4.5, so choice B is way too low. In a few seconds of visualizing you have the best answer without having to write out an equation and do math.

So the point here is that it is a very good question that has a purpose in teaching a method for quickly solving math questions.

 

[BerkReviewTeach]

From my experiences with AAMC 3 and AAMC 4, they are pretty basic questions--nothing this advanced.

The reality is that this isn't advanced but is actually a shortcut. It takes a little time to learn the technique, but once you do, it makes acidbase calculation questions the simplest questions on the MCAT. This thread shows an example of how it can be applied on an AAMC exam.

And for what it's worth, AAMC 4 has a question in the PS section asking about the H₂PO₄^- to HPO₄^2- ratio at a given pH (8.7 I believe it is) that if you used this technique you could finish in 5 seconds. If you have the time and patience, learning the BR approach to acid and base chemistry can be extremely helpful for getting right answers really fast.

 

[circulus vitios]

You have a triprotic acid, H₃PO₄ that when treated with a strong base can be converted into three different species. A triprotic curve is really just three separate curves attached equivalence point to starting point. So in this question, you are given 0.1 moles of H₂PO₄^- and 0.2 moles HPO₄^2-. Those species are involved in the second titration curve, which starts at the first equivalence point and ends at the second equivalence point. If the two species were in equal concentration then pH would equal pK_a2. But, you have more of the conjugate base, so the pH is slightly higher than pK_a2 but not as high as the second equivalence point.

So let's make this question a number question and see how it goes.

Assuming pK_a1 = 1.8, pK_a2 = 7.2, and pK_a3 =12.0, then what will the pH be when 0.131 moles KH₂PO₄ is mixed with 0.083 moles K₂HPO₄?
a) 1.91
b) 4.64
c) 7.02
d) 7.88

The easiest way to get this within ten seconds or less is to visualize the titration curve and see that you are at a point slightly before the pH = pK_a2, which makes it just less than 7.2. To be safe, you know that the first equivalence point is an average of 1.8 and 7.2 = 4.5, so choice B is way too low. In a few seconds of visualizing you have the best answer without having to write out an equation and do math.

So the point here is that it is a very good question that has a purpose in teaching a method for quickly solving math questions.

Maybe you should re-write the TBR material because you explain it in a way that makes much more sense. 👍

 

[BerkReviewTeach]

Maybe you should re-write the TBR material because you explain it in a way that makes much more sense. 👍

Thank you for your kind words. There are some things I'd write a little differently, but all-in-all, I think the BR books do a great job at explaining things. I've suggested for years that they add a few video lessons to explain some of their tricks in the books. I think that would be more beneficial than rewriting.

 

[Muzette]

Thank you so much for your thorough explanation. I think I can see the bigger picture now. I did your practice problem and got it right! Thank you!