# Acids and Bases

## Homework Statement

The pKa of acetylsalicylic acid (aspirin) is 3.5. The pH of gastric juice in the stomach is about 2-3 and the pH in the small intestine is about 8. Aspirin will be
Answer is ionised in the small intestine and almost unionised in the stomach.

## The Attempt at a Solution

I understand from the pH values given that the stomach is acidic and small intestine basic. So, I could already qualitatively figure out what the answer would be. However, is it quantitatively correct to say that aspirin is unionised in the stomach because the pH of stomach is less than the pKa of aspirin? What if the pKa of aspirin was 1.5? Would it then be ionised in the stomach?
Basically, I just want someone to clarify what pKa tells us in this context.

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I was just looking for a relationship between pH and pKa. Found it!

Borek
Mentor
I was just looking for a relationship between pH and pKa. Found it!
Wouldn't hurt if you will show what you have found. This is by no means a trivial relationship (actually there is NO relationship between just pKa and pH).

The Henderson Hasselbalch equation. I know it's for buffers, but pH is directly proportional to pKa and I was looking for some quantitative relationship. If you could expand more though, I'd more than appreciate it.

What if the pKa of aspirin was 1.5? Would it then be ionised in the stomach?
Also, maybe answer this question? I think it wouldn't based off pH directly proportional to pKa, but it's not a linear proportion so I'm not very sure.

Borek
Mentor
pH is directly proportional to pKa
That's a serious misrepresentation of the HH equation.

However, HH equation is a good start here. It contains $\log \frac {[A^-]}{[HA]}$ expression which is what is important. Rearrange the equation in such a way this ratio is expressed as a function of both pH and pKa. When this ratio is small, acid is mostly unionized. When this ratio is high, acid is mostly ionized. This is quantitative.

Actually you were quite close to the correct answer in your first post:

is it quantitatively correct to say that aspirin is unionised in the stomach because the pH of stomach is less than the pKa of aspirin? What if the pKa of aspirin was 1.5? Would it then be ionised in the stomach?
When pH = pKa exactly half of the acid is ionized (and the other half unionized). When pH < pKa, there is more unionized form.

Ohhhh, that's really cool!
[A-]/[HA] = 10pH-pKa
So it's the difference that counts.
Thanks :)

On second thought, shouldn't the HH equation be viable only for a buffer? Gastric acid in the stomach is HCl which is a strong acid and aspirin (a weak acid) couldn't possibly form a buffer with HCl (or for that matter, the weak base of the small intestine). So, isn't using HH incorrect for this situation?

Borek
Mentor
HH equation is derived just by rearranging dissociation constant definition (reaction quotient), so it holds for any acid. It just happens to be a form that makes buffer calculations easy.

Ok!