I am unsure if I am doing this right.

Question

The question is: Aspirin (acetylsalicylic acid) can cause stomach bleeding. Only the acid form can cross the stomach lining. Determine the ratio of base to its conjugate acid when the stomach pH=2.00. Ka aspirin = 2.75x10^-5.

I used pH = pKa - log([HA]/[A])
pKa = -logKa
= -log(2.7x10^-5)
=4.56

2.0 = 4.56 + log(2.00/2.7x10^-5)
2.0 = 9.43
divide both by 2.0 and got 4.715

Is this right?

Answer 1

I didn't check the arithmetic but you started with the correct equation although I prefer pH = pKa + log (A^-/HA)
It appears to me that you didn't substitute correctly for HA/A. You apparently substitute pH and Ka for that fraction. What you want to do is to solve for the fraction; i.e.,
pH = pKa + log [(A^-)/(HA)]
2.00 = 4.56 + log base/acid
2.00-4.56 = log base/acid
-2.56 = log (base/acid)
Solve for base/acid which is (A^-)/(HA)