# What's the pH of a solution knowing only pKa, mass and volume? (no molecular mass known)

Is it possible to calculate the pH of a given solution knowing only the pKa (but not the structure of the acid, i. e. its molecular mass), its mass and the volume of the solution? E. g. What is the pH of a 400 ml solution with 9 g of mandelic acid (pKa = 3.39)? Suppose you don't know its structure or its molecular mass and you can't look it up online or someplace else. There's an online pH calculator that can do it (https://www.omnicalculator.com/chemistry/ph) where I only specified the pKa of the acid, the grams of acid in the solution and its volume but I don't know how the algorithm behind it works and I couldn't find anything else online.

• Once the name is available, calculating molecular weight is trivial. Look it up. There is no mysterious calculation.
– ACR
Commented Jan 31, 2023 at 1:26
• As I stated in the question body you cannot look it up online or someplace else. I didn't write the name of the acid in the website I used, only the pKa of the acid. I was wondering if there is a way of calculating the pH of the solution in the example only with the given data (pKa = 3.39, 400 ml, 9 g) and no extra knowledge. Commented Jan 31, 2023 at 1:30
• Can you post a screenshot, where you are entering this information? Just putting in pKa will not lead to the correct pH. You do need molar concentration.
– ACR
Commented Jan 31, 2023 at 1:38
• It seems the "custom" acid option in the calculator you linked has a molar mass default set to match $\ce{HCl's}$, since reverse-working the problem (using pH, Ka, V, m) leads to a molar mass of approximately $\pu{36.45g/mol}$. I don't believe it is possible to calculate pH with m, V, Ka alone. Commented Jan 31, 2023 at 2:33
• It cannot be done. With the same pKa, acid A with the molar mass 1/2 of molar mass of acid B would have pH at the same mass concentration lower by 0.15. Commented Jan 31, 2023 at 5:20

## 1 Answer

Unfortunately knowing only the pKa, the mass of the acid in the solution and the volume of the entire aqueous mixture it's not enough, one will always end up with an equation with two variables, which is impossible to solve. E. g. Assuming acid A and B have the same pKa, acid A with the molar mass 1/2 of molar mass of acid B would have pH at the same mass concentration lower by 0.15. Using the "custom" option the online pH calculator assumes a molar mass of 36.45 g/mol (identical to HCl's). I would like to thank everybody who took their time to read and comment this question.