# pH value of a strong acid, and why

I've been experimenting with random things on the material of pH in a matter of the ones that we consider "strong" acids and bases. I've been told in my school that the way to find $$\ce{[H+]}$$ is given by multiplying [molarity of the acid/base] · [n], where $$n$$ is the number of hydrogen atoms in the acid. I'm trying to play around with calculating values of $$\mathrm{pH}$$ when I stumble upon using sulfuric acid. So, I'm trying to find the molarity of it while only knowing $$\mathrm{pH}$$, but I come into a problem. I've tried to find the molarity of the acid by knowing that $$\mathrm{pH} = 3 - \log(5)$$. My attempt is at follows:

• It's clear that $$\ce{[H+]} = \pu{5E-3 M}$$.
• $$n = 2$$.
• The molarity should just be $$\pu{5E-3 M}/2 = \pu{2.5E-3 M}$$.

However, I checked a few calculators with this molarity and I was off by $$0.3$$ which is a bit much in terms of $$\mathrm{pH}$$. And, it turns out that if I tried the first molarity ($$\pu{5E-3 M}$$) it gives me the answer. My question here is:

Why do I not need to divide by $$2$$ here? Shouldn't the value of $$n$$ be $$2$$ and therefore I had to divide by 2? I prefer to be given an answer that doesn't tell me 100% the answer, but rather makes me discover it myself. However, it's okay if you decide to give the full answer.

Note: The calculator isn't asking the value of $$\ce{[H+]}$$. I've tested this with other values and I indeed had to divide by the $$n$$ to get the supposed answer. Perhaps it's just a sulfuric acid thing?

• Consider that sulfuric acid has two different pKa's Feb 12 at 12:54
• Ah, I see so do you mean that there could be 2 different pH values? Feb 12 at 13:20
• $\ce{H2SO4}$ is a strong acid, but $\ce{HSO4-}$ is not, so the ratio of molar amount of H+(aq) and initial $\ce{H2SO4}$ amount depends on pH, in contrary to $\ce{HCl}$ solution. Feb 12 at 14:59
• no, there can only be one pH value for a given solution, since it is a function only of [H+]. Since you asked for guidance to discover the answer, I suggest you read up on what a pKa is and then about the Henderson-Hasselbalch equation. In your system, the molarity of "sulfuric acid" is the sum of three concentrations - [$\ce{HSO4-}$] + [$\ce{H2SO4}$] + [$\ce{SO4^2-}$]. The pKa's and pH can be used to determine the relative concentrations of each. Feb 13 at 12:38