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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?

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    $\begingroup$ Consider that sulfuric acid has two different pKa's $\endgroup$
    – Andrew
    Feb 12 at 12:54
  • $\begingroup$ Ah, I see so do you mean that there could be 2 different pH values? $\endgroup$ Feb 12 at 13:20
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    $\begingroup$ $\ce{H2SO4}$ 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. $\endgroup$
    – Poutnik
    Feb 12 at 14:59
  • $\begingroup$ 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. $\endgroup$
    – Andrew
    Feb 13 at 12:38

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