What is the pH of sulfuric acid?

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What is the pH of sulfuric acid?
Sulfuric acid can not be defined by a single pH, and can only have a pH as such when it is in a solution of water, where the pH is a measure of the hydrogen ion concentration: pH=-log10(H+) which occurs from dissociation.

The pH of sulfuric acid in water, and any other acid in water, for that matter depends upon its concentration (moles of the acid per litre of the acid/water mixture, where 1 mol is the amount of pure substance containing the same number of chemical units as there are atoms in exactly 12 grams of carbon-12). We usually say that 'X' mol L-1 of a substance has a pH of 'Y'.
For the case of sulfuric acid, first consider its dissociation. Sulfuric acid is diprotic, meaning that it has 2 ionizable hydrogen atoms per molecule and dissociates in a 2-step process:
H2SO4 H+(aq) + HSO4−(aq)
The second step in dissociation is:
HSO4− H+(aq) + SO42−(aq)

The dissociation is not as straightforward as it may appear since the completeness of the dissociation in each case is governed by Ka values (dissociation constants), which are different for each step: one proton is a strong acid and dissociates completely (i.e., dissociation in the first step is complete), and the other is a weak acid and does not (i.e., dissociation in the second step is not complete). Without going in to unnecessary detail (which only a chem major would need to worry about), we'll assume that dissociation in the second step is negligible, and hence we consider one H+ in our calculation of pH.

X mol L-1 H2SO4 therefore produces X mol L-1 H+.
The pH of X mol L-1 H2SO4 is therefore:
pH = -log10(X)
Hence, if we have, for example, a 0.2 mol L-1 H2SO4 solution, it has a pH of -log10(0.2)=0.7. A higher concentration of sulfuric acid will have an even lower pH.
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