Polyprotic Acid pH Calculator
Diprotic pH from Ka₁, solved exactly rather than approximated.
Work out Polyprotic Acid pH. Diprotic pH from Ka₁, solved exactly rather than approximated. Free, with no account and nothing to download.
Carbonic acid 4.3e-7, sulfurous 1.5e-2, phosphoric 7.5e-3.
Carbonic 4.7e-11, sulfurous 6.3e-8, phosphoric 6.2e-8.
pH
3.68
The second proton is negligible — Ka₂ is far below Ka₁
For nearly every polyprotic acid the first ionisation determines the pH on its own, because each successive proton is far harder to remove than the last — pulling a positive charge off an already-negative ion. Carbonic acid's Ka₂ is ten thousand times smaller than its Ka₁. The first ionisation here is solved exactly from the quadratic rather than assuming the change is small. That assumption fails badly for acids with a large Ka₁, such as sulfurous, where it can overstate the hydronium concentration substantially. Sulfuric acid is the exception to the whole pattern: its first proton is strong, fully dissociating, so it needs different treatment entirely.
How the Polyprotic Acid pH Calculator works
Enter the concentration and both dissociation constants. The first ionisation is solved from the quadratic rather than assuming the change is small, and the page then says explicitly whether the second proton contributes enough to bother with.
Also known as: diprotic acid ph calculator · ka1 ka2 calculator · ph of carbonic acid · phosphoric acid ph calculator
Frequently asked questions
How do I find the pH of a polyprotic acid?
Almost always from Ka₁ alone. Each successive proton is far harder to remove, so the first ionisation dominates — carbonic acid's Ka₂ is ten thousand times smaller than its Ka₁.
Why is the second proton so much harder to remove?
Because you are pulling a positive hydrogen ion away from an already-negative ion, which is electrostatically unfavourable. That is why Ka₂ is typically 10⁴ to 10⁵ times smaller than Ka₁.
When does the approximation fail?
When Ka₁ is large enough that a meaningful fraction of the acid ionises. Assuming x is small then overstates the hydronium concentration, which is why this page solves the quadratic exactly instead.
Why is sulfuric acid different?
Because its first proton is strong and dissociates completely, so it is not a weak acid at all in the first step. It needs to be treated as a strong acid contributing one proton, plus a weak acid for the second.
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