Free tool
Convert between [H3O+], [OH-], pH and pOH, or find the pH of a strong acid, a strong base, a weak acid or a weak base. Weak acids are solved with the exact quadratic, and the tool tells you whether the 5% shortcut would have held.
Built for General Chemistry IIScientific notation works: type 1.8e-5 for 1.8 x 10^-5.
All results assume 25 °C, where Kw = 1.0 x 10^-14 and pH + pOH = 14.00.
Enter a value to see the pH.
pH problems get fast once the setup is automatic. Encodr keeps Ka, Kw and the ICE setup on a spaced-repetition schedule so they stick through the final.
Get started freepH = -log[H3O+], pOH = -log[OH-], and at 25 °C
[H3O+][OH-] = Kw = 1.0 x 10^-14, so pH + pOH = 14.00.
Strong acids and bases ionize completely, so [H3O+] is the acid concentration and [OH-] is the base concentration times the number of OH- per formula unit. 0.010 M HCl has pH 2.00.
Weak acids ionize only partly. With x = [H3O+], the ICE table gives
Ka = x^2 / (C - x). The exact answer is x = (-Ka + sqrt(Ka^2 + 4 Ka C)) / 2. The shortcut
drops the x in C - x, giving x = sqrt(Ka C), and is accepted when x is under 5% of C.
Worked example: 0.10 M acetic acid, Ka = 1.8 x 10^-5. The shortcut gives x = sqrt(1.8 x 10^-6) = 1.34 x 10^-3 M, pH 2.87, which is 1.3% of 0.10 M, so the shortcut holds. The exact quadratic gives x = 1.33 x 10^-3 M and pH 2.88. For 0.10 M H3PO4 (Ka1 = 7.5 x 10^-3) the shortcut would be 27% of C, so only the quadratic answer, pH 1.62, is acceptable. The full walkthrough is in how to calculate pH for strong and weak acids, and the whole course is in the free General Chemistry II deck.
Limits: this tool treats every acid as monoprotic. For weak acids and bases it ignores water's own H3O+ and OH-, as the course does. For very dilute strong acids and bases (below about 10^-6 M) it includes them, which is why 1.0 x 10^-8 M HCl comes out slightly acidic (pH 6.98), not pH 8.
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