Calculator of Alexandria

pH, pOH, [H⁺] and [OH⁻] calculator

Convert between pH, pOH, hydrogen ion and hydroxide concentration at 25 °C, with the logarithms explained.

I know the
pH
pOH
[H⁺]
M
[OH⁻]
M

Formula

pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]
How it's derived

The formula

pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+] pOH=−log⁡10[OH−]\text{pOH} = -\log_{10}[\text{OH}^-] pH+pOH=14.00\text{pH} + \text{pOH} = 14.00

Square brackets mean concentration in mol/L. The last equation holds at 25 °C.

Where it comes from

Hydrogen ion concentrations in water span more than 14 powers of ten, from about 1 M in strong acid to 10−1410^{-14} M in strong base. In 1909 the chemist Søren Sørensen proposed using the exponent instead. The minus sign makes everyday values positive. So [H+]=10−4.5[\text{H}^+] = 10^{-4.5} M becomes pH 4.5.

Water itself splits slightly into ions:

H2O⇌H++OH−\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-

At equilibrium the product of the two concentrations is a constant, KwK_w, equal to 1.0×10−141.0 \times 10^{-14} at 25 °C:

[H+][OH−]=1.0×10−14[\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}

Taking −log⁡10-\log_{10} of both sides turns the product into a sum, which is where pH+pOH=14\text{pH} + \text{pOH} = 14 comes from. Pure water has equal amounts of each, 10−710^{-7} M, which is why neutral is pH 7.

Worked example

A dilute acid with [H+]=0.25[\text{H}^+] = 0.25 mM, which is 2.5×10−42.5 \times 10^{-4} M:

pH=−log⁡10(2.5×10−4)=3.60\text{pH} = -\log_{10}(2.5 \times 10^{-4}) = 3.60 pOH=14−3.60=10.40\text{pOH} = 14 - 3.60 = 10.40 [OH−]=10−10.40=4.0×10−11 M[\text{OH}^-] = 10^{-10.40} = 4.0 \times 10^{-11}\ \text{M}

Watch out for

  • Each pH unit is a factor of ten. pH 3 is ten times more acidic than pH 4, not a little more.
  • Temperature. KwK_w grows with temperature. At 37 °C, neutral water is about pH 6.8, and the 14.00 sum no longer holds.
  • Concentration vs activity. Strictly, pH uses ion activity. In concentrated solutions (above roughly 0.1 M) a measured pH can differ from this calculation.

Sources

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