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Lesson 42 · Concentration from pH
Undoing the logarithm
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Undoing the logarithm

Every machine in this room runs backwards. The pH came from a log, so the concentration comes back by ten-to-the-power: [H+]=10−pH[\mathrm{H^+}] = 10^{-\mathrm{pH}} — read aloud: H-plus equals ten to the minus pH. pH 4 means 1×10−4 mol/L1 \times 10^{-4}\ \mathrm{mol/L}; the pH was the exponent all along, wearing its coat inside out.

Keep the minus on BOTH trips. Ten to the PLUS pH climbs the wrong way — it would say acids strengthen as pH rises, and every lemon disagrees. Sanity rail: higher pH, SMALLER [H+][\mathrm{H^+}]. If a mild sample hands you a concentration above 1 mol/L, the sign fell off in transit.

pH[H+]

pH=−log⁡10 [H+]\mathrm{pH} = -\log_{10}\,[\mathrm{H^+}]

  • pH\mathrm{pH}= pH
  • [H+][\mathrm{H^+}]= Hydrogen ion concentration (molar concentration)
pH from Hydrogen Ion Concentration solver →