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pH, pOH and Concentration Rules

Dec 1, 2025

Overview

These notes summarize formulas and steps for calculating pH, pOH, acid concentration, and base concentration, including significant figure rules.

Question 1: Given Acid Concentration → Find pH, pOH, [Base]

  • We are given an acid concentration and must find pH, pOH, and base concentration.
  • All answers must follow specific significant figure rules for pH and pOH.

Steps and Formulas Used

  • To find pH from acid concentration:
    • Use formula: pH = −log[H⁺]
    • Plug in the given acid concentration as [H⁺].
  • Significant figures for pH and pOH:
    • The number of significant figures in [H⁺] or [OH⁻] equals the number of decimal places in pH or pOH.
    • Example: 2 significant figures in concentration → pH = 3.39 (two decimal places).
  • To find pOH from pH:
    • Use formula: pH + pOH = 14.00
    • Rearrange: pOH = 14.00 − pH
    • Example: pH = 3.39 → pOH = 10.61 (two decimal places).
  • To find base concentration from pOH:
    • Use formula: pOH = −log[OH⁻]
    • Rearranged: [OH⁻] = 10^(−pOH)
    • On calculator: press 2nd, then log, then enter exponent −10.61.
    • Round [OH⁻] to same number of significant figures as original acid concentration.
    • Example result: [OH⁻] = 2.5 × 10⁻¹¹ M (2 significant figures, units of molarity).

Structured Summary for Question 1

GivenFindMain FormulaCalculator StepSig Fig Rule Applied
[H⁺]pHpH = −log[H⁺]log of [H⁺], change signSig figs in [H⁺] = decimal places in pH
pHpOHpH + pOH = 14.0014.00 − pHpOH has same decimal places as pH
pOH[OH⁻][OH⁻] = 10^(−pOH)2nd log, exponent −pOHSig figs in [H⁺] → sig figs in [OH⁻]

Question 2: Given pH → Find [Acid], [Base], pOH

  • We are given pH and must find acid concentration, base concentration, and pOH.
  • Significant figure rules now depend on decimal places in pH.

Part A: Find Acid Concentration from pH

  • From pH to acid concentration:
    • pH = −log[H⁺] → [H⁺] = 10^(−pH)
    • On calculator: press 2nd, then log, then enter exponent −8.5.
    • The result is the acid concentration [H⁺].
  • Significant figures when going pH → [H⁺]:
    • Number of decimal places in pH equals number of significant figures in [H⁺].
    • Example: pH = 8.5 (1 decimal place) → [H⁺] has 1 significant figure.

Part B: Find Base Concentration from Acid Concentration

  • Use relationship between [H⁺] and [OH⁻]:
    • [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (Kw at 25 °C, implied).
    • Rearranged: [OH⁻] = (1.0 × 10⁻¹⁴) / [H⁺]
    • Plug in acid concentration found in Part A.
  • Round base concentration:
    • Round [OH⁻] to same number of significant figures as [H⁺].
    • For this question, rounded to one significant figure.

Part C: Find pOH (Two Methods)

  • Method 1: From base concentration
    • pOH = −log[OH⁻]
    • Plug in [OH⁻] from Part B.
  • Method 2: From pH
    • pH + pOH = 14.00
    • Rearrange: pOH = 14.00 − pH
    • Example: pOH = 14.00 − 8.5 → same pOH as Method 1.
  • Both methods give the same pOH value when done correctly.

Structured Summary for Question 2

GivenFindMain FormulaCalculator StepSig Fig Rule Applied
pH[H⁺][H⁺] = 10^(−pH)2nd log, exponent −pHDecimal places in pH = sig figs in [H⁺]
[H⁺][OH⁻][H⁺][OH⁻] = 1.0 × 10⁻¹⁴Divide 1.0 × 10⁻¹⁴ by [H⁺]Sig figs in [H⁺] = sig figs in [OH⁻]
[OH⁻]pOHpOH = −log[OH⁻]log of [OH⁻], change signDecimal places in pOH follow sig fig rule from [OH⁻]
pHpOHpH + pOH = 14.0014.00 − pHDecimal places in pOH match decimal places in pH when using this relationship

Formula Summary and When to Use Each

  • From acid concentration to pH:
    • Use pH = −log[H⁺] when [H⁺] (acid concentration) is given.
  • From pH to acid concentration:
    • Use [H⁺] = 10^(−pH) when pH is given and [H⁺] is needed.
  • From base concentration to pOH:
    • Use pOH = −log[OH⁻] when [OH⁻] (base concentration) is given.
  • From pOH to base concentration:
    • Use [OH⁻] = 10^(−pOH) when pOH is given and [OH⁻] is needed.
  • Between pH and pOH:
    • Use pH + pOH = 14.00 when one is given and the other is unknown.
  • Between acid and base concentrations:
    • Use [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ to convert between [H⁺] and [OH⁻].

Formula Use Table

Start WithWantFormula to Use
[H⁺] (acid concentration)pHpH = −log[H⁺]
pH[H⁺][H⁺] = 10^(−pH)
[OH⁻] (base concentration)pOHpOH = −log[OH⁻]
pOH[OH⁻][OH⁻] = 10^(−pOH)
pHpOHpH + pOH = 14.00
pOHpHpH = 14.00 − pOH
[H⁺][OH⁻][H⁺][OH⁻] = 1.0 × 10⁻¹⁴
[OH⁻][H⁺][H⁺] = (1.0 × 10⁻¹⁴) / [OH⁻]

Key Terms & Definitions

  • pH:
    • Negative logarithm of hydrogen ion concentration, pH = −log[H⁺].
  • pOH:
    • Negative logarithm of hydroxide ion concentration, pOH = −log[OH⁻].
  • Acid concentration [H⁺]:
    • Molar concentration of hydrogen ions in solution, measured in molarity (M).
  • Base concentration [OH⁻]:
    • Molar concentration of hydroxide ions in solution, measured in molarity (M).
  • Significant figures for pH/pOH:
    • Number of digits after decimal point equals number of significant figures in corresponding [H⁺] or [OH⁻].

Action Items / Next Steps

  • Practice converting between pH, pOH, [H⁺], and [OH⁻] using the listed formulas.
  • Remember and apply the specific significant figure rules for pH, pOH, and concentrations.
  • Use the relationships consistently to check answers by working problems in reverse directions.

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