Library / Foundations: Chemistry / FCH-31
Foundations: Chemistry
pH after mixing a strong acid and a strong base
pH of the mixture of a strong acid and a strong base at 25 °C, from the concentration of the reagent in excess.
- Ref
- FCH-31
- Rev
- v1
- Field
- Foundations: Chemistry
- Result
- pH
After mixing a strong acid and a strong base, the pH comes from the excess that remains. If acid is left over, [H⁺] = cexcess and pH = −log₁₀ cexcess. If base is left over, [OH⁻] = cexcess, pOH = −log₁₀ cexcess and pH = 14 − pOH at 25 °C. If the two are equal in amount, the solution is neutral, pH 7. Very close to the equivalence point the auto-ionisation of water matters and this simple calculation is only approximate.
pH of the mixture of a strong acid and a strong base at 25 °C, from the concentration of the reagent in excess. At exact equivalence the pH is 7 for a neutral salt, and the logarithm of zero is not taken.
Calculator
- Excess concentration0.01111 mol/dm³
- Net moles left (acid minus base; positive means acid in excess)0.5 mmol
- Volume of this base needed to neutralise the acid exactly25 cm³
- pOH, 14 − pH12.05
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With 25 cm³ of 0.1 M acid and 20 cm³ of 0.1 M base, acid is left over and the pH is 1.954.
- The pH changes very steeply close to the equivalence volume (25 cm³ of this base): a fraction of a cm³ moves it by several pH units, which is why an indicator or meter is needed to find the end point.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| cA Concentration of the strong acid | 0.001 to 2 mol/dm³ | −0.02803 | 12.64 | 12.67 | +10% | −9.01 % |
| cB Concentration of the strong base | 0.001 to 2 mol/dm³ | 1.259 | 13.92 | 12.66 | +10% | +11.4 % |
| VA Volume of the acid | 1 to 200 cm³ | 1.087 | 12.96 | 11.87 | +10% | −7.81 % |
| VB Volume of the base | 1 to 200 cm³ | 1.035 | 12.89 | 11.86 | +10% | +12.3 % |
Sweep of Volume of the base
| Volume of the base (cm³) | pH of the mixture |
|---|---|
| 1 | 1.035 |
| 25.88 | 11.24 |
| 50.75 | 12.53 |
| 75.63 | 12.7 |
| 100.5 | 12.78 |
| 125.4 | 12.82 |
| 150.3 | 12.85 |
| 175.1 | 12.88 |
| 200 | 12.89 |
Sweep one variable
Variables and how each one contributes
pH of the mixture
What the equation gives you. Everything else feeds it.
Concentration of the strong acid
The concentration of the acid, in mol/dm³. Lowers the pH in either region: more acid means more acid left over, or less base left over. Raising it by 0.01 (to 0.11) moves the result by −9.01 %, from 1.954 to 1.778.
Volume of the acid
The volume of acid, in cm³. Lowers the pH in either region: more acid means more acid left over, or less base left over. Raising it by 5 cm³ (to 30 cm³) moves the result by −13.1 %, from 1.954 to 1.699.
Concentration of the strong base
The concentration of the base, in mol/dm³. Raises the pH in either region: more base neutralises more acid, or leaves more base over. Raising it by 0.01 (to 0.11) moves the result by +11.4 %, from 1.954 to 2.176.
Volume of the base
The volume of base, in cm³. Raises the pH in either region: more base neutralises more acid, or leaves more base over. Raising it by 2 cm³ (to 22 cm³) moves the result by +12.3 %, from 1.954 to 2.195.
Worked example with the values above
- Excess: |2.5 − 2| = 0.5 mmol in 45 cm³, so cexcess = 0.01111 mol/dm³ of acid.
- Acid is left, so [H⁺] = 0.01111 mol/dm³.
- pH = 1.954.
Assumptions and limits
- A strong monoprotic acid and a strong monobasic base, each fully dissociated.
- Volumes add on mixing, and the temperature is 25 °C so that Kw = 10⁻¹⁴.
- The excess is well above 10⁻⁶ mol/dm³; below that, the auto-ionisation of water cannot be ignored.
Common mistakes
- Forgetting that for excess base the pH is found from pOH: pH = 14 − pOH, not −log₁₀ of the base concentration.
- Ignoring the added volume.
- Applying it to a weak acid or base.
Statistics and uncertainty
The pH is logarithmic, so errors in the excess count less than they seem: a 10 % error in the excess changes the pH by only 0.04. Near equivalence the excess itself is the difference of two large numbers and is the real source of error.
Where it is used
- The pH of a mixture or of a titration at a given volume of base.
- Choosing the volume of neutraliser to bring an effluent into range.
Maths you need
- Moles: concentration times volume
- Neutralisation: H⁺ + OH⁻ → H₂O, one mole for one mole
- pH scale: pH = −log₁₀[H⁺]