Library / Solution chemistry, equilibria and kinetics / SCH-20
Solution chemistry, equilibria and kinetics
Fraction of indicator in its basic colour form
Fraction of a two-colour acid–base indicator present in its basic form at a given pH.
- Ref
- SCH-20
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- fIn⁻
For an indicator HIn ⇌ H⁺ + In⁻ the ratio of the two forms is set by the pH: [In⁻]/[HIn] = 10^(pH − pKIn). The fraction in the basic form is 1/(1 + 10^(pKIn − pH)), which is one half at pH = pKIn. The eye generally sees one colour when that form is about ten times the other, so the colour changes over about pKIn ± 1.
Fraction of a two-colour acid–base indicator present in its basic form at a given pH. It is 0.5 at pH = pKIn, and the eye sees a clear change over about one pH unit either side.
Calculator
- Fraction in the acid form, 1 − f0.09091
- Ratio [In⁻]/[HIn], 10^(pH − pKIn)10
- pH at which 90 % is in the basic form, pKIn + 0.9546.954 pH
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.
- At pH 7 the indicator is 90.91 % in its basic form and 9.091 % in its acid form, a ratio of 10.
- Pick an indicator whose pKIn is close to the pH at the equivalence point, so that the colour change falls within the steep part of the titration curve.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| pKIn pKa of the indicator | 0 to 14 | 1e-7 | 1 | 1 | +10% | −21.3 % |
| pH Solution pH | 0 to 14 | 1e-6 | 1 | 1 | +10% | +7.85 % |
Sweep of Solution pH
| Solution pH | Fraction in basic form |
|---|---|
| 0 | 1e-6 |
| 1.75 | 5.623e-5 |
| 3.5 | 0.003152 |
| 5.25 | 0.151 |
| 7 | 0.9091 |
| 8.75 | 0.9982 |
| 10.5 | 1 |
| 12.25 | 1 |
| 14 | 1 |
Sweep one variable
Variables and how each one contributes
Fraction in basic form
What the equation gives you. Everything else feeds it.
pKa of the indicator
The pKa of the indicator. A higher pKIn needs a higher pH for the same basic fraction, so the fraction falls. Raising it by 10 % (to 6.6) moves the result by −21.3 %, from 0.9091 to 0.7153.
Solution pH
The solution pH. A higher pH raises the basic fraction towards 1. Raising it by 10 % (to 7.7) moves the result by +7.85 %, from 0.9091 to 0.9804.
Worked example with the values above
- Exponent: pKIn − pH = 6 − 7 = −1; 10^(that) = 0.1.
- Denominator: 1 + 0.1 = 1.1.
- f = 1 / 1.1 = 0.90909.
Assumptions and limits
- A monoprotic weak acid and its conjugate base, both at appreciable concentration, in dilute solution.
- Constant volume, with concentration-based constants and negligible activity effects.
Common mistakes
- Adding the strong acid or base to the wrong component.
- Using a buffer more than about one pH unit from its pKa.
- Forgetting that the buffer ratio is of amounts in the same final volume.
Statistics and uncertainty
Buffer pH shifts with temperature, ionic strength and dilution, typically by 0.01 to 0.05 pH units, and the pKa itself carries an uncertainty of about 0.02 to 0.05.
Where it is used
- Preparing buffers and predicting their response to added acid or base.
- Choosing an indicator for a given pH range.
Maths you need
- Henderson–Hasselbalch equation: pH = pKa + log₁₀([A⁻]/[HA])
- Conjugate pair: a weak acid and its base
- Buffer capacity: the base needed per unit pH change