Library / Solution chemistry, equilibria and kinetics / SCH-34
Solution chemistry, equilibria and kinetics
Distribution ratio of an extractable weak acid
Total-acid distribution ratio between organic and aqueous phases when only neutral HA enters the organic phase, from the partition coefficient KD of HA, the aqueous pH and the pKa.
- Ref
- SCH-34
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- D
If only the neutral acid HA crosses into the organic solvent, the total-acid distribution ratio is D = KD × (fraction of acid as HA in the water) = KD/(1 + 10^(pH − pKa)). D falls by a factor of ten for each pH unit above the pKa, so acids are extracted from acidic solutions and returned to water with base. The result excludes dimers, ion pairs and partition of the anion.
Total-acid distribution ratio between organic and aqueous phases when only neutral HA enters the organic phase, from the partition coefficient KD of HA, the aqueous pH and the pKa. D falls as the aqueous phase becomes more basic.
Calculator
- Neutral fraction of the acid in water, 1/(1 + 10^(pH − pKa))0.09091
- Recovery in one extraction at equal volumes, 100 D/(1 + D)64.52 %
- log₁₀ D0.2596
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 6 the distribution ratio is 1.818, so one extraction at equal volumes takes 64.52 % of the acid into the organic phase.
- Lowering the pH to about two units below the pKa would raise D to nearly KD = 20, which is how acids are pulled into the organic layer.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| KD Partition coefficient of neutral HA (organic/aqueous) | 0.01 to 100,000 | 9.091e-4 | 9,091 | 9,091 | +10% | +10 % |
| pKa pKa of the acid | 0 to 14 | 2e-5 | 20 | 20 | +10% | +164 % |
| pH Aqueous pH | 0 to 14 | 2e-8 | 20 | 20 | +10% | −73 % |
Sweep of Aqueous pH
| Aqueous pH | Distribution ratio |
|---|---|
| 0 | 20 |
| 1.75 | 19.99 |
| 3.5 | 19.39 |
| 5.25 | 7.199 |
| 7 | 0.198 |
| 8.75 | 0.003556 |
| 10.5 | 6.325e-5 |
| 12.25 | 1.125e-6 |
| 14 | 2e-8 |
Sweep one variable
Variables and how each one contributes
Distribution ratio
What the equation gives you. Everything else feeds it.
Partition coefficient of neutral HA (organic/aqueous)
The partition coefficient of neutral HA, organic over aqueous. Raises D in direct proportion. Raising it by 10 % (to 22) moves the result by +10 %, from 1.818 to 2.
Aqueous pH
The aqueous pH. A higher pH ionises more of the acid, so D falls. Raising it by 10 % (to 6.6) moves the result by −73 %, from 1.818 to 0.4901.
pKa of the acid
The pKa of the acid. A higher pKa keeps more acid neutral at the same pH, so D rises. Raising it by 10 % (to 5.5) moves the result by +164 %, from 1.818 to 4.805.
Worked example with the values above
- Ionisation term: 10^(pH − pKa) = 10^(6 − 5) = 10.
- Denominator: 1 + 10 = 11.
- D = 20 / 11 = 1.8182.
Assumptions and limits
- A 1:1 complex, or a single neutral species partitioning, with constants in concentration units.
- Equilibrium reached in each step, and no side reactions unless the conditional constant includes them.
Common mistakes
- Using the total ligand concentration for the free ligand when binding depletes it.
- Using the absolute EDTA constant at a pH where much of the EDTA is protonated.
- Mixing the units of the two phase volumes.
Statistics and uncertainty
Formation constants depend on the medium and the temperature, and a quoted constant for a different ionic strength can be off by a factor of two or more. Extraction results are sensitive to pH near the pKa.
Where it is used
- Designing complexometric titrations and metal-binding experiments.
- Planning solvent extractions and pH-controlled separations.
Maths you need
- Formation constant: Kf = [ML]/([M][L])
- Partition coefficient: the ratio of a species in two phases
- Mass balance: total equals free plus bound