pH and buffers
The exact pH of any mixture of acids, bases and salts, what to weigh out for a buffer, and the titration curve with its equivalence points.
Result
Species at pH 2.88
| Species | mol/L | Fraction |
|---|---|---|
| Acetate · pKa 4.76 | ||
| CH3COOH | 0.0986 | 98.6 % |
| CH3COO− | 1.37 × 10⁻³ | 1.37 % |
| Water | ||
| H+ | 1.37 × 10⁻³ | |
| OH− | 7.92 × 10⁻¹² | |
Speciation
- CH3COOH
- CH3COO−
Details
- pOH
- 11.119
- pH, more digits
- 2.8810
- pH without activity correction
- 2.881−log[H⁺], ionic strength ignored
- Ionic strength
- 1.37 × 10⁻³ mol/L
- Activity coefficient, singly charged ion
- 0.959
- Buffer capacity β
- 6.27 × 10⁻³ mol L⁻¹ pH⁻¹
- Ion product of water
- Kw = 1.0 × 10⁻¹⁴ at 25 °C
- Charge balance residual
- 1.08 × 10⁻¹⁸ mol/L
Recipe
1 L · 100 mM · pH 7.40- 2.777 gSodium dihydrogen phosphate monohydrateNaH2PO4·H2O · 137.99 g/mol · 20.13 mmol
- 11.34 gDisodium hydrogen phosphateNa2HPO4 · 141.96 g/mol · 79.87 mmol
Dissolve in about 800 mL of water, check the pH with a calibrated meter at 25 °C, then make up to 1 L.
Phosphate species
- H3PO4
- H2PO4−
- HPO42−
- PO43−
Details
- Check: full equilibrium of this recipe
- pH 7.400solved again from the amounts above
- Sodium dihydrogen phosphate
- 20.126 mmol20.13 mM in the final solution
- Disodium hydrogen phosphate
- 79.874 mmol79.87 mM in the final solution
- All pKa values
- 2.15, 7.20, 12.35
- d pKa / dT
- −0.0021 K⁻¹from ΔrH° = 3.60 kJ/mol; at 4 °C the pKa is about 7.24, at 37 °C about 7.17
- Activity correction
- Davies, target is the activity pH
Titration curve
0.1 M NaOH into 25 mL of 0.1 M acetic acidKey points
| Point | Titrant, mL | pH |
|---|---|---|
| Start | 0.00 | 2.88 |
| Half-equivalencepKa 4.76 | 12.50 | 4.68 |
| Equivalence pointThymol blue (8.0–9.6, yellow to blue) or Phenolphthalein (8.2–10.0, colourless to pink) | 25.00 | 8.64 |
Details
- Jump at equivalence point 1
- 3.94 pH unitsbetween 99 % and 101 % of 25.00 mL
- Curve
- 537 points, 0 to 40.00 mLvolumes solved exactly for each pH, dilution included
How the pH is calculated
Every species of every acid and base in the solution is written as a fraction of its total concentration, and the pH is the one value at which the positive and negative charges balance exactly, water's own H+ and OH− included. No approximation such as Henderson–Hasselbalch or "neglect x against c" is made, which is why 10−8 M HCl comes out at pH 6.98 and not 8. The balance is solved by a bracketed Newton iteration between pH −1 and 15 with Kw = 1.0 × 10−14.
Buffer recipes run the same balance backwards: the target pH fixes every species, and the charge balance then says how much of each reagent is needed. The recipe is then solved forwards again as a check. Titration curves solve for the titrant volume at each pH, with dilution included, so steep jumps are drawn with as many points as flat buffer regions. Equivalence points are the stoichiometric volumes; the indicator suggested for each is one whose colour change spans the equivalence pH.
Activity correction
On by default, so the pH is −log a(H+), what a calibrated pH meter reads, and a buffer recipe reads its target pH on the meter. Activity coefficients follow the Davies equation, log γ = −0.509 z2 (√I / (1 + √I) − 0.3 I) at 25 °C, with the ionic strength I solved together with the pH. Switched off, the pH is −log[H+], the number textbook exercises work with. The difference matters for salts and concentrated buffers: 0.05 M Na2HPO4 is pH 9.27 with activities and 9.69 by concentrations, and 100 mM sodium phosphate at pH 7.4 needs NaH2PO4 and Na2HPO4 close to 20 : 80 rather than the 39 : 61 that concentrations alone give.
Where the constants come from
All pKa values are for 25 °C and zero ionic strength, from the CRC Handbook of Chemistry and Physics. Buffer substances, phosphate, carbonate, borate, sulfate, citrate and the other entries covered there come from its table of thermodynamic quantities for the ionization of buffers (Goldberg, Kishore and Lennen, J. Phys. Chem. Ref. Data 31, 231, 2002), which also gives the reaction enthalpies used for the temperature coefficient d pKa/dT. Other organic acids and bases come from the Handbook's table of dissociation constants of organic acids and bases, and HF, HCN, HOCl, HNO2, H2S and hydroxylamine from its table of inorganic acids and bases. Indicator ranges and colours are from its table of acid-base indicators. The densities of glacial acetic acid (1.0446 g/mL, 25 °C) and formic acid (1.220 g/mL, 20 °C) are from CAS Common Chemistry. Molar masses are summed from IUPAC standard atomic weights.
Where the numbers stop being reliable
- Dilute aqueous solutions at 25 °C. Above an ionic strength of about 0.5 M neither the tabulated pKa values nor the Davies equation hold, and the tool says so.
- Temperature changes pKa: Tris drops by about 0.028 per °C, so a Tris buffer set to pH 8.0 at 25 °C reads near 8.6 at 4 °C. The recipe details give the coefficient for each buffer.
- PIPES has a second, strongly acidic proton that the table does not list. It is counted as fully released, which holds above pH 5, the whole range where PIPES buffers.
- Carbonate buffers exchange CO2 with air, borate at high concentration forms polyborates, and metal ions that bind the buffer (citrate, phosphate) shift the pH. None of this is modelled.
- Strong acids and bases are taken as fully dissociated, H2SO4 in its first step only.