Library / Solution chemistry, equilibria and kinetics / SCH-15
Solution chemistry, equilibria and kinetics
Species fractions of a diprotic acid
Fraction of a diprotic acid present as H₂A at a given hydronium concentration h, from the stepwise constants K₁ and K₂.
- Ref
- SCH-15
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- α0
For a diprotic acid H₂A at hydronium concentration h, the fractions of the three forms are α₀ = h²/D, α₁ = K₁h/D and α₂ = K₁K₂/D, where D = h² + K₁h + K₁K₂, and α₀ + α₁ + α₂ = 1. This calculator returns α₀ for H₂A, with the other two in the derived rows. The fractions depend on pH alone, not on the total concentration.
Fraction of a diprotic acid present as H₂A at a given hydronium concentration h, from the stepwise constants K₁ and K₂. The fractions of HA⁻ and A²⁻ are in the derived rows, and the three add up to one.
Calculator
- Fraction as HA⁻, K₁h/D0.8333
- Fraction as A²⁻, K₁K₂/D0.08333
- Sum of the three fractions1
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 h = 1×10−5 mol/L the acid is 8.333 % H₂A, 83.33 % HA⁻ and 8.333 % A²⁻.
- The HA⁻ fraction peaks at pH = (pK₁ + pK₂)/2, where it is largest when the two constants are well separated.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| K1 First dissociation constant | 1e-10 to 1 | 9.091e-6 | 1 | 1 | +10% | −8.4 % |
| h Hydronium concentration | 1e-12 to 1 mol/L | 1e-14 | 0.9999 | 0.9999 | +10% | +9.92 % |
| K2 Second dissociation constant | 1e-14 to 0.1 | 9.999e-6 | 0.09091 | 0.0909 | +10% | −0.826 % |
Sweep of Hydronium concentration
| Hydronium concentration (mol/L) | Fraction as H₂A |
|---|---|
| 1e-12 | 1e-14 |
| 3.162e-11 | 1e-11 |
| 1e-9 | 9.99e-9 |
| 3.162e-8 | 9.693e-6 |
| 1e-6 | 0.004975 |
| 3.162e-5 | 0.2346 |
| 0.001 | 0.909 |
| 0.03162 | 0.9968 |
| 1 | 0.9999 |
Sweep one variable
Variables and how each one contributes
Fraction as H₂A
What the equation gives you. Everything else feeds it.
Hydronium concentration
The hydronium concentration, in mol/L. A higher h shifts the acid towards the fully protonated form H₂A, so α₀ rises. Raising it by 10 % (to 1.1×10−5) moves the result by +9.92 %, from 0.08333 to 0.0916.
First dissociation constant
The first dissociation constant (concentration form). A larger K₁ gives up the first proton more readily, so α₀ falls. Raising it by 10 % (to 1.1×10−4) moves the result by −8.4 %, from 0.08333 to 0.07634.
Second dissociation constant
The second dissociation constant (concentration form). A larger K₂ has only a small effect on α₀ unless it is close to K₁. Raising it by 10 % (to 1.1×10−6) moves the result by −0.826 %, from 0.08333 to 0.08264.
Worked example with the values above
- Terms: h² = 1×10−10, K₁h = 1×10−9, K₁K₂ = 1×10−10.
- Sum D = 1.2×10−9.
- α₀ = 1×10−10 / 1.2×10−9 = 0.083333.
Assumptions and limits
- Dilute solutions in which concentrations stand for activities, with constants on the concentration scale.
- No other acids, bases or dissolved gases such as CO₂ unless included.
Common mistakes
- Using pKa where Ka is needed, or the reverse.
- Using the Kw of 25 °C at other temperatures.
- Ignoring water autoionisation for acids below about 10⁻⁶ M.
Statistics and uncertainty
Acid constants change with ionic strength and temperature, so results are best to about 0.05 pH units even with accurate constants. Calibration of a pH electrode contributes about 0.02 pH.
Where it is used
- Calculating pH of dilute acids, salts and intermediate ions.
- Finding which species dominates at a given pH.
Maths you need
- pH: pH = −log₁₀ [H⁺]
- Acid dissociation constant: Ka = [H⁺][A⁻]/[HA]
- Water ion product: Kw = [H⁺][OH⁻]