Species Distribution vs pH
Chemical context
Species distribution indicates which protonation state dominates at a specific pH. In polyprotic systems, equilibrium shifts stepwise with pKa values.
\[ \alpha_i = \frac{c_i}{C_T} \]
Fractions \(\alpha_i\) are dimensionless and always sum to 1. This is useful for buffer design, separations, and selecting reaction windows in analytical workflows.
Formulas (MathJax)
\[ K_{a,i}=10^{-\mathrm{p}K_{a,i}},\quad [H^+]=10^{-\mathrm{pH}} \]
\[ \alpha_0+\alpha_1+\alpha_2(+\alpha_3)=1 \]
\[ \text{Diprotic: }D=[H^+]^2+K_{a1}[H^+]+K_{a1}K_{a2} \]
\[ \alpha_0=\frac{[H^+]^2}{D},\;\alpha_1=\frac{K_{a1}[H^+]}{D},\;\alpha_2=\frac{K_{a1}K_{a2}}{D} \]
\[ \text{Triprotic: }D=[H^+]^3+K_{a1}[H^+]^2+K_{a1}K_{a2}[H^+]+K_{a1}K_{a2}K_{a3} \]
\[ \alpha_0=\frac{[H^+]^3}{D},\;\alpha_1=\frac{K_{a1}[H^+]^2}{D},\;\alpha_2=\frac{K_{a1}K_{a2}[H^+]}{D},\;\alpha_3=\frac{K_{a1}K_{a2}K_{a3}}{D} \]
Symbol legend
- \(\alpha_i\): mole fraction of species i
- \(c_i\): concentration of species i [mol/L]
- \(C_T\): total concentration of all species [mol/L]
- \([H^+]\): proton concentration [mol/L]
- \(K_{a1},K_{a2},K_{a3}\): stepwise acid dissociation constants
- \(\mathrm{p}K_{a1},\mathrm{p}K_{a2},\mathrm{p}K_{a3}\): negative decimal logarithms of \(K_a\)
- \(D\): normalization denominator of distribution functions
Detailed examples
Example 1 (diprotic near pKa2):
When pH is close to pKa2, \(\alpha_1\) and \(\alpha_2\) are often comparable. The transition between \(\mathrm{HA^-}\) and \(\mathrm{A^{2-}}\) is most pronounced.
When pH is close to pKa2, \(\alpha_1\) and \(\alpha_2\) are often comparable. The transition between \(\mathrm{HA^-}\) and \(\mathrm{A^{2-}}\) is most pronounced.
Example 2 (acidic region):
If pH is much lower than pKa1, the more protonated form dominates (e.g., H₂A or H₃A), relevant for extraction and separation conditions.
If pH is much lower than pKa1, the more protonated form dominates (e.g., H₂A or H₃A), relevant for extraction and separation conditions.
Example 3 (triprotic near neutral pH):
For systems like phosphate, an intermediate species can dominate around neutral pH, explaining characteristic buffering behavior.
For systems like phosphate, an intermediate species can dominate around neutral pH, explaining characteristic buffering behavior.
Example 4 (absolute concentrations):
With \(C_T\), fractions convert directly to absolute concentrations through \(c_i=\alpha_iC_T\), enabling quantitative distribution assessment.
With \(C_T\), fractions convert directly to absolute concentrations through \(c_i=\alpha_iC_T\), enabling quantitative distribution assessment.
Deeper insight
Dominant-species window
Dominant species gives a practical criterion for selecting pH windows for reactions, complexation, and separation workflows.
Activities vs concentrations
At elevated ionic strength, activities deviate from concentrations. For high-accuracy work, activity corrections may shift effective pKa positions and distribution profiles.
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