Degree of dissociation

The dimensionless degree of dissociation α (also protolysis called grad) is the ratio of the dissociated acid or base particles for the formal initial concentration of undissociated acid or base in an aqueous solution of. The degree of dissociation of an acid or base depends on its acid constant (or base constant ), its concentration and the existing pH value of a solution. If there is only one acid or base in a solution, the degree of dissociation can be determined experimentally from the electrolytic conductivity of the solution. If the pH value of a solution is known, the degree of dissociation can be estimated by calculation .

The degree of dissociation can assume values ​​between 0 and 1.

Monoprotonic acids HA

Degree of dissociation α
as a function of the concentration ( logarithmic scale )
of a)  HCl , b)  HNO ₃ , c)  HClO ₂ , d)  HF , e)  HOAc , f)  HClO , g)  HCN

For a one protonic acid  HA with the formal starting concentration c ₀ , which dissociates according to the equation

${\displaystyle \mathrm {HA+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{-}} ,}$

applies:

${\displaystyle \alpha ={\frac {[\mathrm {A^{-}} ]}{c_{0}}}}$

${\displaystyle \alpha }$thus indicates the relative proportion of dissociated acid, c ₀ the initial concentration of the undissociated acid.

The definition of a degree of dissociation for bases is not specifically required because it is already contained in. ${\displaystyle \alpha }$

The degree of association ( " degree of formation ") the relative proportion of non- dissociated acid, is given by: ${\displaystyle \alpha ',}$

${\displaystyle \alpha '={\frac {[\mathrm {HA} ]}{c_{0}}}=1-\alpha .}$

The combination of the law of mass action for the protolysis equilibrium

${\displaystyle K_{\mathrm {s} }={\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )}}}$

(K _S is the acid constant , which is a measure of the acid strength )
with the conservation of mass of the acid in the solution

${\displaystyle {\begin{aligned}\![\mathrm {A^{-}} ]+[\mathrm {HA} ]&=c_{0}\\\Leftrightarrow \alpha \!\ +\alpha '&=1\end{aligned}}}$

leads to the following expression for the degree of dissociation:

${\displaystyle \Rightarrow \alpha =\!\ {\frac {K_{\mathrm {S} }}{[\mathrm {H_{3}O^{+}} ]+K_{\mathrm {S} }}}.}$

The equation shows that the degree of dissociation of a certain acid with a known p K _s value only depends on the pH value of the solution. It can be transformed into:

${\displaystyle {\begin{aligned}\Leftrightarrow [\mathrm {H_{3}O^{+}} ]&=\!\ K_{\mathrm {S} }\cdot {\frac {1-\alpha }{\alpha }}\\\Leftrightarrow \mathrm {pH} &=\!\ \mathrm {p} K_{\mathrm {S} }+\lg {\frac {\alpha }{1-\alpha }}\end{aligned}}}$

d. H. the pH of such a solution is itself a function of the total concentration  c _{0 of} the acid.

Biprotonic acids H ₂ A

In the case of two or more protonic acids, it is advisable to dispense with the distinction between the degree of dissociation and the degree of association . Instead, one generally defines the proportion of the formal starting concentration c _{0 of} the acid that is attributable to one of the species present in solution . The distribution among the various forms depends on the pH of the solution. ${\displaystyle \alpha }$ ${\displaystyle 1-\alpha }$ ${\displaystyle \alpha }$

A biprotonic acid dissociates in aqueous solution in two equilibrium reactions :

${\displaystyle \mathrm {H_{2}A+H_{2}O\rightleftharpoons H_{3}O^{+}+HA^{-}\qquad HA^{-}+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{2-}} }$

The equilibria are described by the two acid dissociation constants :

${\displaystyle K_{S1}=\mathrm {\frac {[H_{3}O^{+}]\cdot [HA^{-}]}{[H_{2}A]}} \qquad K_{S2}=\mathrm {\frac {[H_{3}O^{+}]\cdot [A^{2-}]}{[HA^{-}]}} }$

The proportions attributable to the various acid species at a given pH value are then calculated as follows:

${\displaystyle {\begin{aligned}\alpha _{0}&={\frac {\mathrm {[H_{2}A]} }{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]^{2}} }{D}}\\\alpha _{1}&={\frac {\mathrm {[HA^{-}]} }{c_{0}}}={\frac {K_{S1}\cdot \mathrm {[H_{3}O^{+}]} }{D}}\\\alpha _{2}&={\frac {\mathrm {[A^{2-}]} }{c_{0}}}={\frac {K_{S1}\cdot K_{S2}}{D}}\end{aligned}}}$

with the auxiliary variable ${\displaystyle D=\mathrm {[H_{3}O^{+}]^{2}} +K_{S1}\mathrm {[H_{3}O^{+}]} \!\ +K_{S1}K_{S2}.}$

Titration curves can be obtained by plotting the (generalized) degree of association as a function of the pH value. The analogous degree of dissociation is then given by . The procedure is analogous in the case of a polyprotonic acid. ${\displaystyle {\bar {n}}=2\alpha _{0}+1\alpha _{1}}$ ${\displaystyle 2-{\bar {n}}}$

Multi-protonic acids H _n A

A multi-protonic acid H _n A is subject to coupled protolysis equilibria in solution n, described by the acid dissociation constants . At a given pH value, the proportion attributable to the species is calculated according to: ${\displaystyle K_{1},K_{2},\ldots ,K_{n}}$ ${\displaystyle H_{n-m}A^{m-}}$ ${\displaystyle (m\in \{0,1,2,\ldots ,n\})}$ ${\displaystyle \alpha _{m}}$

${\displaystyle \alpha _{m}={\frac {[{\text{H}}_{n-m}{\text{A}}^{m-}]}{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]} ^{n-m}}{D_{n}}}\cdot \prod _{i=0}^{m}K_{i}\qquad (K_{0}=1)}$

${\displaystyle D_{n}=\mathrm {[H_{3}O^{+}]} ^{n}+K_{1}\mathrm {[H_{3}O^{+}]} ^{n-1}+K_{1}K_{2}\mathrm {[H_{3}O^{+}]} ^{n-2}+\ldots +K_{1}K_{2}\cdot \ldots \cdot K_{n}}$

In all cases, always: . ${\displaystyle \sum \alpha _{i}=1}$

Analogously to the case of the biprotonic acid, the degree of association for the n-protonic acid is given by. ${\displaystyle {\bar {n}}=\sum _{i=0}^{n}(n-i)\cdot \alpha _{i}}$

Conductometric determination

For acids with one hydrogen atom, the degree of dissociation can be determined by conductometric measurements according to the formula:

${\displaystyle \alpha ={\frac {\Lambda _{\mathrm {m} }}{\Lambda _{0}}}}$

With

• the molar conductivity ${\displaystyle \Lambda _{\mathrm {m} }}$
• the molar limit conductivity ${\displaystyle \Lambda _{0}.}$

A similar determination is also possible for acids with several hydrogen atoms or with salts ( activity (chemistry) ).

See also

• Ostwald's law of dilution
• Dissociation constant

Web links

• Distribution diagrams of polyprotic systems

Individual evidence

1. ↑ James Newton Butler: Ionic Equilibrium: Solubility and PH Calculations . John Wiley & Sons, 1998, ISBN 978-0-471-58526-8 , pp. 185 ff.