Hägg diagram
The Hägg diagram (English Hägg's diagram or bjerrum plot according to Niels Janniksen Bjerrum ), also called speciation diagram (cf. speciation ), is used in analytical chemistry to quickly get an overview of the proportions of an aqueous acid, base or salt solution known concentration. It provides a logarithmic representation of the concentration ratios of a conjugate acid-base pair (i.e. the concentrations of the individual chemical species ) as a function of the pH value and is also used for titrations .
The presentation goes back to the Swedish chemist Gunnar Hägg .
Principle and construction
Compared to the simple logarithmic representation of the regular titration curve, where the degree of titration is plotted against the pH value, the concentration under consideration is also logarithmized here, since the changes in concentration during titrations extend over many powers of ten .
The pH value is plotted on the abscissa ; on the ordinate the negative decadic logarithm of the formal concentration of the substance to be considered. The law of mass action of the acid-base pair sought is rearranged and it is resolved in such a way that the concentration of acid and conjugate base only depends on the acid constant , hydronium concentration and initial concentration. After taking the logarithm of the equations obtained, curves with oblique and horizontal asymptotes are obtained, which can easily be approximated for the ranges pH < pKs and pH> pKs by simple straight lines with slopes 0 and 1. For the hydronium concentration there is a straight line through the origin, the hydroxide concentration is correspondingly orthogonal and intersects it at the neutral point with pH = 7, since both concentrations are the same here. Multi-protonic acids can be obtained simply by combining the Hägg diagrams of the individual protolysis stages ; one assumes here approximately independent equilibria.
Distinctive points in the titration
The approximations of the Hägg diagram are amazingly accurate, the accuracy only drops for the range of ± 1 pH unit around the point pH = pKs. The pKa value is temperature-dependent and applies to infinite dilution; In practice, 0.001 to 0.1 molar solutions are titrated at 25 ° C.
Distinctive points can be read off by considering the equilibria in the course of a fictitious titration.
- So at the beginning only the concentration of the acid is available; this determines the pH value of the solution by dissociating into conjugate base and proton . Accordingly, the starting point is at the intersection of the straight line of the base and hydronium concentration.
- The same concentrations of acid and conjugate base are present at the buffer point , so that the corresponding intersection point can simply be used here as well.
- At the equivalence point only conjugate base is present; this breaks down with water to form hydroxide and acid, the pH value is provided by the intersection of this concentration line.
In addition, it is possible to make further statements about the titration accuracy , i.e. the degree of dissociation of the conjugate base at the equivalence point, and about other concentration ratios for any pH value.
To do this, read off the logarithm at the corresponding points and use this to calculate the present concentration.
Conversely, the existing concentration ratio (e.g. 90% titration: only 10% of the original acid concentration is still present) is converted logarithmically into the logarithm for the desired pH values and thus the desired pH value is determined graphically.
Other uses of the Hägg diagram
The double-logarithmic representation can not only be used for protolysis equilibria, but can also theoretically be applied to all equilibrium systems, including redox and solubility equilibria . There are similarly easy to construct diagrams.
- For redox equilibria, the redox potential is plotted on the abscissa instead of the pH value ; the analog equations result from the logarithmic conversion of the Nernst equation .
- For example, a Hägg diagram can also be formulated for the simultaneous argentometric titration of halides and pseudohalides ; the logarithmic silver concentration is plotted on the abscissa; the equations result from taking the logarithm of the solubility equilibria .
See also
literature
- Udo R. Kunze: Basics of quantitative analysis . Thieme Verlag, Stuttgart 1990, ISBN 3-13585-803-0 .
Web links
- Heiner Grimm, Clausthal-Zellerfeld: pH value in water and aqueous solutions (acids, bases, salts, salt mixtures): pH calculation and determination of the pH using the Hägg diagram . Retrieved on January 15, 2009, (page with extensive explanations of Hägg diagrams).