Biomedical subjects
Publications and source records attributed to H Rilbe.
Dole's and Longsworth's solution of the whole set of moving boundary equations by using the dimensionless transference numbers is reviewed. Longsworth's teachings on the nature of transference numbers and his pondering over transference numbers of proteins led the author to inquire why transference numbers of ampholytes were never measured. Logical reasoning on this subject led to the invention of isoelectric focusing.
The equation for the hydrogen ion activity in solutions of salts of a strong acid and a weak base, or vice versa, is of the third degree. Nevertheless, explicit equations for pH of such solutions can be formulated as linear functions of the logarithm of the salt concentration. The equations are valid within the major parts of pH and concentration intervals of experimental interest. The ranges of validity are given in terms of mathematically defined pH intervals. Close relations with pH of free base or free acid solutions of the same concentration as the salt are demonstrated. For instance, the pH difference between solutions of the salt and the free base or acid having unit activities is +/- 7 pH units.
The general equation for the relative molar buffer capacity, earlier shown to be valid for bivalent acids, bases, and ampholytes, is shown to hold also for equimolar, binary mixtures of monovalent protolytes if only the parameter s = square root of K1'/4K2' is exchanged for t = s + 1/4s. The same applies to the equations for the mean valence of the two classes of protolytes. As a consequence thereof, the titration and buffer capacity curves of a bivalent protolyte are identical with those of a monovalent protolyte with a pK' value equal to the with those of a monovalent protolyte with a pK' value equal to square root of K1'K2' of the bivalent one (the isoprotic point of an ampholyte). For a hypothetical bivalent acid, base, or ampholyte with s = 1, delta pK' = log 4, this implies that the intrinsic rather than the hybrid dissociation constants are responsible for the titration and buffer capacity curves.
Exact relations between pH and concentrations of water solutions of acids, bases, and simple ampholytes are presented in the form of computer-created curves. These are mathematically analysed with respect to linearity and inflexion points. The extreme invariance of pH in the immediate vicinity of the isoelectric points of ampholytes is demonstrated in curves of the logarithm of molarity as a function of the logarithm of magnitude of pH-pI magnitude of. These considerations include a discussion of the suitability of ampholytes as pH standards.
A general theory for buffers consisting of one weak acid and one weak base is developed, particular interest being devoted to the special case of doubly weak salts. The pH course as it varies with the acid/base concentration ratio is presented in equations and graphs. The influence of delta pK' = pK'b-pK'a, which can be negative as well as positive, is discussed and visualized in graphs. The buffer capacity is deduced as a function of pH. The buffer range is, at a maximum, 2.67 times that of a monovalent weak protolyte for delta pK' = 2.7 pH units. The buffer capacity curve has two maxima for delta pK' values bigger than 0.77. For negative delta pK' values the buffer capacity curve has only one maximum, and the buffer range is not better than that of a monovalent protolyte. A general equation for the ionic concentrations is deduced, and as a corollary the degree of hydrolysis of the doubly weak salt is obtained as a function of delta pK'. For solutions of this salt, the relation between concentration and pH is elucidated by equations and graphs.
It is shown that stoichiometric rather than thermodynamic dissociation constants can and should be used in the buffer capacity theory. The mean valence of bivalent weak acids and bases is deduced in a form with dimensionless parameters. The expressions for the molar buffer capacities of bivalent weak acids and bases are identical with that for a bivalent ampholyte, and the theory for the latter given earlier is thus valid in all details for bivalent weak acids and bases.
The general equation for the buffer capacity of trivalent weak acids is derived by way of the mean valence. It is valid for trivalent bases and ampholytes as well. Special interest is devoted to protolytes with symmetrically spaced pK values since both phosphoric acid and citric acid have this property. The symmetry implies a mathematical simplification which makes it possible to deduce the locations and magnitudes of the maxima and minima. Thus it is shown that the buffer capacity curve has three maxima and two minima for delta pK values bigger than 1.29.
A complete mathematical account of the buffer capacity of bivalent ampholytes is given. The consistent use of dimensionless parameters makes it possible to obtain very neat expressions and equations. Direct proof of the well-known condition K1 > or = 4 K2 is presented. Since water is also an ampholyte, its buffer capacity is considered as well.
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