Analysis of variance in determinations of equivalence volume and of the ionic product of water in potentiometric titrations.
Homogeneous sets of data from strong acid-strong base potentiometric titrations in aqueous solution at various constant ionic strengths have been analysed by statistical criteria. The aim is to see whether the error distribution matches that for the equilibrium constants determined by competitive potentiometric methods using the glass electrode. The titration curve can be defined when the estimated equivalence volume VEM, with standard deviation (s.d.) sigma (VEM), the standard potential E(0), with s.d. sigma(E(0)), and the operational ionic product of water K(*)(w) (or E(*)(w) in mV), with s.d. sigma(K(*)(w)) [or sigma(E(*)(w))] are known. A special computer program, BEATRIX, has been written which optimizes the values of VEM, E(0) and K(*)(w) by linearization of the titration curve as a Gran plot. Analysis of variance applied to a set of 11 titrations in 1.0M sodium chloride medium at 298 K has demonstrated that the values of VEM belong to a normal population of points corresponding to individual potential/volume data-pairs (E(i); v(i)) of any titration, whereas the values of pK(*)(w) (or of E(*)(w)) belong to a normal population with members corresponding to individual titrations, which is also the case for the equilibrium constants. The intertitration variation is attributable to the electrochemical component of the system and appears as signal noise distributed over the titrations. The correction for junction-potentials, introduced in a further stage of the program by optimization in a Nernst equation, increases the noise, i.e., sigma(pK(*)(w)). This correction should therefore be avoided whenever it causes an increase of sigma(pK(*)(w)). The influence of the ionic medium has been examined by processing data from acid-base titrations in 0.1M potassium chloride and 0.5M potassium nitrate media. The titrations in potassium chloride medium showed the same behaviour as those in sodium chloride medium, but with an s.d. for pK(*)(w) that was smaller and close to the expected instrumental noise, whereas the titrations in nitrate medium had a high noise level and even the determination of VEM was less certain. Procedures are also proposed for obtaining reference sets of data and checking the conformity of the solutions and apparatus to the chosen reference.
Braibanti
A
A
Istituto di Chimica Farmaceutica/Sezione di Chimica Fisica, Università di Parma, Parma, Italy.
Bruschi
C
C
Fisicaro
E
E
Pasquali
M
M