Although the first section is mostly a repeat of a previous blog, I think it is better to include it. The proposition is that ignoring the dustortion of the surface excess in solution chemistry has an impact in creating perceived "non'idealities" and "experimental" and reproducibility errors. Such errors would not exist, but be the consequence of assuming bulk phase models to be true. This distortion plus precision errors and real human errors would be the sources of non'reproducibility and dispersion of data.
INSTRUMENT EFFECTS: AN EXAMPLE.
After showing in previous blogs that that the surface excess model of solubility lends itself to predict the existence of a constant solubility product while a bulk-phase concentration model would beg for a variable solubility depending on initial concentrations, we are going to show how observed variations in the absorbance of samples with length of optical path can be explained by a surface excess model (Talens, 2011). Let us assume two spectrophotometric cells, both 50 mm high and 10 mm wide, with a depth of 1mm and 10 mm. It is trivial that this can lead to a lower concentration in the narrower cell due to the higher “stress” caused on the resource (the number of molecules) by stretching the surface per unit of volume. It only takes k to be a significant number, which it often is.
If we reconsider the expression for the light absorbance of a solution, to include both surface excess (twice, as there are two surfaces involved in the absorbance test) and bulk phase concentration and take the 10 mm depth cell as reference
the distortion expected for the 1 mm depth cell is:
One thing explained by the 2 weight factor for the surface excess contribution to the absorbance is why often reducing the thickness by a factor does not lead to the same drop in absorbance. Of course, this has been explained away by entrance effects etc, but the point here is that certain levels of intrinsic human irrationality (adherence to magical explanations, gremlins, and some form of “original sin by proxy”, assuming man made artefacts are meant to be intrinsically flawed because, well, they are man made) may be interfering with our better judgment.
There is a potentially very important implication in this example about colorimetric reading distortion by surface excess. Do surface excesses distort readings in general? If a chemical reaction takes place at the surface of a solution primarily, and we are controlling the temperature with a thermometer which generates its own surface, is the local temperature different than the bulk temperature one? How many of our readings are surface property readings, and introduce a distortion when we assume they are bulk phase? Does this influence scale-up factors in the chemical industry, for example? Are our Platonic “Myth of the Cave” shadows on the surface of liquids?
The second aspect of this discussion is about reproducibility. If the end point of a tritation was really the condition where the content of a certain chemical has been depleted so that its surface excess is not high enough to keep reacting, then some of what we call experimental error may be just a device - related dimensional adjustment factor. Equation Set 2 shows a set of equations. Equations a) and b) indicate the equations for the linear portion of the relationship between surface excess and concentration of titration target T and titration standard S at the end point “ep”. The initial number of moles of the target T will be equal to the titrated (reacted) moles plus the residual moles at the end point (equation d). The residual moles will be equal to the surface excess time area of the volume plus bulk concentration in equilibrium times volume (equation d). Equations e) and f) show that if the area changes and the volume remains constant the surface excess and bulk phase concentrations of the target change. This may seem strange because of the stated hypothesis that the surface excess dictates the end point and should be equal, until we remember that this area/volume change also affects the titration standard, and that the condition for end point is not a surface excess value but the product of two of them (equation g).
Equations h) and I) give trivially the final concentrations of the titration standard for a titration with 1:1 stoichiometry , which would be the titrated concentration of the target plus the end point concentration of the standard. Equations j) and k) show that, for a substance AnBm assumed to have a conventional equilibrium constant it is perfectly reasonable to expect a discrepancy in the experimentally calculated value derived from a dimensional setup distortion (equation l). With standard glassware nowadays it can be expected that such distortions will be smaller than in the past, and with chemicals where the surface excess is smaller the distortion will be less important, but nevertheless the prediction can be used to verify of this theory.
Plato, “Book VII” in: The Republic