A more conceptual look to ciVi = cfVf equation in “Analytical Chemistry”

The analytical chemistry skills required to support the development and improvement of chemical processes have been described recently [1]. The misconception addressed here in has been broadly disseminated in recent quantitative analytical chemistry educational literature [2]. Equation 1 shows the volumetric dilution equation using IUPAC recommended symbols, where cx represents the amount concentration with SI units of moles meter-3 and Vx represents the mixture volume with SI units of meter3: ciVi = cfVf (1)Equation 2 will be used in this manuscript to describe a common misconception derived from equation 1: CiVi = CfVf (2)The misconception consists in believing that Cx represents any measure of composition or of “concentration”. In fact, this overgeneralization (believing that Cx can represent any measure of composition) is explicitly or implicitly proposed in at least two contemporary analytical chemistry textbooks [2]. Learners exposed to such information form the mis-conception that “you can use any units for concentration and volume as long as you use the same units on both sides”. The contextual suggestion is that beyond volumetric units of concentration, mass-based measures of composition may also be used by direct substitution into equation 2. This equation may be employed analytically using mass-based units of “concentration” such as percent, ppm, ppb, and so forth, only if the initial density of the concentrated solution and the final density of the dilute solution (ρi and ρf) are identical. It is well known that changes in solution composition are usually accompanied by concomitant changes in solution density. Hence, equation 2 is seldom analytically applicable when mass-based units are involved. In fact, the systematic percentage relative error introduced by use of equation 2 when solution composition is expressed with mass-based units may be estimated through the use of eq 3:Percent Relative Error = [(ρf/ρi) − 1]100 (3)