Modifiying Relative Proportions of Chromatographic Mobile Phases A freqmnr task in liquid chromatograpy 1;. mtdifying the solvcnt stlpngth bv rhan~6npthe relativc volumr o f t h e eompments d m initial rnlxture. For rxarnplc, a rypienl prnhlem in HPLC might br For nn initial i d u t m at 40 10 50 of methanol arrronnrile water. what volumes of each component must be added to ohrnin a final wlutlon of GO 5 35' The problem can be solved bytaking a final volume large-enough, calculate its content in each solvent and make up the differences with the initial volumes. As the HPLC solvents are relatively expensive, however, the problem could be better stated as: For an initial total volume V. of solution, what are the volumes of each component to be added to obtain a minimum final volume Vr? The optimum is attained when the volume added of one component is zero (if one imagines adding nonzero amounts of every component, one can always then imagine reducing the value of the final solution until one of the components hits zero addition). Let the initial and final proportion of the N component mixture he Xi and Yi, respectively, for i = 1,...,N. Then it is clear that the critical campanent(s) for which there is zero addition, i = e, is that far which the ratiozi = Xi /Yj is maximum. The fmal total volume has therefore to he Vr=Z,V., and finally the volumes to add of each component are given by the expression:
In the example above, Zi is maximum for acetonitrile. For a n initial 200 fiof solution we get a n addition of 160 mL of methanol and 40 mL of water to reach the final proportions (possible volume changes in mixing are neglected). Calculations can be made quickly with a programmable pocket calculator.
Gregorio Cruz Private Laboratory San Pedro de Alcantara,5,1D 06001,Badajoz,Spain
90
Journal of Chemical Education
