Sequential Preparation of Series of Ternary Solutions

For ternary (and more general multicomponent) liquid-phase systems, solution preparation is a necessary step in measuring thermodynamic and transport property data and in identifying compositions useful in specific applications. We consider a ternary system comprised of liquid components A, B, and C (typically, nonelectrolytes), fully miscible over the entire range of composition. Achieving uniform coverage of the ternary triangle of compositions, with mass fraction increments of 1/N corresponding to mass fractions of wA=m/N, wB=n/N, w_C= 1 - w_A- w_B, for 0 ≤ m≤ N and 0 ≤ m+ n≤ N, requires preparation of (N+1)(N+2)/2 solutions. If the minimum quantity required for each composition is characterized in terms of a volume, as for, say, viscometry, then the volume required, if each solution is prepared directly from pure components, will grow with N more rapidly than quadratically. We develop an approach that mixes previously prepared solutions to make new compositions, and substantially reduces the amount of material needed. We illustrate this approach in detail when the components are liquids with the same density, miscible in all compositions, with no volume change on mixing, and each solution can be fully recovered to prepare subsequent solutions. For N= 10 , only nine units are required, compared to 66 units for the conventional approach, while the number of weighings is reduced by 55%. Modifications to deal with cases in which the pure components have different densities, some material is not recovered after measurement, and the components have different costs, are discussed.