The Effect of Ethanol–Sucrose Interactions on Specific Gravity. Part 2: A New Algorithm for Estimating Specific Gravity

Abstract

One method for the estimation of specific gravity is the Tabarie equation: SGv = 1 + Σ(SGvi — 1), which combines volume-adjusted binary solution specific gravities (SGvi) independently. In a previous study, the Tabarie equation was found to be within the observed 95% confidence level for solute concentrations below 5% sucrose and 18% ethanol (by weight). However, when ethanol exceeds 7 mol% the deviation from observation is extreme. In this region, ternary solutions appear to expand because the mixing collapse of hydrogen-bonded bulk water is overestimated by the Tabarie model. In this paper, a new algorithm is proposed that assumes that change in solution volume during mixing is related only to change in water structure or the specific gravity of water in the presence of solutes. The model then takes the form of an ideal solution: SG = (Σwi/SGi−1, where wi is the mass fraction of species i. Ethanol-sucrose aqueous solutions were prepared by weight, mixed via sonication, and analyzed for density across the full range of sucrose solubility. Least squares regression analysis was used to fit the difference between the experimental specific gravity and theoretical ideal solution using polynomial cross-products of solute concentration (adjusted R2 = 0.998; SE = 2.9 × 10−5; and n = 153).