Empirical Formula for Sound Velocity in Liquid Mixtures

An empirical formula V =( R / v ) 3 ={( n A R A + n B R B )/( n A v A + n B v B )} 3 , was derived for the sound velocity in binary liquid mixtures consisting of two component liquids A and B , on the assumption of the linear dependence of the molecular sound velocity R = v V 1/3 ( v =molar volume and V =sound velocity) on concentration (molar fractions n A , n B ) and the additivity of the molar volume. The suffixed quantities correspond to the component liquids. This formula holds true for such mixtures for which the linearity of the molecular sound velocity and the additivity of the molar volume is comparatively good, the mixtures of two hydrocarbons and those of two monovalent alcohols being the examples. The values of the empirical sound velocity were compared with those calculated by this formula for 38 mixtures with comparatively small values of the percentage deviation from linearity of R , and 28 of them showed deviations not larger than 1% in V . Of the 31 liquid mixtures with Δ R / R ≦0.3%, 5 showed deviations of V larger than 1%, 4 of them being the mixtures consisting of two component liquids of widely different molar volumes.