Coexistence Phenomena in the Critical Region: I. The Gravity Effect in Ethane From Light Scattering

Abstract

A method of measuring density gradients caused by gravitational compression in gases near the critical region is described. Relative light scattering coefficients of ethane in bombs 40 cm. long increase, remain constant, or decrease in the downward direction, depending upon the mean filling density. These observations have been correlated with the variation of scattering coefficient with density, and show that appreciable density gradier~ts exist. These observations are confirmed by parallel studies of condensation, and serve to explain the flat portion of the liquid-vapor coexistence curve found with a carefully puritied system. INTRODUCTIONThe variation of pressure with height in an isothernlal fluid is given by the equation where x is the vertical distance (downwards) from a datum. and p and v respectively are the density and specific volume. Using the transformation and introducing the isothermal compressibility = ---, one can write t ( Z ; ) . Equation ( I ) in the form :Near the liquid-vapor critical point, a t which P -+ m , Equation ( and p , = 0.73 gm. per cc., the density gradient calculated from Equation (2) is 0.9 % per cm. For a methane-propane mixture of unstated AT, Blosser and Drickamer (3) report fl = 112 atn1os.-I a t p = 0.21 gin. per cc., a value derived from light scattering measurements. The calculated gradient for this case is 2.4% per cm.

Coexistence Phenomena in the Critical Region: V. The Gravity Effect in the Binary Liquid System Aniline-Cyclohexane From Light Scattering

“…In previous publications (3,4), the authors reported large vertical gradients in density near the liquid-vapor critical point in one-component systems. These gradients, due t o gravitational compression, were anticipated owing to the large compressibility of a fluid in the critical region.…”

“…The essential details of the apparatus have already been described (3,4). In the present experiments, only the methods of filling and changing the compositioi~ of the fluid were altered.…”

“…I t was, however, shown by Yvon (9) that such concentration gradients are predicted theoretically. Since Rice and Rowden (6) reported a flat apex on the coexistence curve for aniline-cyclohexane, it was of interest to see if this flat top could be ascribed t o concentration gradients by analogy to the gravity effect in one-component systems (3,4,7,8).…”

“…By combining Equations [2] and [3] the variation of concentration with height becomes B' is a constant for any given concentration, temperature, and wave length of the incident light. Equation [4] is analogous to the relationship between turbidity ant1 density gradient in a one-component system near the gas/liquid critical point.…”

“…I t was, however, shown by Yvon (9) that such concentration gradients are predicted theoretically. Since Rice and Rowden (6) reported a flat apex on the coexistence curve for aniline-cyclohexane, it was of interest to see if this flat top could be ascribed t o concentration gradients by analogy to the gravity effect in one-component systems (3,4,7,8).The critical solution point for a binary liquid system is defined by the conditions where p1 ancl cl are respectively the chemical potential and mole fraction of component 1 in the solution.For the variation of concentration with height in a binary liquid mixture, Yvon (9) obtained an expressioil which may be simplified to the form where x is distance measured positive downward and G(x) is a finite function of x. From Equation [2], Yvon concluded that when the solution approaches the critical state, i.e.…”