Thermodynamic Theory of Affinity

Abstract

K = usual equilibrium constant M = net rate of phase change ni = number density a t surface n, O = equilibrium density P = pressure Q = nonequilibrium concentration func-R = usual gas constant T = absolute temperature V* = volume/molecule in the liquid W = molecular weight tion Greek letters pi = chemical potentials of the chemical components or phases undergoing the changes being considered v; = stoichiometric coefficients LITERATURE CITED 1. Hildenbrand, D. L., and A. G. Whie taker, That phase equilibrium exists at the gas-liquid interface during gas absorption is usually assumed in the analysis and design of absorption equipment, but the validity of this assumption has been in doubt since Higbie's pioneering gas-absorption studies. Accurate measurements are reported herein of the absorption rates at 25°C. of carbon dioxide into short water jets in which the liquid was in laminar flow. The jets issued from circular nozzles of about 1.5-mm. diam., flowed intact downward through an atmosphere of carbon dioxide at average velocities of from 75 to 550 cm./sec. over distances of 1 to 15 cm., and were collected in a receiver slightly larger in diameter than the nozzles. The measured absorption rates are in excellent agreement with predictions based on unsteady state diffusion theory, when one assumes interfacial equilibrium. It is concluded from these results and those of other investigators that equilibrium prevails at a freshly formed, relatively clean, carbon dioxide-water interface and that the same statement probably applies to the absorption of other slightly soluble gases in water. Evidence is discussed which indicates that an accumulation of minute quantities of surface-active materials may seriously reduce the rate of gas absorption, either by affecting the hydrodynamic characteristics of the system or perhaps by offering resistance to the transfer of solute molecules across the interface. That phase equilibrium exists a t the gas-liquid interface has commonly been assumed in applications of the film theory (21, 32) and the more realistic penetration theory (6, 15, 16, 52) to gas absorption. In attempting to test the validity of this assumption, various previous investigators have obtained conflicting results (4, 7 , 8, 1 1 , 16, 23, 25, 55).