Gravimetric measurement of adsorption from binary gas mixtures

A precise experimental method for studying binary vapor-liquid equilibrium is to measure total pressure (P) as a function of the mole fraction in the liquid phase (2). The mole fraction in the vapor (y) is calculated from imthermal P-x experimental data using the Gibbs-Duhem equation. A similar procedure for adsorption is to measure total mass (m) of gas adsorbed as a function of the mole fraction in the vapor phase (y). Then the composition of the adsorbed phase is calculated from isothermal m-y experimental data using the Gibbs isotherm. Only a few experimental points are needed for the mixture. The method is rigorous even when the adsorbed phase is nonideal. INTRODUCTION The standard experimental procedure for equilibrium adsorption from a binary gas mixture is to report two measured variables: total amount adsorbed per unit mass of adsorbent (at ) and mole fraction of component number 1 in the adsorbed phase (5'). Independent variables for each experimental point are temperature (T), total pressure (P), and mole fraction of component number 1 in the gaseous phase (yl). The volumetric method used to measure adsorption of pure gases is less successful for mixtures because the rate of counterdiffusion of different species within the pores is very slow. Equilibration is accelerated by recirculating the gas mixture through the adsorbent. The composition of the adsorbed phase is determined by desorption into an evacuated space followed by analysis. Measuring the composition of the adsorbed phase is actually unnecessary. x1 can be calculated from experimental data on the total amount adsorbed n,(T, P, yl) using rigorous thermodynamic equations. Data on the total mass adsorbed rn,(T, P, yl) obtained with a gravimetric apparatus provide sufficient information to calculate xl. The gravimetric method is more convenient and easier to automate than the volumetric method. This paper describes a new procedure for calculating adsorbed-phase composition from gravimetric data. THERMODYNAMICS The thermodynamic principles can be clarified by reference to a similar method that is well established for vapor-liquid equilibrium (VLE) measurements. Barker' proposed a thermodynamic procedure, which wm refined and applied to a series of binary and ternary mixtures by Van Ness and coworkersa, for calculating vapor-phase composition from total pressure measurements as a function of liquid-phase composition. The vapor space of the equilibrium cell is made very small so that the composition of the liquid is very nearly equal to the composition of the charge to the cell. Degassing of the liquid phase before the experiment is essential. Experimental data for a binary mixture are isothermal measurements of the total pressure as a function of liquid-phase composition, P(zl). The numerical procedure is to optimize values for constants in an equation for liquid-phase activity coefficients using as objective function the sum of squares of deviations A P between the calculated and experimental points on the P(xl) curve. The equation for activity coefficients must be sufficiently flexible to account for the nonideality of the liquid phase, as judged by a statistical test of whether the deviations A P lie within the estimated experimental error. The thermodynamic procedure for VLE is based on the Gibbs-Duhem equation, which is a differential equation connecting the variables P, zl, and yl. For adsorption the situation is complicated by an additional independent variable: the spreading pressure IT in the adsorbed phase. In the folbwing, spreading pressure will be written in terms of the variable $ = rIA/RT, which has the same units as n, the specific amount adsorbed (mol/kg). The Gibbs adsorption isotherm is: d$ = nt[zldln(Pyl) + zadln(P~a)] (1) for which the only assumption is that the fugacity coefficient & = 1 in the equation for gas-phase fugacity fi = Pyidi. Extension of the method to imperfect gases is readily accomplished if necessary. The important point is that Eq. (1) is correct even when the adsorbed phase is nonideal.