Gibbs, adsorption equation phase rule

Gibbs-Duhem relations, the Gibbs adsorption equation and the Phase Rule... 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

Turning now to adsorption equilibrium, let us apply algebraic methods to a two component 1,2 phase system. From the phase rule there will be two degrees of freedom, but we shall reduce this to one by maintaining the temperature constant. Then for the total system there exists a Gibbs-Duhem equation... 

The next step is to make clear the Gibbs adsorption amount, using the above relative adsorption. Recall (8.27), in which the interfacial tension is a function of i -H 2 independent variables. However, the Gibbs phase rule permits only i independent variables for two phases including i components. Therefore, the problem is how to reduce the number of intensive variables by two while keeping thermodynamical consistency. The Gibbs-Duhem equations for two homogeneous phases a and respectively, are... 

This is the Gibbs-Duhem equation for surface adsorption. Now y can be expressed in terms of i independent intensive variables, which is consistent with the phase rule. The important point is that the coefficient of the second term is the relative adsorption of component i with respect to component 1. Then, we have... 

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