Gibbs rule, equation

Gibbsitic [14762-49-3] Gibbs-Kelvin equation Gibbs phase rule Gibbs s phase rule Gibbs s theorem Gibbs-Thomson equation... 

For the ternary solution, the Gibbs-Duhem equation can be easily integrated to calculate the activity coefficient of water when the expressions for the activity coefficients of the electrolytes are written at constant molality. For Harned s rule, integration of the Gibbs-Duhem equation gives the activity of water as ... 

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 derivation of the phase rule is based upon an elementary theorem of algebra. This theorem states that the number of variables to which arbitrary values can be assigned for any set of variables related by a set of simultaneous, independent equations is equal to the difference between the number of variables and the number of equations. Consider a heterogenous system having P phases and composed of C components. We have one Gibbs-Duhem equation of each phase, so we have the set of equations... 

Applications of the Gibbs-Duhem equation and the Gibbs phase rule... 

The Gibbs-Duhem equation is applicable to each phase in any heterogenous system. Thus, if the system has P phases, the P equations of Gibbs-Duhem form a set of simultaneous, independent equations in terms of the temperature, the pressure, and the chemical potentials. The number of degrees of freedom available for the particular systems, no matter how complicated, can be determined by the same methods used to derive the phase rule. However, in addition, a large amount of information can be obtained by the solution of the set of simultaneous equations. 

It is also important to understand that all these properties obey all the rules of calculus. As a consequence these properties are related through fundamental equations, Maxwell equations, Gibbs-Helmholtz equations, and Gibbs-Duhem equations. 

The Gibbs-Duhem equation is the basis for the phase rule of Gibbs. According to the phase rule, the number of degrees of freedom F (independent intensive variables) for a system involving only PV work, but no chemical reactions, is given by... 

Gibbs-Duhem Equation and the Phase Rule at Chemical Equilibrium... 

GIBBS-DUHEM EQUATION AND THE PHASE RULE AT CHEMICAL EQUILIBRIUM... 

An alternative, and equally satisfactory, proof of the Phase Rule emerges in Frame 50, section 50.3 using the Gibbs-Duham Equation as the starting point. 

The Gibbs-Duhem equation (50.6), derived below, proves to be a useful starting point for an alternative derivation of the Clausius Claperyron equation to that offered in Frame 26) and offers an alternative proof of the Phase Rule to that given in Frame 30. 

Derivation of the Phase Rule using the Gibbs-Duhem Equation... 

The Gibbs/ Duhem equation provides a relation between the Lewis/Randall rule and Henry s law. Substituting dGt from Eq. (11.28) for dAft in Eq. (11.8) gives, for a binary solution at constant T and P,... 

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

Enthalpy-concentration charts are particularly useful for two-component systems in which vapor and liquid phases are in equilibrium. The Gibbs phase rule (Equation 6.2-1) specifies that such a system has (2 -I- 2 - 2) = 2 degrees of freedom. If as before we fix the system pressure, then specifying only one more intensive variable—the system temperature, or the mass or mole fraction of either component in either phase—fixes the values of all other intensive variables in both phases. An H-x diagram for the ammonia-water system at 1 atm is shown in Figure 8.5-2. 

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