Gibbs-Duhem equation partial molar quantities

The Gibbs-Duhem equation also follows from the definition of partial molar quantities nid/Hi + r 2d 2 0. With the Gibbs-Duhem equation, d G/dc2 becomes... 

The well-known Gibbs-Duhem equation (2,3,18) is a special mathematical redundance test which is expressed in terms of the chemical potential (3,18). The general Duhem test procedure can be appHed to any set of partial molar quantities. It is also possible to perform an overall consistency test over a composition range with the integrated form of the Duhem equation (2). 

Equation (15) is called the general Gibbs—Duhem relation. Because it tells us that there is a relation between the partial molar quantities of a solution, we will learn how to use it to determine a Xt when all other X/ il have been determined. (In a two-component system, knowing Asolvent determines Asolute.) This type of relationship is required by the phase rule because, at constant T, P, and c components, a single-phase system has only c — 1 degrees of freedom. 

Gibbs-Duhem equation — The relationship between partial molar quantities of different components when... 

This equation, which is one example of the Gibbs-Duhem equation, shows that changes in the partial molar volume of one component may be related to changes in the same quantity for the other component. Experimentally, it means that one only has to measure one partial molar volume as a function of composition provided one has a value of the second partial molar volume at a reference point. In order to illustrate this point, equation (1.4.8) is written in a form suitable for calculating ua from ug ... 

A review of chemical thermodynamics, especially as it relates to the properties of liquid solutions, has also been presented. Partial molar quantities such as the chemical potential are an important feature of the treatment of this subject. It is often the case that the activity and chemical potential of one quantity is relatively easy to determine directly by experiment, whereas that of another component is not. Under these circumstances, the change in chemical potential of one component can be related to that of another through the Gibbs-Duhem equation. This relationship and its use in estimating thermodynamic properties are extremely important in solution chemistry. 

Equation (49a) is the exact differential of quantity Z [Eq. (3)] at constant pressure and temperature. Equation (49b) is a Gibbs-Duhem-Margules type of equation, indicating the mutual dependence of partial molar quantities. 

Solubility of water in chlorine. Expressing the free energy of a system in terms of partial molar quantities (chemical potentials) and comparing the result of differentiation of the whole function with an expression for the rate of change of free energy with composition leads to what is known as the Gibbs-Duhem relation [55,56]. The Gibbs-Duhem equation can be written as... 

At constant T and P, the Gibbs-Duhem equation simplifies to Si=i 0. Analogous to chemical potential are partial molar properties such as V,-, Hi, and S. Show that for all partial molar quantities such as V , Hi, and Si, at constant Tand Pone can also write... 

The Gibbs-Duhem equation can be used in calculating the partial molar quantity of one component in a binary solution,when the variation of the partial molar quantity for the other with concentration is known. Let us consider that in a binary solution A-B, the partial molar quantity Zg as a function of mole fraction of B, x , is known,and it is required to calculate the partial... 

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