Partial molar variables

The partial mass and the partial molar variables are simply related by ... 

We may easily rewrite the important quantities in (2.472) to molar basis as the partial mass and partial molar variables of species s are simply related by the molecular weight. We start by changing the thermodynamic quantities within the two first terms on the RHS of (2.455) using molar concentrations defined by = M Cs-... 

In this section we will consider phases with N components and we will choose the following variables the N quantities of matter n, and the p intensive variables for the other conjugate couples. We call the partial molar variable of an extensive funetion its derivative with respect to the amount of matter of a compound whose intensive variables and all the amounts of... 

We define the electrochemical potential ]i as the partial molar variable of G for component /. ... 

Theorem 5.- The partial molar variables are elements of the characteristic matrix associated with the intensive variables. 

The involvement of several components in a phase consequently introduces new couples of intensive and extensive variables (one couple per component) chemical potentials and amounts of matter (see section 2.2.4), and then the involvement of new variables compositions, partial molar variables (see section 2.3), chemical potentials (see section 2.6) and mixing variables. 

Let us consider a partial molar variable. In a uniform solution, this variable is a function of the variables of the problem, i.e. some intensive and extensive variables belong to other conjugate couples of J. If we have one mole of a solution overall, by having the molar fractions jc, as the composition... 

The operation [3.11] can also be applied to any Unear combination of partial molar variables and particularly to the combination ... 

As the partial molar Gibbs energy is confused with the chemical potential, the corresponding partial molar variables for each substance in the solution will be in the form ... 

Xj is the partial molar variable corresponding to variable X. Applying the same relation to the reference solution, we obtain ... 

With this variable being extensive, it therefore corresponds to partial molar variables, relative to each component of the solution, defined by ... 

This challenge is not unique to the chemical potential but can also be found for all partial molar variables that call on the same type of partial derivatives. We are going to attempt to circumvent this issue. 

The partial derivation of the definition of a partial molar variable introduees a virtual term in the ehemieal potential this ean be written in the following form... 

So, the tangent to the curve of the molar variable at composition point x intersects, on both vertical axes x = 0 and x = 1, two segments whose lengths are respectively the values of the corresponding partial molar variables for the chosen composition. This method of determining the chemical potentials is called the tangent method. 

This property is trae regardless of the molar variable chosen. This can therefore be applied when determining any partial molar variable of a binary solution, form the curve giving the integral molar variable according to the molar fraction. 

These notions are useful in thermodynamics since many functions such as the characteristic functions, volume etc. are homogeneous with a degree of 1 with regard to the amount of matter, that is to say, the number of moles The corresponding partial molar variables derived from the previous... 

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