Solvent behavior in the ideal-dilute solution

We now use the Gibbs-Duhem equation to investigate the behavior of the solvent in an ideal-dilute solution of one or more nonelectrolyte solutes. The Gibbs-Duhem equation applied to chemical potentials at constant T and p can be written xt dp,i = 0 (Eq. 9.2.43). We use subscript A for the solvent, rewrite the equation as xa d/iA + = 0, 

This equation shows how changes in the solute chemical potentials, due to a composition change at constant T and p, affect the chemical potential of the solvent. 

In an ideal-dilute solution, the chemical potential of each solute is given by /l/ = + 

Now since the sum of all mole fractions is 1, we have the relation XIjVa - -a whose differential is Making this substitution in Eq. 9.4.32 gives us 

Consider a process in an open system in which we start with a fixed amount of pure solvent and continuously add the solute or solutes at constant T and p. The solvent mole fraction decreases from unity to a value x, and the solvent chemical potential changes from jji to We assume the solution formed in this process is in the ideal-dilute solution range, and integrate Eq. 9.4.33 over the path of the process  

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