The valve between the two containers is initially

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Unformatted text preview: a per mole basis, by dividing the system thermodynamic property by the total number of moles) as a function of the mole fraction and then draw the tangent of that curve at the point of interest (i.e. for the composition at which you want the partial molar quantity). The intercept of the tangent with the ordinate xA = 1 gives you the partial molar quantity for A and the intercept for xB = 1 gives you the partial molar quantity for B. Gibbs- Duhem Equation: We will see shortly that we can estimate the chemical potential of a substance in a liquid mixture if we can measure its vapor pressure above the liquid mixture. However, there are cases, where such estimations are difficult because one of the mixture components is not very volatile (i.e. it has a low vapor pressure). For example, let us consider a mixture of A and B molecules. Let us assume we can easily determine experimentally the chemical potential of substance A in the mixture from the vapor pressure of A above the mixture. On the other hand, let us assume B is a solid at room temperature, and its vapor pressure is so low that it cannot be measured. Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 161 So we cannot estimate the chemical potential of B from its vapor pressure. There is however a way around this experimental problem thanks to the Gibbs- Duhem Equation. We start with the change in the free energy of the solution with temperature, pressure and change in the number of moles of A and B. dG = - S dT + V dP + µA dnA + µB dnB At constant pressure and temperature, this leads to: dG = µA dnA +...
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