{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 5

# which is identical to the equation obtained before we

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: µB dnB At the same time we know that G = nA µA + nB µB therefore: dG = µA dnA + µB dnB + nA dµA + nB dµB Therefore, we must have: µA dnA + µB dnB + nA dµA + nB dµB = µA dnA + µB dnB which leads to: nA dµA + nB dµB = 0 which we can generalize for any number of substances in the mixture: Σ nJ dµ J = 0 or Σ xJ dµ J = 0 (Gibbs- Duhem Equation) So we if know experimentally the variation of the chemical potential of substance A with composition in the mixture, then we can estimate the variation in the chemical potential of substance B with composition. Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 162 Mixing of Ideal Gases Consider the following set up consisting of two gas containers connected via a pipe, which can be closed by a valve. At the beginning of the experiment, the first container holds nA moles of molecules of an ideal gas A, at pressure P, temperature T in a volume VA. The second container holds nB moles of molecules of a gas B, at pressure P, temperature T in a volume VB. The valve between the two containers is initially closed. Now, we open the valve and the gases mix, so that, when equilibrium is reached, molecules of type A are under a partial pressure PA and molecules of type B are under a vapor pressure PB. The total pressure P has not changed and the temperature T also remains the same. Let us calculate the free energy change for this process. This free energy change can be calculated by considering the fact that gas A expands isothermally from VA to VA + VB and that gas B expands isothermally from VB to VA + VB. We note that dG = VdP = nRT dP/P = - nRT dV/V (since nRT = PV = cst, then dV/V + dP/P = 0) Marand’s Notes: Chapter 5 - The Properties of Simple Mixtures 163 We apply this relationship to both A and B and get for th...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online