Chapter 9

1. Chapter 9 The chemical potential and open systems

2. Chemical Potential. We give a brief introduction to this concept as we will need to refer to it later in the course. As the name suggests, it is very important for studying chemical reactions and your will encounter this concept in a first course in physical chemistry. Just as the temperature governs the flow of energy between two systems, the chemical potential governs the flow of particles. When the chemical potential of the two systems are equal, they are in diffusive equilibrium. We are now going to consider the introduction of matter into a system. If we introduce, say, dn kilomoles of matter into a system, there will be a change in energy of the system and dU will be proportional to dn Closed system: System does not exchange matter with surroundings. Open system: Quantity of matter not fixed.

3. For a pure substance, with a constant number of particles, we had, for a quasi-static process: đ and for a reversible process, dU=TdS –PdV ………(2) We now consider a more general case where a system may consist of several different constituents. Furthermore, the system is no longer necessarily closed so that the number of moles of the various constituents may vary. = number of moles of constituent i We now generalize equation (2) to allow for the possibility of adding of removing particles from our system. Before we had U(S,V) and now In the first two derivatives, all the n are constant and in the third derivative all the n are constant except

4. Comparing equations (2) and (3) and now we define the chemical potentials by Equation (3) can now be written as Solving for dS: and so The Helmholtz function is F=U-TS

5. (reciprocity relations) EXAMPLE: Mixture of two ideal monatomic gases We will take as given the Helmholtz Thermodynamic Potential. From the viewpoint of thermodynamics this comes from experiment. In statistical mechanics this is derived from a model in which two types of molecules are present.

6. m=molecular mass =Avogadro’s number h=Planck’s constant If we have If we have so Dalton’s Law The pressure of a mixture of ideal gases is equal to the sum of the partial pressures. The partial pressure of a gas is the pressure that it would exert if it alone occupied the volume V at temperature T.

7. From the fact sheet we obtain G=F+PV so

8. Comparison with the expression for and a similar expression for gives In general For a system consisting of just one constituent (one phase) we have We see that for such a simple system, the chemical potential is just the Gibb’s function. {We mentioned earlier that the Gibbs Potential was particularly important in physical chemistry.}