Lecture 16. Thursday, October 27. Free Energy and Chemical Potential

Lecture 16. Thursday, October 27. Free Energy and Chemical Potential

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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 1 John Kuriyan: University of California, Berkeley Chem C130/MCB 100A, Fall 2005, Lecture 17 FREE ENERGY To review the concept of free energy: We are interested in determining the conditions that define the direction of spontaneous change for a process occurring in the system. In general this is given by the 2 nd Law of Thermodyanamics: dS SYS + dS SURR 0 (1) i.e., total entropy increases for a spontaneous process
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 2 By using the first law of thermodynamics to link the entropy change in the surroundings dS SURR to changes in system properties, we obtained the following conditions: A SYS = U SYS – T S SYS Helmholtz Free Energy (2) G SYS = H SYS – T S SYS Gibbs Free Energy (3) Δ A SYS 0 (4) condition for spontaneous change or equilibrium under constant temperature and volume Δ G SYS 0 (5) condition for spontaneous change or equilibrium under constant temperature and pressure The free energy refers only to system properties and so the subscript “SYS” will be dropped.
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 3 The parameters of the system will move until G is at a minimum value. G is a function of variables, such as the temperature, the pressure, and the number of particles:
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 4 G = G (T, P, N 1 , N 2 , N 3 …) (6) N 1 , N 2 , N 3 = numbers of different kinds of molecules in the system. If the numbers of molecules change, then the energy and entropy change, and so G will change. We are very interested in what happens when the number of molecules changes because this is what happens in chemical reactions and transport processes: dG = G P T,N dP + G T P,N dT + G N 1 P,T,N i 1 dN 1 + G N 2 P,T,N i 2 dN 2 + ... (7) If the pressure and temperature are constant, then: dG = G N i P , T , N j i i=1 t dN i (8) The term G N i P , T , N j i is known as the chemical potential of the i th type of molecule.
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 5 Suppose we have a system containing N i molecules of type i. Now see what happens when we add one molecule of type i to the system: Δ G = G final – G initial (9) But since we have added only 1 molecule, the change in free energy is essentially the free energy of one molecule. Hence
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This note was uploaded on 01/12/2010 for the course MCB 100A taught by Professor Kuryian during the Fall '09 term at University of California, Berkeley.

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Lecture 16. Thursday, October 27. Free Energy and Chemical Potential

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