Lecture 17. Tuesday, October 31. Equilibrium Constants. Free Energy and Work.

Lecture 17. Tuesday, October 31. Equilibrium Constants. Free Energy and Work.

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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY 1 John Kuriyan: University of California, Berkeley Chem C130/MCB 100A, Fall 2006, Lecture 17 Equilibrium Constants To review: the chemical potential, μ, is an intensive property that determines the direction of spontaneous change. G = H – TS Gibbs Free Energy (used when pressure is constant) G N i T , P = μ i Chemical potential For ideal dilute solutions the chemical potential is essentially the molar free energy. Note that if energy and volume is constant then the H term is constant. This allows us to calculate chemical potential for simple lattice problems. In this case i = T S N i To calculate (estimate) the chemical potential, move a few atoms in or out of a region and calculate T Δ S Δ N
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY 2 Dependence of chemical potential on concentration: C 1 = concentration in region 1 C 2 = concentration in region 2 For ideal, dilute solutions: Δ μ = 1 2 = RT ln C 1 C 2 -chemical potential is here defined as G n i where n i = number of moles or Δ = 1 2 = k B T ln C 1 C 2 -chemical potential is here defined as G N i where N i is the number of molecules We are usually interested in knowing the chemical potential at some specific concentration relative to the standard state (typically 1M solution).
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY 3 In that case we write: μ C ( ) = + RT ln C 1 μ (C) = chemical potential for the molecule of interest at concentration C μ° = chemical potential for the molecule of interest at standard state (1M solution) Now let us look at the equilibrium point of a chemical reaction. In the last lecture we wrote a general chemical reaction as follows: aA + bB cC + dD It can get confusing to have all these letters, so we shall now write this as: v a A + v b B v c C + v d D where v a , v b , v c , v d are the stoichiometric coefficients.
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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2006 ONLY 4 How does the free energy of the system change when the reaction proceeds? dG = G n A dn A + G n B dn B + G n C dn C + G n D dn D where n A , n B , n C , n D are the number of moles of A, B, C, D. G
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Lecture 17. Tuesday, October 31. Equilibrium Constants. Free Energy and Work.

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