Lect13 - Physics 213: Lecture 13, Pg 1 Lecture 13 Lecture...

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Unformatted text preview: Physics 213: Lecture 13, Pg 1 Lecture 13 Lecture 13 Chemical equilibria, Surfaces, Chemical equilibria, Surfaces, and Phase Transitions and Phase Transitions Agenda for today Agenda for today • Chemical equilibria --“Law of Mass Action” • Surface chemistry • Phase equilibria and chemical potentials • Gibbs Free Energy • Vapor pressure of a solid Re fe re nc e fo r this Le c ture a nd ne xt: Ele m e nts Ch 13 Physics 213: Lecture 13, Pg 2 Problems involve exchange of particle types A,B,C. The reaction equation is written: aA + bB ↔ cC , with integers a,b,c . 0 using C C B A B A A A A A A A B C dN dN dN dN dN dF F F F F b F c F dN N N dN N dN N a N a N a b c ∂ ∂ ∂ ∂ ∂ ∂ = + + = +- = = = - ∂ ∂ ∂ ∂ ∂ ∂ Determine Equilibrium Condition : Total free energy, F , is a minimum. A B C a b c for the reaction aA + bB cC μ + μ = μ ↔ General Chemical Equilibrium Procedure General Chemical Equilibrium Procedure If F is minimum we must have ∆ F =0 when the reaction occurs, forward or back. Physics 213: Lecture 13, Pg 3 Interaction Potentials and Chemistry (1) Interaction Potentials and Chemistry (1) ● In addition to simple PE terms from external fields, there are usually PE terms from interactions between particles (not ideal, overall) ● Often: Atoms can combine in any of several molecular forms , each of which has a different binding energy. Interactions between the molecules can often be neglected: the overall system is the sum of several ideal molecular components. ● The U term in F includes all those binding energies (which we’ll call ∆ ’s) , so they must be included in the μ ’s. (dF/dN) ● The material will NOT all convert to ‘the lowest μ molecules’ because μ depends on n for each type of molecule. As any type becomes rare, its μ drops, until equilibrium is reached with some of each type present . (Just as not all air molecules settle into the lower atmosphere.) Physics 213: Lecture 13, Pg 4 Chemical Equilibrium Procedure (ideal case) Chemical Equilibrium Procedure (ideal case) ln form of (n) comes from ( ) ! N i i i Ti n M kT N n N μ μ = - ∆ Ω μ ÷ We plug these ideal chemical potentials into the exact equilibrium condition on μ ’s, and solve for density ratios. E.g., when two components (A and B) combine to make one (C) with some binding ∆ : a μ A +b μ B =c μ C If the components are ideal gases or solutes, then : here ( ) ( ) c TC a b TA TB c C a b A B c kT n K T e n n n K T n n + ∆ = = “Equilibrium constant” depends on ∆ ’s and T, doesn’t depend on densities: “Law of Mass Action” Interaction energy per molecule Physics 213: Lecture 13, Pg 5 Chemical Equilibrium of Ideal Gases and Solutes Chemical Equilibrium of Ideal Gases and Solutes Dissociation of hydrogen molecules H 2 H 2 ↔ 1 2 2 μ = μ Process Reaction Equilibrium Condition Ionize H atoms to electron + proton p e H + ↔ p e H μ + μ = μ General chemical reaction...
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This note was uploaded on 12/11/2011 for the course PHYS 213 taught by Professor Kuwait during the Spring '09 term at University of Illinois at Urbana–Champaign.

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Lect13 - Physics 213: Lecture 13, Pg 1 Lecture 13 Lecture...

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