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

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

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

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...
View Full Document

## 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.

### Page1 / 25

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online