{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lect19 - Misce ous Note llane s The end is near dont get...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 19, p 1 Miscellaneous Notes The end is near – don’t get behind. All Excuses must be taken to 233 Loomis before noon, Friday, Dec. 3. The PHYS 213 final exam times are * 7-9 PM, Monday, Dec. 13 and * 8-10 AM, Tuesday, Dec. 14 . The deadline for changing your final exam time is 10pm, Tuesday, Nov. 30. Homework 6 is due Saturday , Dec. 4 at 8 am. Course Survey = 2 bonus points (accessible at the top of HW6)
Background image of page 1

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

View Full Document Right Arrow Icon
Lecture 19, p 2 Lecture19: Chemical Equilibria, Surfaces, and Phase Transitions Chemical equilibria - Law of mass action Surface chemistry Phase equilibria and chemical potentials Vapor pressure of a solid Reading for this Lecture: Elements Ch 13
Background image of page 2
Lecture 19, p 3 “Chemical” is a bit of a misnomer. We’re describing any process in which things combine (or rearrange) to form new things. These problems involve reactions like: aA + bB cC, where A, B, and C are the particle types and a, b, and c are integers. In equilibrium the total free energy, F , is a minimum. We must have F = 0 when the reaction is in equilibrium , for any reaction that takes us away from equilibrium: Therefore: a μ A + b μ B = c μ C using 0 C B A A B A C A A B B C C A dN dN dF F F F dN N N dN N dN F b F dN dN dN a b c c F N a N a N = + + = + - = = - = Chemical Equilibrium
Background image of page 3

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

View Full Document Right Arrow Icon
Lecture 19, p 4 Interactions between the particles ( e.g. , molecules): In addition to simple PE terms from external fields, there are usually PE terms from interactions between particles (which are not usually ideal gases). Interactions between the molecules can often be neglected. That is, we’ll treat the molecules as ideal gases. Internal energy of each particle ( e.g. , molecule): Atoms can combine in any of several molecular forms, each of which has a different binding energy. 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 reaction will NOT proceed to completion in either direction , because μ depends on n for each type of molecule. As any one 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.) Chemical Equilibrium (2)
Background image of page 4
Lecture 19, p 5 Treating the components as ideal gases or solutes: Plug these chemical potentials into the equilibrium condition, a μ A + b μ B = c μ C , and solve for the density ratios: K(T) is called the “ equilibrium constant ”. It depends on ’s and T, but not on densities. This equilibrium condition is a more general version of the law of mass action that you saw before for electrons and holes. The exact form of the equilibrium condition (how many things in the numerator and denominator, and the exponents) depends on the reaction formula: aA + bB cC RHS numerator LHS denominator , where ( ( ) ) C A C c T c C C A B a b T a b A B T n kT K T e c a b n n n K T n n + = ∆ ≡ - = - ln i T i n i i n kT μ = - ∆ Internal energy per molecule Chemical Equilibrium (3)
Background image of page 5

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

View Full Document Right Arrow Icon
Lecture 19, p 6 Examples of Chemical Equilibrium [ ] ( ) [ ] [ ] c a b C K T A B = Process
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}