Chem 402 Lecture 23: L23 3:20:17
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Department
University College - Chemistry
Course
University College - Chemistry Chem 402
Professor
Barnes Alexander
Semester
Spring

Description
20 March 2017 L23: Chemical Potential and Equilibrium I. Chemical Potential A. Recap 1. Entropy is S = ๐‘˜๐‘™๐‘›ฮฉ a. Maximize microstates at equilibrium to maximize entropy of universe st 2. 1 Law a. ๐‘‘๐‘ˆ = รฐ๐‘ž + รฐ๐‘ค, with only expansionary work, ๐‘‘๐‘ˆ = รฐ๐‘ž โˆ’ ๐‘๐‘‰ 3. 2 Law รฐ๐‘ž a. ๐‘‘๐‘† โ‰ฅ ๐‘‡ b. At equilibrium, ๐‘‡๐‘‘๐‘† = รฐ๐‘ž ๐‘Ÿ๐‘’๐‘ฃ c. For a spontaneous process, , ๐‘‡๐‘‘๐‘† > รฐ๐‘ž ๐‘–๐‘Ÿ๐‘Ÿ๐‘’๐‘ฃ 4. Combined a. ๐‘‘๐‘ˆ โˆ’ รฐ๐‘ž + ๐‘๐‘‘๐‘‰ = ๐‘‘๐‘ˆ โˆ’ ๐‘‡๐‘‘๐‘† + ๐‘๐‘‘๐‘‰ = 0 (at equilibrium) b. ๐‘‘๐‘ˆ โˆ’ ๐‘‡๐‘‘๐‘† + ๐‘๐‘‘๐‘‰ < 0 (for spontaneous processes) 5. Criteria for spontaneous change a. At constant P and T: ๐‘‘๐‘ˆ โˆ’ ๐‘‡๐‘‘๐‘† + ๐‘๐‘‘๐‘‰ = ๐‘‘๐‘ˆ โˆ’ ๐‘‡๐‘‘๐‘† โˆ’ ๐‘†๐‘‘๐‘‡ + ๐‘๐‘‘๐‘‰ + ๐‘‰๐‘‘๐‘ < 0 b. ๐‘‘ ๐‘ˆ โˆ’ ๐‘‡๐‘† + ๐‘๐‘‰ = ๐‘‘ ๐บ ( ) ๐‘,๐‘‡< 0 โ€ข For spontaneous change, minimize G โ€ข ๐บ = ๐‘ˆ โˆ’ ๐‘‡๐‘† + ๐‘๐‘‰ = ๐ป โˆ’ ๐‘‡๐‘† = ๐ด + ๐‘๐‘‰ โ€ข Directly form the second law c. To maximize entropy of the universe, looking at system variables 6. G(p) independence on pressure at constant temperature a. ๐‘‘๐บ = ๐‘‰๐‘‘๐‘ โˆ’ ๐‘†๐‘‘๐‘‡ ฬ… ฬ… b. In condensed (incompressible) phases: โˆ†๐บ = ๐‘‰(๐‘ƒ โˆ’ ๐‘ƒ 2 1 ฬ… ๐‘ ๐‘›๐‘…๐‘‡ ๐‘๐‘“ c. For gases (compressible): โˆ†๐บ = โˆซ๐‘0 ๐‘ ๐‘‘๐‘ = ๐‘…๐‘‡๐‘™๐‘›( ) ๐‘0 B. Multicomponent Systems 1. Fundamental equations for closed systems a. ๐‘‘๐‘ˆ = ๐‘‡๐‘‘๐‘† โˆ’ ๐‘๐‘‘๐‘‰ b. ๐‘‘๐ด = โˆ’๐‘†๐‘‘๐‘‡ โˆ’ ๐‘๐‘‘๐‘‰ c. ๐‘‘๐ป = ๐‘‡๐‘‘๐‘† + ๐‘‰๐‘‘๐‘ d. ๐‘‘๐บ = โˆ’๐‘†๐‘‘๐‘‡ + ๐‘‰๐‘‘๐‘ 2. For a 2 component system ๐œ•๐บ ๐œ•๐บ ๐œ•๐บ ๐œ•๐บ a. ๐‘‘๐บ = ( ) ๐œ•๐‘‡ ๐‘‘๐‘‡ + ( ๐œ•๐‘ ๐‘‘๐‘ + ( ๐œ•๐‘› 1) ๐‘‘๐‘›1+ ( ๐œ•๐‘›2) ๐‘‘๐‘› 2 ๐‘,๐‘›1,2 ๐‘‡,1 ,2 ๐‘,๐‘‡,2 ๐‘,๐‘›1,๐‘‡ b. ๐‘‘๐บ = โˆ’๐‘†๐‘‘๐‘‡ + ๐‘‰๐‘‘๐‘ + ๏ญ ๐‘‘๐‘› + 1 ๐‘‘๐‘› 1 2 2 โ€ข Define ๏ญ is the chemical potential of species โ€œiโ€ โ€ข (๐œ•๐บ ) = ๏ญ for I: j โ‰  ni ๐œ•๐‘›๐‘– ๐‘,๐‘‡,๐ผ ๐‘– c. ๏ญ(i, p, n)jis an intensive variable d. This gives a new set of fundamental equations for OPEN systems (mass can flow in and out, composition can change) 3. Fundamental Equations for open systems a. ๐’…๐‘ฎ = โˆ’๐‘บ๐’…๐‘ป + ๐‘ฝ๐’…๐’‘ + โˆ‘ ๐’Š๏ญ ๐’…๐’ ๐’Š ๐’Š b. ๐‘‘๐ป = ๐‘‘๐บ + ๐‘‡๐‘‘๐‘† + ๐‘†๐‘‘๐‘‡ = โˆ’๐‘†๐‘‘๐‘‡ + ๐‘‰๐‘‘๐‘ + โˆ‘ ๏ญ ๐‘‘๐‘› + ๐‘‡๐‘‘๐‘† + ๐‘†๐‘‘๐‘‡ ๐‘– ๐‘– ๐‘– โ€ข ๐’…๐‘ฏ = ๐‘ป๐’…๐‘บ + ๐‘ฝ๐’…๐’‘ + โˆ‘ ๐’Š๏ญ๐’Š๐’…๐’ ๐’Š c. ๐ป = ๐‘ˆ + ๐‘๐‘‰ โ†’ ๐‘ˆ = ๐ป โˆ’ ๐‘๐‘‰ โ€ข ๐‘‘๐‘ˆ = ๐‘‘๐ป โˆ’ ๐‘‘ ๐‘๐‘‰ = ๐‘‡๐‘‘๐‘† + ๐‘‰๐‘‘๐‘ + โˆ‘ ๐‘–๏ญ ๐‘–๐‘› โˆ’๐‘–๐‘‰๐‘‘๐‘ โˆ’ ๐‘๐‘‘๐‘‰ โ€ข ๐’…๐‘ผ = ๐‘ป๐’…๐‘บ โˆ’ ๐’‘๐’…๐‘ฝ + โˆ‘ ๐’Š๏ญ๐’Š๐’…๐’ ๐’Š d. ๐ด = ๐‘ˆ โˆ’ ๐‘‡๐‘† โ†’ ๐‘‘๐ด = ๐‘‘๐‘ˆ โˆ’ ๐‘‘ ๐‘‡๐‘† = ๐‘‡๐‘‘๐‘† โˆ’ ๐‘๐‘‘๐‘‰ + โˆ‘ ๏ญ ๐‘‘๐‘› โˆ’ ๐‘‡๐‘‘๐‘† โˆ’ ๐‘†๐‘‘๐‘‡ ๐‘– ๐‘– ๐‘–
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