Lecture9-10 Summary

Lecture9-10 Summary - UC Davis, BME BIM 162 Quantitative...

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Unformatted text preview: UC Davis, BME BIM 162 Quantitative Concepts in Biomolecular Engineering Summary of lectures 9/10: (Bio)molecules in solution Strength in numbers G dG dNi i N i p ,T , N j i and G i N i i i Sd T V d p N i d i 0 i (Gibbs-Duhem equation) kT Osmotic B pressure v* ln 1 xsolute H 2O i ,,sln * kBT ln xi sln i, Osmolality osm Cs 1 w N A k BT Using Osmotic Pressure to Measure Membrane Permeability Definition of permeability P: Follow-up Things worth remembering (among others) Ideal gas law “colligative properties” Open system: Gibbs free energy ↔ Chemical potential Gibbs-Duhem equation Chemical potential of a substance in solution in terms of number fraction potential of substance in solution in terms of number fraction Osmotic pressure: Intuitive definition & calculation “Osmolality” Permeability Mixing entropy Mixing Entropy Gmix S mix T p , Ni Gmix Gmixed Gunmixed G i N i i Mixing Entropy of an Ideal Gas p T V1 N1 p T V2 N2 p T V N dU 0 TdS pdV 0 S12 S1 S 2 kB x1 ln x1 x2 ln x2 N N Mixing Entropy Boltzmann’s expression for entropy: S kB ln W number of configurations How many ways are there to arrange N = NA + NB molecules of two “species” “A” and “B” (e.g., of a gas or liquid mixture)? HW W What is the entropy of mixing for this case? HW S AB kB x A ln x A xB ln xB N xi Ni n i N j nj j j ...
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Lecture9-10 Summary - UC Davis, BME BIM 162 Quantitative...

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