Chem 402 Lecture 25: L25 3:24:17
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Department
University College - Chemistry
Course Code
University College - Chemistry Chem 402
Professor
Barnes Alexander

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24 March 2017 L25: Equilibrium, Biophysical Applications, and Temperature I. The Equilibrium Constant and Applications A. Equilibrium Constant Review 1. PKC, Drug Design, and Entropy of Mixing a. PKC has a C2 domain in lipid bilayer and a catalytic domain b. The c1b regulatory domain prevents PKC activation c. Must consider the active conformation of the protein for when a drug (Bryostatin) is just about to bind • This conformation is present in the ensemble d. The active state present in the ensemble at equilibrium because there is a huge entropic advantages with the ensemble at equilibrium to sample more microstates e. Binding essentially stabilizes certain protein conformations that are already present in the ensemble • Binging of c1b lowers the energy of that particular state, and thus that state becomes more favorable in the ensemble  larger population in that lower energy state • Events will pull out an already stable conformation in the ensemble (conformational selection) f. All driven by the entropy of mixing 0 −∆𝐺 𝑟𝑥𝑛/𝑅𝑇 2. ∆𝐺 𝑟𝑥𝑛 = −𝑅𝑇𝑙𝑛𝐾 → 𝐾𝑝= 𝑒 𝑝 𝑝𝑣𝑐𝑝𝑣𝐷 a. Note: 𝐾 ≠ 𝐶 𝐷  always need the p (reference) = 1 bar in the bottom 𝑝 𝑝𝑣𝐴𝑝𝑣𝐵 𝑣𝑐𝐴 𝐵 𝑣𝐷 (𝑡𝑜𝑡) (𝑡𝑜𝑡) 𝑣𝑐 𝑣𝐷 ∆𝑣 𝑝0 𝑝0 𝑋𝐶 𝑋𝐷 𝑝𝑡𝑜𝑡 b. 𝐾 =𝑝 𝑝𝑡𝑜𝑡 𝑣𝐴 𝑝𝑡𝑜𝑡𝑣𝐵 ∗𝑋 𝑣𝐴𝑋𝑣𝐵 = ( 𝑝0) 𝐾 𝑥 ( 𝑝0 ) (𝑝0 ) 𝐴 𝐵 • Note: ∆𝑣 = 𝑣 + 𝐶 𝐷) − 𝑣 +𝐴𝑣 𝐵 ) 𝑋 𝑐𝑋 𝑣𝐷 • 𝐶 𝐷 = 𝐾 𝑋𝑣𝐴 𝑋𝑣𝐵 𝑥 𝐴 𝐵 • Note: K Pnd K arX unitless! c. For shifts with respect to pressure, look at the change in X : 𝑝 𝑡𝑜𝑡−∆𝑣 • 𝐾 𝑥 ( 0 ) 𝐾 𝑃 tells us how equilibrium shifts with total pressure 𝑝 3. Note on N O2= 4NO equi2ibrium and reaction progress () 1 a.  = 4(𝑃𝑡0) 1 (1+ 𝑃 )2 𝐾𝑝 𝑃𝑡𝑜𝑡 b. As ( 𝑃 0) increases,  decreases c. LeChatelier’s Principle: if you increase total pressure, you push the equilibrium towards the reactants here 4. LeChatelier’s Principle and Lenz’s Law a. Gly263 of PKC c1b domain can be tagged and identified via NMR b. The part of the residue (a snipped, rest attached to backbone) is shown to the right c. NMR looks at the chemical shift anisotropy of the C=O in the middle • Since the carbon has different things attached to it, the e distribution will be asymmetric - • Furthermore, if the top O is involved in H-bonding, it further alters the e distribution around the C=O • In a 7.0T magnetic field oriented in +y (if this page is in the x-y plane), by - Lenz’s law, the e will move in a way to oppose the large magnetic field so that e spinning creates a small magnetic moment in the –y direction 5. Entropy of Mixing a. For a generic reaction, we can quantify the entropy of mixing for the reactants b. We know for A + B = C + D: 0 𝑃𝐴 𝑉𝐴 0 𝑃𝐵 𝑉𝐵 • 𝑑𝐴=  +𝐴𝑅𝑇𝑙𝑛( ) 𝑃 0 and 𝑑 𝐵  +𝐵𝑅𝑇𝑙𝑛( ) 𝑃0 0 1 1 0 • If a = nB: ∆𝐺𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∆𝐺 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠+ 𝑅𝑇𝑙𝑛( ) 2 𝑅𝑇𝑙𝑛( ) =2∆𝐺 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠+ 1 𝑅𝑇𝑙𝑛( ) = ∆𝐺 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠− 𝑅𝑇𝑙𝑛 4 ) 4 c. “-RTln(4)” is the mixing term, = the entropy of mixing • It is negative because mixing increases the number of microstates, decreasing 0 free energy, so it i
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