Lecture 9- Enzyme Kinetics

Lecture 9- Enzyme Kinetics - Comparing Reaction Rate...

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Comparing Reaction Rate Theories RT H R S B e e h T k k o o Δ Δ = RT E A Ae k = Arrhenius Theory: Collision Theory: Transition State Theory: Ca 2+ (aq) + SO 4 2- (aq) [Ca 2+ ---SO 4 2- ] CaSO 4 (s) Δ S tot = Δ S reactants + Δ S solvent Δ S solvent is positive because H 2 O less ordered around the neutral transition state. Δ S reactants is negative because reactants more disordered than transition state. If | Δ S solvent | > | Δ S reactants |, then Δ S tot > 0, usually indicates a fast reaction rate. μ π T k d B A Z B AB AB 8 ] ][ [ 2 = RT E AB A e B A Z P k = ] ][ [ = 10 11 M -1 s -1
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If A and B have same charge (z a z b > 0), rate constant k increases with If A and B have opposite charge (z a z b < 0), rate constant k decreases with If either A or B are uncharged (z a z b = 0, k is independent of ionic strength. Kinetic Salt Effect I I I z z k k B A salt 36 . 2 log 0 = A + + B - AB P k [Co(NH 3 ) 5 Br] 2+ + Hg 2+ S 2 O 8 2- + I - [NO 2 NCO 2 C 2 H 5 ] - + OH -- H + + Br - CH 3 CO 2 C 2 H 5 + OH - RT H R S B e e h T k k o o Δ Δ =
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Example: Proteins are polymers of amino acids that have net charge at pH 7. The rate constant of dimerization of a cationic protein P vs. ionic strength (I): P ?+ + P ?+ [P ?+ --- P ?+ ] I 0.01 0.015 0.02 0.025 0.03 0.035 0 k k salt 8.10 13.3 20.5 27.8 38.1 52 () I z z k k B A ideal non 36 . 2 ln = Plot ideal non k k ln vs. I 1/2 has slope = 2.36z 2 (infer charge (z) from slope). I 1/2 0.1 0.122 0.141 0.158 0.173 0.187 ideal non k k ln 2.09 2.58 3.02 3.32 3.64 3.95 The slope of the plotted data is 21, indicating z 2 = 9 and charge number (z) is +3.
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Diffusion Controlled Kinetics Fastest reactions have rate constants ~10 9 –10 12 s -1 . Rate limited by how quickly reactants diffuse together: Diffusion-controlled reaction . ) )( ( 4 Products C B C B C B A D D D r r N k + + = + π D B and D C are the diffusion coefficients r B and r C are the radii of the molecules B and C η is the viscosity of the solvent r T k D B πη 6 = If D B = D C = D and r B = r C = r: 1 1 10 10 3 8 = s M RT k D η in H 2 O at 298 K
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Rapid Mixing for Fast Reactions Flow Method to study fast reactions (millisecond mixing time).
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Lecture 9- Enzyme Kinetics - Comparing Reaction Rate...

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