110c-lecture24 - Instantaneous Rate of Reaction Reaction...

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Instantaneous Rate of Reaction Reaction rate at specific time point (t 1 ) is called instantaneous rate. [R](t) [P](t) [] [ ] dt R d dt P d = = rate Time dP dt Concentration P R t 1 Instantaneous rate equals the slope of the tangent at a specific time (t 1 ). Slope of tangent expressed by a derivative from calculus (e.g. d[P]/dt). Units of rate: M s -1 or M min -1 0 ] [ < dt R d (i.e. [R] decrease vs t) Minus sign because
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Reaction Rate vs Rate Law dD cC bB aA + + General rate expression determine from balanced eqn: [ ] [ ] [ ] [ ] dt D d 1 dt C d 1 dt B d 1 dt A d 1 d c b a rate = = = = Divide by stoichiometric coefficient. Add minus sign for each of reactants. Rate law determined empirically: [] [ ] y x B A k rate = [A] vs time Rate vs [A] Reaction order given by x and y
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Zero-order Kinetics A products Zero-order k v(t) = - [A] = k [A] 0 v(t) t v(t) = k [A] d t = k - d [A] v(t) = Slope = k [A] t = - kt + [A] 0 Half Life: t 1/2 = 0.5[A] 0 /k
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First-Order Kinetics A products What is [A] vs time? First order reaction: rate = k[A] 1 [units of k] = s -1 = k [A] d[A ] dt rate = - = - k dt [A] d[A ] [A] 0 [A] t 0 t ln x 2 ln x 1 = ln x 2 x 1 1 x dx = ln x Recall calculus: = -kt ln [A] t [A] 0 [A] t = [A] 0 exp(-kt) ln[A] t = -kt + ln[A] 0 Slope = -k ln[A] [A] time Integrated Rate law time
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Examples of First-Order Reactions Common First-order reactions: β S P 0 1 32 16 32 15 + [ ] [ ] kt e A A = 0 [] kt A A = 0 ln Radioactive decay ) ( (g) N 4 ) ( O 2N 2 2 5 2 g O O g + Thermal Decomposition CN CH NC CH 3 3 Isomerization
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Half-life (t 1/2 ) vs. Average Lifetime ( τ = 1/k) kt A A = 0 ] [ ] [ ln when t=t 1/2 , 0 2 1 ] [ ] [ A A = and we have 2 1 0 0 2 1 ] [ ] [ ln kt A A = 2 1 2 ln 2 1 ln kt = = 2 1 2 ln t k = where ln2 = 0.693…
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This note was uploaded on 06/22/2010 for the course CHEM 21360 taught by Professor Ame during the Spring '09 term at East Los Angeles College.

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110c-lecture24 - Instantaneous Rate of Reaction Reaction...

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