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Reaction Kinetics

Reaction Kinetics. aA + bB  cC + dD. Rate (r) = -(1/a) (d[A]/dt) or -(1/b) (d[B]/dt) or …. +(1/c) (d[C]/dt) or +(1/d) (d[D]/dt). Reaction rates are followed by monitoring the rate of disappearance of reactants or the rate of appearance of products.

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Reaction Kinetics

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  1. Reaction Kinetics aA + bB  cC + dD Rate (r) =-(1/a) (d[A]/dt) or -(1/b) (d[B]/dt) or …. +(1/c) (d[C]/dt) or +(1/d) (d[D]/dt) Reaction rates are followed by monitoring the rate of disappearance of reactants or the rate of appearance of products. Rate Law: rate = k [A]a [B]b [L]l k = rate constant - A and B are reactants – L is a catalyst or intermediate a/b/l = partial reaction order with respect to A, B, and L, respectively n = a + b + l the overall order of the reaction (n) is the sum of all the partial orders

  2. Most Common Reaction Orders 1st order: rate = k [A] rate = k [A]2 or.... 2nd order: rate = k [A][B] 3rd order: rate = k [A]2[B] etc.

  3. Rate of loss of Reactant 2nd order reversible 1st 1st order

  4. LINEAR RATE EQUATIONS 1st: ln ([A]/[Ao]) = -kt ln [A] = -kt + ln[Ao] plot ln[A] vs. t (slope = -k) 2nd: 1/[A] – 1/[Ao] = kt 1/[A] = kt + 1/[Ao] plot 1/[A] vs. t (slope = k)

  5. ~ 1 half-life ln[A] vs. t 2nd order 1st order

  6. ~ 1 half-life 1/[A] vs. t 1st order 2nd order

  7. Rate of loss of Reactant 2nd order reversible 1st 1st order

  8. Nature of reaction catalyst Temperature (k = f(T)) [reactants] Factors that affect Reaction Rates A + B  D + E r = k [A]a [B]b [C]g Why and How do these factors influence rate? collision theory and activation energy, Ea.

  9. Transition state Eact Energy (G) A + B-B DG˚ A-B + B Collision Theory (pg 668) & Transition State Theory (pg 669) A + B2 AB + B + (free energy) A – B -- B

  10. ln k 1/T ln k = -Ea/R  1/T + ln A ln (k2/k1) = - Ea/R (1/T2 – 1/T1)

  11. A – B -- B Transition state Eact Transition state Eact Energy (G) A + B-B DG˚ A-B + B Catalyst – Species that is part of the reaction but regenerated reusable – function by lowering the activation energy A + B2 AB + B + (free energy) A – B -- B

  12. Radioactive decay is 1st Order Ln(Ao/A) = kt & t1/2 = 0.693/k or k = 0.693/t1/2 14C t1/2 = 5730 years – What is k? isotope half-lifeemits 3H 12.26 yr b 14C 5730 yr b 32P 14.26 days b 60Co 5.272 yr b g 90Sr 28.8 yr b g 222Rn 3.824 days a g 235U 7.04 x 108 yr 238U 4.51 x 109 yr 239Pu 2.41 x 104 yr

  13. Radiocarbon dating (pg 949) The natural abundance of 14Cis ……. It remains constant because it is constantly produced by cosmic ray neutrons according to the following …. 147N + 10n  146C + 11H Living plants maintain 14C at a constant level . When the organism dies the 14C begins to decay ….. 14C  14N + 0-1b A priest brings you a small sliver of wood from a relic that he was told came from the cross on Calvary. He asks you to test its validity. You find that it contains 0.850 times the 14C activity as fresh wood. Could this relic be from the true cross?

  14. Dating older rocks t1/2 for 23892U is 4.51 x 109 years Uranium decays by a radioactive series ending with 206Pb. (pg 950) A meteorite sample is found to contain 1.2 mg 206Pb and 4.4mg 238U. When was the ore contained in the meteorite formed? [238U]o = 238/206  1.2 + 4.4 = 5.8mg k = 0.693/(4.51 x 109) = 1.54 x 10-10 yr-1 ln (4.4/5.8) = -1.54 x 10-10• t = 1.7 billion years

  15. NO2(g) + CO(g) NO(g) + CO2(g) r = k [NO2]2 why not r = k [NO2][CO]? Elementary reaction – rate expression reflects reaction rarely exceeds 2nd order. Mechanism – reaction as series of elementary steps Rate expression – determined by ‘slow’ or ‘rate determining’ step (RDS). NO2 + NO2 NO3 + NO slow NO3 + CO  NO2 + CO2 fast

  16. What if RDS is not first step? NO + Br2 NOBr2 fast, equilibrium NOBr2 + NO  2 NOBr slow r = k [NO] [Br2] ? 2NO + Br2 2 NOBr • Write rate expression for ‘slow’ step • Write equilibrium expression for 1st step • Rearrange equilibrium to solve for [intermeidate] • Sub this expression back into RDS rate expression

  17. The Arrhenius Equation k = A e(-Ea/RT) The rate of a reaction depends on the thermal energy available relative to the Activation Energy barrier that must be overcome. ln k = – Ea/RT + ln A or …. ln k = -Ea/R  1/T + ln A Measure k for a reaction at various temperatures.. Plot ln k vs. 1/T: slope = -Ea/R If only two values of T … ln (k2/k1) = Ea/R (1/T2 – 1/T1)

  18. Catalysts Speed up reaction rates by lowering Eact. Catalysts get involved in the reaction but are regenerated at the end. (reusable) Homogeneous – catalyst in same phase as reactants Heterogeneous – catalyst in different phase than reactant. A catalyst will show up in the mechanism as a reactant in an early step and a product of a step occurring after the RDS. (pg 681)

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