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final study guide - Exam I Kinetics Rates Relationships...

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Exam I Kinetics Rates Relationships - Rate: change that occurs in a given interval of time - speed (average rate): Δx/Δt = rate of travel (change in position over change in time) - instantaneous rate: always changing lim t 0 Δx/Δt = dx/dt (as t approaches zero, limit of avg. rate approaches instantaneous rate - chemical rate laws: describe instantaneous rates in terms of Δ[reactant]/Δt or Δ[product]/Δt - Express rate of rxn in terms of: disappearance of reactants, appearance of products, stoichiometry of reaction tells how these are related aA + bB cC + dD rate = -(1/a)(Δ[A]/Δt) = -(1/b)(Δ[B]/Δt) = +(1/c)(Δ[D]/Δt) = +(1/d)(Δ[D]/Δt) - 4 factors affect rate of reactions: rate depends on FREQUENCY of collisions btw molecules 1. physical state of reactants (solid, liquid, gas) smaller molecules result in faster reactions 2. concentration of reactants, increasing conc faster rates 3. temperature, increasing T faster rates 4. presence of catalyst, catalyst facilitates rxn faster rates Rate Laws - rate law: relationship btw rate of rxn and conc of its reactants rate = k[A] x [B] y k is rate constant, independent of [A] and [B], varies with T (as T inc, k inc) x and y are reaction orders ( > 0) order of rxn = sum of exponents, overall order of rxn = x + y RATE LAW MUST BE DETERMINED EXPERIMENTALLY, exponents cannot be predicted from the overall reaction . Reaction Orders Using experimental data to determine the rate law: 1. Observe effect of changing initial concentration of reactants on initial rate reaction 2. Most reactions have exponents of 0, 1 or 2 (can be fraction or negative) 3. Change in concentration of zero order reactants has no effect on the rate 4. Doubling concentration of first order reactants doubles rate 5. Doubling concentration of second order reactants increases rate 2 2 =4 (quadruples rate) 6. Tripling concentration of second order reactants increases rate by 3 2 =9 7. Third order reactants, doubling concentration increases rate by 2 3 =8 Rate vs. Time - differential rate law for 1 st order reaction (x = 1) k[A] = -Δ[A]/Δt ln[A]/[A] 0 = -kt linear equation ln[A] = -kt + ln[A] 0 in form of y = mx + b plot ( ln[A] vs. time ) gives straight line slope = -k y intercept is ln[A] 0 - integrated second order rate law (x = 2) 1/[A] = kt + 1/[A] 0 linear plot ( 1/[A] vs. time ) Half Lives t 1/2 is the time is takes for the concentration of a reactant to drop to half its initial value for reaction A products t 1/2 [A] = [A] 0 /2 1 st order reactions: t 1/2 = -0.693/k depends on k and temperature (doesn’t depend on concentration)
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t 1/2 = t 1/2 ALWAYS EQUAL FOR 1ST ORDER REACTIONS 2 nd order reactions: t 1/2 = 1/k[A] 0 depends on initial concentration [A] 0 t 1/2 increases as [A] 0 decreases for 2 nd order reactions - temperature dependence of reaction rates: rate increases as temperature increases, k increases as temperature increases Activation Energy (E a ) - defn: energy required to go from reactants to a transition state - transition state or activated complex: high energy transitory complex that cannot be isolated -
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