Reaction rate and rate laws Kinetics Reaction rate and rate laws

Reaction rate: rate = Δ concentration of species Δt aA + bB → cC + dD rate = Δ[C] = Δ[D] = -Δ[A] = -Δ[B] cΔt dΔt aΔt bΔt

Dependence on concentration of reactants: single reactant, A: rate = k[A]m; k = rate constant, m = order two reactants, A & B: rate = k[A]m[B]n m + n = overall order Generally, m and n are positive integers but can be zero or fractions.

Two important things about this form of the rate law: 1. The concentrations of the products do not appear in the rate law b/c the reaction rate is being studied under conditions where the reverse reaction does not contribute to reaction rate. 2. The values of m & n must be determined by experiment.

Determination of m and k from rate-concentration data: CH3CHO(g) → CH4(g) + CO(g) rate [CH3CHO] 2.0 M/s 1.0 M 0.5 M/s 0.50 M 0.080 M/s 0.20 M

rate1 = k[A]1m = [A]1 m rate2 k[A]2m [A]2 2.0 / 0.50 = (1.0/0.50)m 4.0 = 2.0m m = 2 so rate = k[CH3CHO]2 plug any data set back in to solve for k.

Integrated rate laws: zero order reactions: [A] = [A]o - kt plot of [A] vs. t is linear slope = -k, b = [A]o first order reactions: ln[A] = ln[A]o - kt plot of ln[A] vs t is linear slope = -k, b = ln[A]o

second order reactions: 1/[A] = kt + 1/[A]o plot of 1/[A] vs. t is linear slope = k, b = 1/[A]o

Zero order reactions most often involve a catalyst Zero order reactions most often involve a catalyst. When the catalyst is completely in use the concentration of reactants does not matter. When the same reaction occurs with no catalyst, the reaction is not zero order. For first order reactions: t1/2 is independent of the original concentration t1/2 is inversely related to k. If t1/2 is small, k is large and vice versa

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