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Rate Law rate a [Br2] rate = k [Br2] The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. aA + bB cC + dD Rate = k [A]x[B]y Reaction is xth order in A Reaction is yth order in B Reaction is (x +y)th order overall Examples Write the general rate law for the following chemical reactions 1. F2(g) + 2 ClO2(g) 2 FClO2(g) 2. Decomposition of liquid water into hydrogen and oxygen gas Relationship between order and rate AB rate = k[A]x o if x=1 o Rate o If x=2 o Rate o If is directly proportional to [A] varies as the square of [A] x=0 o Rate is independent of [A] Review of Concepts A reaction is second order in A and first order in B. If the concentration of A doubles and the concentration of B is halved, overall what has happened to the rate? Method of Initial Rates F2 (g) + 2ClO2 (g) 2FClO2 (g) rate = k [F2]x[ClO2]y Double [F2] with [ClO2] constant Rate doubles x=1 rate = k [F2][ClO2] 2nd order overall Quadruple [ClO2] with [F2] constant Rate quadruples y=1 7 Example 1 3A Trial Initial [A] (M) B Initial Rate (M/s) 1 0.050 3.0 x 10 -4 2 0.10 12 x 10 -4 3 0.20 48 x 10 -4 Use the data provided to identify the order with respect to A, overall order, and rate law. Example 2 2NO(g) + 2H2(g) N2(g) + 2H2O(g) Trial Initial [NO] (M) Initial [ H2] (M) Initial Rate (mol/Ls) 1 0.100 0.100 2.00 x 10 -3 2 0.200 0.100 4.00 x 10 -3 3 0.200 0.200 16.0 x 10 -3 Use the data provided to identify the order with respect to each reactant, overall order, and rate law. General rate law: rate = k [NO]x[H2]y Pick appropriate experiments to compare *For NO, pick trials 1&2 because the H2 concentration doesn’t change *Same terms on Exp2: 4.00×10−3 = k [0.200]X [0.100]Y the top and −3 X Y Exp1: 2.00×10 = k [0.100] [0.100] bottom cancel out 2 = 2x X=1; 1st order in NO For H2, pick trials 2&3 because the concentration of NO doesn’t change Exp3: 16.0×10−3 = k [0.200]X [0.200]Y Exp2: 4.0×10−3 = k [0.200]X [0.100]Y 4 = 2y y=2; 2nd order in H2 (better) rate=k[NO][H2]2 *Same terms on the top and bottom cancel out 3rd order overall Pick any trial, plug in all the numbers, solve for k k=2.00 1/M2s *Calculating the FINIAL ANSWER units for k is a bonus rate=2.00[NO][H2]2