Determining the Form of the Rate Law

Rate Law The mathematical expression that allows calculations of reaction rate as a function of reactant concentration. Must be determined experimentally by altering the initial concentrations of all reactants and observing the effect on initial rate.

How Data is created

k, m and n must be experimentally determined Rate Law Equation Since the concentrations within a reaction change the instant the reaction starts, chemists look at the effect of the initial concentrations. For any general reaction: aA + bB → products The rate law equation may be expressed as the product of the initial concentrations raised to some exponential value. Rate = k[A]m[B]n k, m and n must be experimentally determined

Method of Initial Rates Used to find the form of the rate law Choose one reactant to start with Find two experiments where the concentration of that reactant changes but all other reactants stay the same Write the rate laws for both experiments Divide the two rate laws Solve for the order Follow the same technique for other reactants

Example Choose one reactant to start with NH4+ Find two experiments where the concentration of that reactant changes but all other reactants stay the same Exp 2 & 3

Write the rate laws for both experiments Exp 2: 2.70x10-7 = k(0.100)x(0.010)y Exp 3: 5.40x10-7 = k(0.200)x(0.010)y Divide the two rate laws 0.50 = 0.50x Use log rules to solve for the order x = 1 so the order for NH4+ is one

Follow the same technique for other reactants NO2-: Exp 1 & 2 Exp 1: 1.35x10-7 = k(0.100)1(0.0050)y Exp 2: 2.70x10-7 = k(0.100)1(0.010)y 0.5 = 0.5y y = 1 So Rate = k[NH4+]1[NO2-]1 Overall Reaction Order – sum of orders of reactants

Finding k We can find k using values from any of the experiments given Units will be different for k depending on order of reactants

Example BrO3- : Exp 1 & 2 Exp 1: 8.0x10-4 = k(0.10)x(0.10)y(0.10)z

Example Br- : Exp 2 & 3 Exp 2: 1.6x10-3 = k(0.20)1(0.10)y(0.10)z

Example H+ : Exp 1 & 4 Exp 1: 8.0x10-4 = k(0.10)1(0.10)1(0.10)z 0.25 = 0.50z or log0.25=zlog0.50 z = 2

Example So Rate = k[BrO3-]1[Br-]1[H+]2 Solve for rate constant, k Overall order of reaction = 4 Solve for rate constant, k

Homework Page 380 #1-5 Monday we will determine the rate law equation for the iodine clock reaction, please read investigation6.5.1 on page 392