6.5 Rate Laws & Order of Reaction Rate Law The rate (r), is proportional to the product of the initial reactant concentrations raised to some exponent. For the general equation; a X + b Y  products 1

Rate Laws & Order of Reaction Rate Law Equation Through the data collected during experimentation the exponents, concentrations and initial rates can be determined. With this information a rate constant, k, can be determined and inserted in lieu of a proportionality relationship. The unit of k will depend on the total order of reaction. 2

Rate Laws & Order of Reaction The exponents of the reactants describe the mathematical relationship and the affect on the rate. The exponent of the individual reactant concentration is called the order of reaction. The sum of the reactants exponents results in the total order of reaction for the reaction 3

Rate Laws & Order of Reaction In the rate law equation: The order of reaction for X is 1 st The order of reaction for Y is 2 nd The order of reaction for Z is 0 The overall order of reaction is ( ) 3 rd 4

Determining Rate Law Equations Use the following experimental data to determine the Rate Law and Rate constant. 2 ClO 2(aq) + 2 OH - (aq)  ClO 3 - (aq) + ClO 2 - (aq) + H 2 O (l) ExperimentInitial [ClO 2 ] (mol/l) Initial [OH - ] (mol/l) Initial rate of formation of products (mol/L s) x x x

What would the rate law expression look like? 2 ClO 2(aq) + 2 OH - (aq)  ClO 3 - (aq) + ClO 2 - (aq) + H 2 O (l)

Determining Rate Law Equations ExperimentInitial [ClO 2 ] (mol/l) Initial [OH - ] (mol/l) Initial rate of formation of products (mol/L s) x x x

Determining Rate Law Equations ExperimentInitial [ClO 2 ] (mol/l) Initial [OH - ] (mol/l) Initial rate of formation of products (mol/L s) x x x 10 -2

Determining Rate Law Equations ExperimentInitial [ClO 2 ] (mol/l) Initial [OH - ] (mol/l) Initial rate of formation of products (mol/L s) x x x

Relating Reaction Rate to time The elapsed time before an observable event occurs in a reaction (i.e. – colour change, presence of gas bubbles, etc.) is an indication of an initial rate of reaction. Since rate = concentration/time rate  1/time As well, rate = k[A] n rate  [A] n Therefore, 1/time  [A] n 10

Relating Reaction Rate to time We can plot 1/  t vs. [A] n, to determine the order of a reaction. Look for a straight line plot to determine the value for “n” and the subsequent order. 1/  t Initial [A] 11

Relating Reaction Rate to time 1/  t Initial [A] 12

Relating Reaction Rate to time 1/  t Initial [A] 1/  t Initial [A] 2 13

Relating Reaction Rate to time 1/  t Initial [A] 1/  t Initial [A] 3 Third order reaction 1/  t Initial [A] 1/  t Initial [A] 5 Fifth order reaction 14