1 Rate equations

The rate of reaction is defined as the change in concentration of a substance in unit time Its usual unit is mol dm-3s -1 When a graph of concentration of reactant is plotted vs time, the gradient of the curve is the rate of reaction. The initial rate is the rate at the start of the reaction where it is fastest Reaction rates can be calculated from graphs of concentration of reactants or products Initial rate = gradient of tangent time concentration For the following reaction, aA + bB  products, the generalised rate equation is: r = k[A]m[B]n r is used as symbol for rate The unit of r is usually mol dm-3 s -1 The square brackets [A] means the concentration of A (unit mol dm-3 ) k is called the rate constant m, n are called reaction orders Orders are usually integers 0,1,2 0 means the reaction is zero order with respect to that reactant 1 means first order 2 means second order NOTE: the orders have nothing to do with the stoichiometric coefficients in the balanced equation. They are worked out experimentally The total order for a reaction is worked out by adding all the individual orders together (m+n) Calculating orders from initial rate data For zero order: the concentration of A has no effect on the rate of reaction r = k[A]0 = k For first order: the rate of reaction is directly proportional to the concentration of A r = k[A]1 For second order: the rate of reaction is proportional to the concentration of A squared r = k[A]2 initial Graphs of initial rate against concentration show the different orders. The initial rate may have been calculated from taking gradients from concentration /time graphs For a rate concentration graph to show the order of a particular reactant the concentration of that reactant must be varied whilst the concentrations of the other reactants should be kept constant. The rate constant (k) 1. The units of k depend on the overall order of reaction. It must be worked out from the rate equation 2. The value of k is independent of concentration and time. It is constant at a fixed temperature. 3. The value of k refers to a specific temperature and it increases if we increase temperature For a 1st order overall reaction the unit of k is s -1 For a 2nd order overall reaction the unit of k is mol-1dm3s -1 For a 3rd order overall reaction the unit of k is mol-2dm6s -1 Example (first order overall) Rate = k[A][B]0 m = 1 and n = 0 – reaction is first order in A and zero order in B – overall order = 1 + 0 = 1 – usually written: Rate = k[A] Remember: the values of the reaction orders must be determined from experiment; they cannot be found by looking at the balanced reaction equation Calculating units of k 1. Rearrange rate equation to give k as subject k = Rate [A] 2. Insert units and cancel k = mol dm-3s -1 mol dm-3 Unit of k = s-1 N Goalby chemrevise.org 2 0.060 0.030 0.015 0.0075 t ½ t ½ t ½ Time (min) [A] Continuous rate data This is data from one experiment where the concentration of a substance is followed throughout the experiment. Continuous rate experiments This data is processed by plotting the data and calculating successive half-lives. If half-lives are constant then the order is 1st order The half-life of a first-order reaction is independent of the concentration and is constant If half-lives rapidly increase then the order is 2nd order Example: Write rate equation for reaction between A and B where A is 1st order and B is 2nd order. r = k[A][B]2 overall order is 3 Calculate the unit of k Unit of k = mol-2dm6s -1 1. Rearrange rate equation to give k as subject k = Rate [A][B]2 2. Insert units and cancel k = mol dm-3s -1 mol dm-3 .(moldm-3 )2 3. Simplify fraction k = s -1 mol2dm-6