11.2 Reaction Rate and Concentration YOU ARE EXPECTED TO BE ABLE TO: Define the initial rate of a reaction as the instantaneous rate at the start of the reaction. Write a rate law expression for a given reaction given experimental results that show the variation of initial rate with concentration. Define the concept of order of reaction and determine the order of a given reaction from initial rate vs concentration data Chemistry 1011 Slot 5

Initial Rate of Reaction The initial rate of reaction is the instantaneous rate measured at the start of the reaction The initial rate can be used as a benchmark Measurements of the initial rate for a reaction at different starting concentrations can be used to determine the effect of concentration on rate Chemistry 1011 Slot 5

The Rate Expression or Rate Law In general: Reactions occur as a result of collisions The higher the concentration of molecules, the greater the rate In some reactions, the rate is directly proportional to the concentration In other cases, the rate may increase much more quickly than the concentration The relationship between rate and concentration is known at the rate law or rate expression Chemistry 1011 Slot 5

Determining the Rate Law Expression The rate law MUST be determined from experiment – it is not related to the stoichiometry of the equation for the reaction Examine the concentration vs time graph for N2O5 Determine instantaneous rates at different times and concentrations of N2O5 Plot instantaneous rate vs [N2O5 ] This is a straight line, (equation y = mx + b) Rate = k[N2O5] ; this is the rate law expression; k is the rate constant P305 fig 11.3 Chemistry 1011 Slot 5

Using Initial Rates to determine the rate Law Measurements of the initial rate of reaction at different initial concentrations can be used to determine the rate law expression If a graph of initial concentration vs initial rate is a straight line, then rate is directly proportional to concentration: rate = k [reactant] If a graph is a curve, then rate = k[reactant]m Chemistry 1011 Slot 5

Order of Reaction The rate law expression is of the form: Rate = k[A]m The power to which the concentration is raised is called the order of reaction If m = 0, then “zero order” If m = 1, then “first order” If m = 2, then “second order” Chemistry 1011 Slot 5

Calculating the Order of Reaction when there is One Reactant If m is not equal to 1, the order of the reaction can be determined by comparing two rates at two different concentrations: Rate1 = k[A]1m Rate2 = k[A]2m Rate1 = k[A]1m = [A]1 m Rate2 k[A]2m [A]2 Chemistry 1011 Slot 5

Example 11.1 CH3CHO(g)  CH4(g) + CO(g) [ ] 0.10M 0.20M 0.30M 0.40M Rate (mol/L.s) 0.085 0.34 0.76 1.4 Choose the first two concentrations Rate2 = 0.34 = 4.0 Rate1 0.085 [CH3CHO]2 = 0.20 = 2.0 [CH3CHO]1 0.10 4.0 = (2.0)m ; m = 2 Rate = k[CH3CHO]2 The reaction is second order Chemistry 1011 Slot 5

Calculate the Rate Constant Rate = k[CH3CHO]2 Choose one set of data 0.085mol/L.s = k x (0.10 mol/L)2 k = 0.085mol/L.s = 8.5 L/mol.s (0.10 mol/L)2 Chemistry 1011 Slot 5

Order of Reaction with More Than One Reactant Most reactions involve >1 reactant aA + bB  products General rate law expression is: rate = k[A]m x [B]n m is “order with respect to A n is order with respect to B Overall order is m + n Chemistry 1011 Slot 5

Determining the Order Hold concentration of one reactant constant and vary other - measure initial rate Repeat, holding concentration of other reactant constant See Example 11.2, page 308 Chemistry 1011 Slot 5

Determining the Order of Reaction Graphically As an alternative to calculating the order of reaction by comparing two pieces of data, a graphical process can be used Plot rate vs concentration If the result is a straight line, there is a first order reaction, slope = k If the result is a curve, it is necessary to construct a graph of (natural) log rate vs (natural) log concentration to determine m Chemistry 1011 Slot 5

Why Use a Logarithm? If rate = k[A]m Then ln rate = ln k + m ln [a] This will be a straight line with slope m Chemistry 1011 Slot 5

Zero Order Reactions In rare cases, the rate of reaction is independent of the concentration of reactant(s) In these cases Rate = k[A]0 A plot of rate vs [A] would be a horizontal straight line Chemistry 1011 Slot 5