Kinetics Until now, we have considered that reactions occur: Reactants form products and conservation of mass is used to find amounts of these Now, we investigate how fast products are formed (or how fast reactants disappear): THE RATE of REACTION We will use differential rate laws to determine order of reaction and rate constant from experimental data

Rate of Reaction Rate = Δ[concentration] or d [product] Δ time dt Rate of appearance of a product = rate of disappearance of a reactant Rate of change for any species is inversely proportional to its coefficient in a balanced equation.

Rate of Reaction Assumes nonreversible forward reaction Rate of change for any species is inversely proportional to its coefficient in a balanced equation. 2N 2 O 5  4NO 2 + O 2 Rate of reaction = -Δ[N 2 O 5 ] = Δ[NO 2 ] = Δ[O 2 ] 2 Δt 4 Δt Δt where [x] is concentration of x (M) and t is time (s)

Reaction of phenolphthalein in excess base Use the data in the table to calculate the rate at which phenolphthalein reacts with the OH- ion during each of the following periods: (a) During the first time interval, when the phenolphthalein concentration falls from M to M. (b) During the second interval, when the concentration falls from M to M. (c) During the third interval, when the concentration falls from M to M. Conc. (M)Time (s)

Reactant Concentration by Time

Finding k given time and concentration Create a graph with time on x-axis. Plot each vs. time to determine the graph that gives the best line: – [A] – ln[A] – 1/[A] – (Use LinReg and find the r value closest to 1) – k is detemined by the slope of best line (“a” in the linear regression equation on TI-83) – 1 st order (ln[A] vs. t): k is –slope – 2 nd order (1/[A] vs t: k is slope)

Rate Law Expression As concentrations of reactants change at constant temperature, the rate of reaction changes. According to this expression. Rate = k[A] x [B] y … Where k is an experimentally determined rate constant, [ ] is concentration of product and x and y are orders related to the concentration of A and B, respectively. These are determined by looking at measured rate values to determine the order of the reaction.

Finding Order of a Reactant - Example 2ClO 2 + 2OH -  ClO ClO H 2 O Start with a table of experimental values: To find effect of [OH - ] compare change in rate to change in concentration. When [OH - ] doubles, rate doubles. Order is the power: 2 x = 2. x is 1. This is 1 st order for [OH - ]. [ClO 2 ] (M)[OH - ] (M)Rate (mol/L-s) x x x x

Finding Order of a Reactant - Example 2ClO 2 + 2OH -  ClO ClO H 2 O Start with a table of experimental values: To find effect of [ClO 2 ] compare change in rate to change in concentration. When [ClO 2 ] triples, rate increases 9 times. Order is the power: 3 y = 9. y is 2. This is 2nd order for [ClO 2 ]. [ClO 2 ] (M)[OH - ] (M)Rate (mol/L-s -1 ) x x x x 9x

Finding Order of a Reactant - Example 2ClO 2 + 2OH -  ClO ClO H 2 O Can use algebraic method instead. This is useful when there are not constant concentrations of one or more reactants. This example assumes you found that reaction is first order for [OH - ] x =k(0.010) x (.030) x = k (0.030) x (.060) =.333 x (.5) For [ClO 2 ]x, x = 2 [ClO 2 ] (M)[OH - ] (M)Rate (mol/L-s -1 ) x x x10 -2

Rate Law: 2ClO 2 + 2OH -  ClO ClO H 2 O Rate = k[ClO 2 ] 2 [OH - ] To find k, substitute in any one set of experimental data from the table. For example, using the first row: k = rate/[ClO 2 ] 2 [OH - ] k = 6.00x10 -4 Ms -1 = 200 M -2 s -1 [0.010M] 2 [0.030M] Overall reaction order is 2+1=3. Note units of k.

Determining units for k given overall reaction order Rate(M/s) = k[A] x x = overall order of reaction [A] = the reactant concentration (M) Overall reaction order ExampleUnits of k 1Rate=k[A](M/s)/M = s -1 2Rate=k[A] 2 (M/s)/M 2 = M -1 s -1 3Rate=k[A] 3 (M/s)/M 3 = M -2 s Rate=k[A] 1.5 (M/s)/M 1.5 = M -0.5 s -1