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.

2N2O5 4NO2 + O2 Rate of reaction = -Δ[N2O5] = Δ[NO2] = Δ[O2]

2 Δt 4 Δt Δtwhere [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 0.0050 M to 0.0045 M.

(b) During the second interval, when the concentration falls from 0.0045 M to 0.0040 M.

(c) During the third interval, when the concentration falls from 0.0040 M to 0.0035 M.

Conc. (M) Time (s)

0.0050 0

0.0045 10.5

0.0040 22.3

0.0035 35.7

0.0030 51.1

0.0025 69.3

0.0020 91.6

Reactant Concentration by Time

Phenolphthalein Concentation in Basic Solution Over Time

0

0.001

0.002

0.003

0.004

0.005

0.006

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Co

nc

. (M

)

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) – 1st order (ln[A] vs. t): k is –slope– 2nd 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 - Example2ClO2 + 2OH- ClO3

- + ClO2- + H2O

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: 2x = 2. x is 1. This is 1st order for [OH-].

[ClO2] (M) [OH-] (M) Rate (mol/L-s)

0.010 0.030 6.00x10-4

0.010 0.060 1.20x10-3

0.030 0.060 1.08x10-2

2x 2x

Finding Order of a Reactant - Example2ClO2 + 2OH- ClO3

- + ClO2- + H2O

Start with a table of experimental values:

To find effect of [ClO2] compare change in rate to change in concentration.

When [ClO2] triples, rate increases 9 times. Order is the power: 3y = 9. y is 2. This is 2nd order for [ClO2].

[ClO2] (M) [OH-] (M) Rate (mol/L-s-1)

0.010 0.030 6.00x10-4

0.010 0.060 1.20x10-3

0.030 0.060 1.08x10-23x 9x

Finding Order of a Reactant - Example2ClO2 + 2OH- ClO3

- + ClO2- + H2O

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-] .

6.00 x 10-4=k(0.010)x(.030)1

1.08 x 10-2 = k (0.030)x(.060)1

0.0556 = .333x(.5)

For [ClO2]x , x = 2

[ClO2] (M) [OH-] (M) Rate (mol/L-s-1)

0.010 0.030 6.00x10-4

0.010 0.060 1.20x10-3

0.030 0.060 1.08x10-2

Rate Law:2ClO2 + 2OH- ClO3

- + ClO2- + H2O

Rate = k[ClO2]2[OH-]To find k, substitute in any one set of

experimental data from the table. For example, using the first row:

k = rate/[ClO2]2[OH-]k = 6.00x10-4Ms-1 = 200 M-2s-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 Example Units of k

1 Rate=k[A] (M/s)/M = s-1

2 Rate=k[A]2 (M/s)/M2 = M-1s-1

3 Rate=k[A]3 (M/s)/M3 = M-2s-1

1.5 Rate=k[A]1.5 (M/s)/M1.5 = M-0.5s-1