16.1 Rate expression16.1 Rate expression

16.1.1 Distinguish between the terms 16.1.1 Distinguish between the terms rate constantrate constant, , overall order of reactionoverall order of reaction and and order of reactionorder of reaction with respect with respect to a particular reactant.to a particular reactant.16.1.2 Deduce the rate expression for a reaction from 16.1.2 Deduce the rate expression for a reaction from experimental data.experimental data.16.1.3 Solve problems involving rate expression16.1.3 Solve problems involving rate expression16.1.4 Sketch, identify and analyze graphical 16.1.4 Sketch, identify and analyze graphical representation for zero-, first- and second-order reactions.representation for zero-, first- and second-order reactions.

Rate Law ExpressionRate Law Expression

Expression that shows how rate depends Expression that shows how rate depends on concentration.on concentration.

A + B => CA + B => C

rate = rate = k k [A][A]m m [B][B]nn

m m and and nn are called are called reaction ordersreaction orders. Their . Their sumsum is is called the called the overall reaction order.overall reaction order.

k k is the is the rate constantrate constant. It is specific to a reaction at a . It is specific to a reaction at a certain temperature.certain temperature.

Rate = k [A]m [B]n

• The exponents in a rate law must be determined by experiment. They are not derived from the stoichiometric coefficients in a chemical equation

• The values of exponents establish the order of a reaction for each species and overall order for the reaction

• The proportionality constant, k, is the rate constant and its value depends on the reaction, the temperature, and the presence or absence of a catalyst.

Exercise 1:Exercise 1:

2NO + 2H2NO + 2H22 N N22 + 2H + 2H22OO

ExperimentNumber

Conc. of NO(M)

Conc. of H2

(M)Rate of N2 forming (Ms-1)

1 0.210 0.122 0.0339

2 0.210 0.244 0.0678

30.420 0.122 0.1356

1. Write the rate law expression;1. Write the rate law expression;

2. To find the order of [NO], keep the 2. To find the order of [NO], keep the other one constant.other one constant.

Study the dataStudy the data

Exp #1 and #2, [NO] is unchanged, [HExp #1 and #2, [NO] is unchanged, [H22] is doubled ] is doubled and this causes the rate to double (0.0678/0.0339 and this causes the rate to double (0.0678/0.0339 =2), the H=2), the H22’s rate order is 1.’s rate order is 1.

Exp #1 and #3, [HExp #1 and #3, [H22] is unchanged, [NO] is doubled ] is unchanged, [NO] is doubled and this causes the rate to quadruple and this causes the rate to quadruple (0.1356/0.0339 =4), NO’s rate order is 2.(0.1356/0.0339 =4), NO’s rate order is 2.

Rate = k [NO]Rate = k [NO]22[H[H22]]

The overall The overall rate orderrate order for this reaction is for this reaction is 33 (1+2)(1+2)

Suppose…Suppose…

If when we ran exp #1 and #3 , the rate If when we ran exp #1 and #3 , the rate didn’t change, what rate law would we didn’t change, what rate law would we expect?expect?

Since it didn’t change when we doubled Since it didn’t change when we doubled [NO], the rate order is 0, meaning the [NO], the rate order is 0, meaning the rate doesn’t depend on the concentration rate doesn’t depend on the concentration of NO at all, so rate= k[Hof NO at all, so rate= k[H22] and the overall ] and the overall

reaction order is 1.reaction order is 1.

Sample Exercise 2:Sample Exercise 2: Use the kinetics data to write the rate law for the Use the kinetics data to write the rate law for the

reaction. What overall reaction order is this?reaction. What overall reaction order is this? 2NO + O2NO + O22 2NO2NO22

Exp # [NO] [O2] Rate forming NO2 (M/s)

1 0.015 0.015 0.048

2 0.030 0.015 0.192

3 0.015 0.030 0.096

4 0.030 0.030 0.384

exp #1 and exp #2, [Oexp #1 and exp #2, [O22] remained constant, ] remained constant,

where [NO] is doubled. The rate is where [NO] is doubled. The rate is quadrupled. The rate order for [NO] is 2.quadrupled. The rate order for [NO] is 2.

Exp #1 and exp #3, [NO] remained constant, Exp #1 and exp #3, [NO] remained constant, where [O2] is doubled. The rate is doubled. where [O2] is doubled. The rate is doubled. The rate order for [O2] is 1.The rate order for [O2] is 1.

Overall reaction orderOverall reaction order (1+2) = (1+2) = 33

Sample Exercise 3Sample Exercise 3Rate data for the reaction: Rate data for the reaction:

CHCH33Br + OHBr + OH-- CH CH33OH + BrOH + Br--

Exp # CH3Br OH- Rate of forming CH3OH

1 0.200 0.200 0.015

2 0.400 0.200 0.030

3 0.400 0.400 0.060

Use the data to find the experimental rate law.

Distinctions Between Rate And Distinctions Between Rate And The Rate Constant The Rate Constant kk

The The raterate of a reaction of a reaction is the change in concentration with is the change in concentration with time, whereas the time, whereas the rate constantrate constant is the proportionality constant is the proportionality constant relating reaction rate to the concentrations of reactants.relating reaction rate to the concentrations of reactants.

The rate constant remains The rate constant remains constantconstant throughout a reaction, throughout a reaction, regardless of the initial concentrations of the reactants.regardless of the initial concentrations of the reactants.

The rate and the rate constant have the same numerical The rate and the rate constant have the same numerical values values andand units only in units only in zerozero-order reactions.-order reactions.

Method Of Initial Rates Summary

The effects of doubling one initial concentration:– For zero-order reactions, no effect on rate.– For first-order reactions, the rate doubles.– For second-order reactions, the rate quadruples.– For third-order reactions, the rate increases

eightfold.

The value of k for the reaction can be calculated.

Graphing Order of Reaction:Graphing Order of Reaction:

http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/IntegratedRateLaws.html

Graphing conc. Vs timeGraphing conc. Vs time Shows the effect of Shows the effect of

reactants being used reactants being used up on the rate of up on the rate of reactionreaction

If constant = If constant = zero orderzero order Decreasing Decreasing

concentration is not concentration is not affecting the rateaffecting the rate

Graphing first orderGraphing first order

If the reaction rate is If the reaction rate is halved when the halved when the concentration is concentration is halved, then the halved, then the reaction is reaction is first orderfirst order

Graphing second orderGraphing second order

If halving the If halving the concentration causes concentration causes the rate to decrease the rate to decrease by a factor of 4, the by a factor of 4, the reaction is second reaction is second orderorder

(1/2 )(1/2 )22 = ¼ = ¼

Rate vs. conc graphsRate vs. conc graphs

First orderFirst order

Conc. shows an exponential decrease, that Conc. shows an exponential decrease, that is the time for the conc. to fall from its initial is the time for the conc. to fall from its initial value to half its initial value, is equal to the value to half its initial value, is equal to the time required for it to fall from half to one time required for it to fall from half to one quarter to one eighth, etc…quarter to one eighth, etc…

This is known as This is known as half-life, t half-life, t ½½ Look at next slide for graphical Look at next slide for graphical

representationrepresentation

Radioactive decayRadioactive decay

First order exponential decayFirst order exponential decay Half life is important and can be found from a Half life is important and can be found from a

graph or the equationgraph or the equation t t ½ ½ = = ln2ln2

kk

Example: if the rate constant of a first order reaction Example: if the rate constant of a first order reaction is 0.005 s-1, then the half life will beis 0.005 s-1, then the half life will be

t t ½ ½ = = ln2 ln2 = 139 s= 139 s

0.0050.005