Unit 6: Kinetics

IB Topics 6 & 16

Part 3: Reaction Mechanisms & Activation Energy

Reaction Mechanisms Reaction Mechanisms: most reactions that

occur at a measurable rate occur as a series of simple steps, each involving a small number of particles.

This sequence of steps is known as the reaction mechanism.

Reaction Mechanisms Individual steps are called elementary steps

usually cannot be observed directly mechanism is in effect a theory about the

sequence of events as the overall reaction proceeds from reactants to products.

Catalyst

speeds up a reaction without being used up (should not appear in overall reaction because it was present initially and then reforms as a product somewhere in the process.

Example: which one is the catalyst?

step 1: H2O2 + I- H2O + IO-

step 2: H2O2 + IO- H2O + O2 + I-

Intermediate / Activated complex

product of one elementary step that is used up in a subsequent step.

Example: which one is the intermediate?

step 1: H2O2 + I- H2O + IO-

step 2: H2O2 + IO- H2O + O2 + I-

Chemical reactions take place as a result of collisions between molecules. Each type of collision in a given reaction is called a single event or an elementary step.

Molecularity: # of species participating as reactants in a given step of a reaction.

Unimolecular: A single reactant particle is involved in the elementary step

Bimolecular: Two particles are involved as reactants

Termolecular: Three particles are involved. Termolecular steps are far less probable than unimolecular or bimolecular

processes and are rarely encountered. The chances that four or more molecules will collide

simultaneously with any regularity is extremely remote, consequently, such collisions are never proposed as a part of a reaction mechanism.

Rate Laws of Elementary Steps

A Products Rate = k[A]

A+A Products Rate = k[A]2

A+B Products Rate = k[A][B]

A+A+A Products Rate = k[A]3

A+A+B Products Rate = k[A]2[B]

A+B+C Products Rate = k[A][B][C]

unimolecular

bimolecular

termolecular

The reaction between NO2 and CO has the overall reaction:

NO2 + CO NO + CO2

A study of the kinetics of this reaction revealed the rate law for the reaction is.

Rate = k[NO2]2

This Rate Law requires that the slow step of the reaction involves a collision between two NO2 molecules. How can this be a step in the seemingly simple reaction above?

Example:

Example: NO2 + CO NO + CO2

NO2 + NO2 NO3 + NO

NO3 + CO NO2 + CO2

2NO2 + NO3 + CO NO3 + NO + NO2 + CO2

NO2 + CO NO + CO2

Further study of this reaction established that two NO2 molecules can react as follows:

NO3 is a highly reactive material which is capable of transferring an oxygen atom.

NO2 + NO2 NO3 + NO

NO3 + CO NO2 + CO2

NO2 + CO NO + CO2

slow

fast

The rate law only provides information about the slowest reaction in the mechanism. The rate law is based off of the first elementary step, so it must be the slow/rate-determining one. Thus, the reaction mechanism can be expressed as follows:

Which molecule is an intermediate in the reaction mechanism above?

Example: NO2 + CO NO + CO2

NO3

Rate = k[NO2]2

Step 1:

Step 2:

Overall:

So if you were given this mechanism, you should be able to produce the rate law (rate = k[NO2]2)

Determining the rate expression for an overall reaction from the reaction mechanism

The sum of the elementary steps must give the overall balanced equation for the reaction.

The rate-determining step, which is the slowest step in the sequence of steps leading to product formation, should predict the same rate law & order as is determined experimentally.

For elementary steps (since they are true single-step reactions), the exponents in the rate laws are the same as the coefficients of the reactants in the chemical equation.

Determining the rate expression for an overall reaction from the reaction mechanism

Equation for rate-determining step

Molecularity Rate law

  

   

  

   

  

   

A → products unimolecular rate=k[A]

2A → products bimolecular rate=k[A]2

A + B→ products bimolecular rate=k[A][B]

The rate law for the rate-determining step, predictable from its equation, leads to the rate expression for the overall reaction. If the rate-determining step is the first step (or only step) in the mechanism, then its rate law is the rate expression for the overall reaction.

Example: The overall reaction 2NO2Cl(g) 2NO2(g) + Cl2(g) is believed to have the following mechanism

NO2Cl(g) NO2(g) + Cl(g)

NO2Cl(g) + Cl(g) NO2(g) + Cl2(g)

2NO2Cl(g) 2NO2(g) + Cl2(g)

slow: rate-determining stepStep 1:

Step 2:

Overall:

fast

The rate expression for the overall reaction is that of the rate-determining step:

rate = k[NO2Cl]

This is a first-order reaction.

What if the rate-determining step is not

the first step in the mechanism?

It’s a little more complicated because the reactant

concentrations depend on an earlier step, so this must be

taken into account.

Example: For the reaction NO(g) + O2(g) 2NO2(g), the following reaction mechanism has been proposed

NO(g) + NO(g) N2O2(g)

N2O2(g) + O2(g) 2NO2(g)

2NO(g) + O2(g) 2NO2(g)

slow: rate-determining step

Step 1:

Step 2:

Overall:

fast

So the rate depends on step 2, for which… rate = k[N2O2][O2]

This is a third-order reaction.

But N2O2 is a product of step 1, so the concentration of this intermediate depends on [NO]2.

Therefore, we substitute this into the equation above and the rate expression for the overall reaction is:

rate = k[NO]2[O2]

Activation Energy

The rate constant, k, is temperature dependent Rxn rate increases as temperature increases

faster particles = increased collision rate

Activation Energy

Rule of thumb: a 10 C increase in temperature leads to a doubling of the rate.

Note: this is only a rule of thumb, not a law of nature. Thus, it is not true for all reactions.

Activation Energy

When activation energy is large, temperature has a greater effect on the number of particles with sufficient energy to react (and thus rate of reaction). This can be shown by studying Maxwell-Boltzman distributions.

Arrhenius Equation: mathematical relationship between temperature, the rate constant and the activation energy.

1859-1927

Svante Arrhenius

The fraction of molecules with energy greater than activation energy, Ea, at temperature T is proportional to the expression e-Ea/RT

Arrhenius Equation: mathematical relationship between temperature, the rate constant and the activation energy.

1859-1927

Svante Arrhenius

Thus, here is my famous equation…

k e-Ea/RT

or

k = Ae-Ea/RT

In the IB data booklet

k = Ae-Ea/RT

k = rate constant A = Arrhenius constant (a.k.a. frequency factor,

pre-exponential factor, and steric factor) Takes into account the frequency with shich successful

collisions occur based on collision geometry and energy requirements

Constant for a rxn & has units the same as k (and so varies with the order of the reaction)

Ea = activation energy (in Joules mol-1) R = 8.31 J mol-1 K-1 (ideal gas constant) T = absolute temperature (in Kelvin)

k = Ae-Ea/RT

Taking the natural logarithm (ln base e) of both sides of the equation above:

or

Notice that this is a form of y = mx + b (straight line)

A ln RTE

- k ln a A ln T1

RE

- k ln a

In the IB data booklet

Arrhenius Plot graph of ln k v. 1/T

ln k

1/T (K-1)

A ln T1

RE

- k ln a

slope =

y-intercept =

RE

- a

A ln

The next few slides contain additional examples to help explain these concepts further… include only if time allows

Examples

Example: What happens to the rate of a reaction if the temperature increases from 20oC to 30oC?

The frequency factor, a, is approximately constant for such a small temperature change. We need to look at how e-(Ea/RT) changes --- the fraction of molecules with energies equal to or in excess of the activation energy.

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Assume an activation energy of 50 kJ/mol. In the equation, we have to write that as 50,000 J/mol. The value of the gas constant R is 8.31 J/K·mol

Now raise the temperature just a little bit to 30oC (303k)

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At 20oC At 30oC

The fraction of the molecules able to react has almost doubled by increasing the temperature by 10oC. That causes the rate of the reaction to almost double.

This is the basis for the old rule of thumb that a reaction rate doubles for every 10oC rise in temperature.

The effect of a catalystA catalyst provides an alternate reaction mechanism, or route for the

reaction. This alternate route necessarily has a lower activation energy. The overall effect of a catalyst is to lower the activation energy.

Continuing our example of a reaction with an activation energy of 50,000 J/mol… What is the effect on the rate of lowering the activation to 25,000 J/mol?

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With Catalyst Without Catalyst

No wonder catalysts speed up reactions!

H-C-C-O-C-H + H2O H-C-C-OH + H-C-OH

H

H H

H

H

H

H

HO

Methyl Acetate + water Acetic Acid + Methanol

Reaction mechanism example:

Experimental evidence for reaction mechanisms ---

Consider the reaction of methyl acetate with water….

The methyl acetate molecule can break in one of two places to complete the reaction…

H-C-C-O-C-H + H2O H-C-C-OH + H-C-OH

H

H H

H

H

H

H

HO

Methyl Acetate + water Acetic Acid + Methanol

H-C-C- O-C-H

O-H

HH

H O H

H

-OR-

H-C-C-O-C-H + H2O H-C-C-OH + H-C-OH

H

H H

H

H

H

H

HO

Methyl Acetate + water Acetic Acid + Methanol

H-C-C- O-C-H

O-H

HH

H O H

H

H-C-C-O- -C-H

H

H

H

H

O

O-H

H

-OR-

How can we determine experimentally which is correct?

H-C-C-O18-HH-O18

H

H

H

Use a radioactive isotope of oxygen, O18

To make up the water

O

H-C-C-O-C-H + H2O H-C-C-OH + H-C-OH

H

H H

H

H

H

H

HO

Methyl Acetate + water Acetic Acid + Methanol

H-C-C- O-C-H

O-H

HH

H O H

H

H-C-C-O- -C-H

H

H

H

H

O

O-H

H

-OR-

Measuring the rate of a reaction. Formulating the

Rate Law

Postulating a reasonable reaction

mechanism

Sequence of steps in the study of a reaction mechanism

Decomposition of Hydrogen Peroxide

The decomposition of Hydrogen Peroxide is facilitated by iodide ions.

The overall reaction is…

2H2O2 2H2O + O2

By experiment, the rate law is found to be…

rate = k[H2O2][I-]

Thus the reaction is first order with respect to both H2O2 and I-.

Example:

rate = k[H2O2][I-]

You can see that H2O2 decomposition does not occur in a single elementary step corresponding to the overall balanced equation.

If it did, the reaction would be second order in H2O2 (as a result of the collision of two H2O2 molecules). What’s more, the I- ion, which is not even part of the overall equation, appears in the rate law expression.

We can account for the observed rate law by assuming that the reaction takes place in two separate elementary steps, each of which is bimolecular:

step 1: H2O2 + I- H2O + IO-

step 2: H2O2 + IO- H2O + O2 + I-

2H2O2 2H2O + O2

step 1: H2O2 + I- H2O + IO-

step 2: H2O2 + IO- H2O + O2 + I-

The first step must be the rate determining step, because it matches the rate law. Thus, the rate of the reaction can be determined from the first step alone:

Note that the IO- ion is an intermediate because it does not appear in the overall balanced equation. Although the I- ion also does not appear in the overall equation, I- differs from IO- in that the former is present at the start of the reaction and at its completion. The function of I- is to speed up the reaction --- that is, it is a catalyst.

rate = k[H2O2][I-]

Slow

Another Example:

Consider the Reaction…

2NO2Cl 2NO2 + Cl2

This is found to be a first order reaction, it’s experimentally determined rate law is…

rate = k[NO2Cl]

Could the overall reaction occur in a single step by the collision of two NO2Cl molecules? This would lead to…

rate = k[NO2Cl]2

Chemists believe the actual mechanism is…

NO2Cl NO2 + Cl

NO2Cl + Cl NO2 + Cl2

Slow

Fast