Chemistry 130
Chemical Kinetics
Dr. John F. C. Turner
409 Buehler Hall
jturner@ion.chem.utk.edu
Chemistry 130 Chemical change
There are two parts to the science of chemistry
The description of matter on an atomic basis as it is observed to exist
The description and control of the change of the form of matter
We have started to study one of the fundamental parts of the first, which is thermodynamics
Chemical kinetics is the major part of the second
Chemistry 130 Chemical change
A chemical reaction converts one ensemble of atoms or molecules into another, different, ensemble of atoms.
Reactions take place at very different rates. Some are very slow:
Growth rate ~ 1mm per million years
Chemical composition: Fe, Mn hydroxides and oxides Chemistry 130 Chemical change
A chemical reaction converts one ensemble of atoms or molecules into another, different, ensemble of atoms.
Reactions take place at very different rates. Some are very fast:
2H2l O2l 2H2 Ol
Initial impact and explosion
A few milliseconds later
Chemistry 130 Chemical change
Even a simple reaction such as the reaction between hydrogen and oxygen
2H2 g O2 g 2H2 O g
can be very complicated:
explosion explosion
steady reaction steady reaction
explosion
Chemistry 130 Chemical change
There is an obvious and intuitive difference in rate between the reaction or explosion of oxygen and hydrogen and the accretion reactions of manganese nodules. The hydrogenoxygen reaction is very very fast (and can take you to the moon) the second is very very slow (and can't).
Chemical kinetics is the quantification of
(i) how fast a reaction proceeds
(ii) how it happens on an atomic or molecular level.
The first is an empirical measurement with respect to concentration of products and reactants
The second is the mechanism of the reaction, which includes a description of the energetics of the reacting system. Chemistry 130 Basic properties of chemical change
In every chemical reaction, the quantity of the reactants decreases and the quantity of the products increases.
Heat is either produced or absorbed by the system; equally heat passes into the universe from the system or leaves the universe and moves into the system.
For the reactions of hydrogen with iodine and chlorine:
HI −1 H2 g I2 g 2HI g H f = 26.5 kJmol HCl −1 H2 g Cl2g 2HCl g H f = −96.3 kJmol
and so the formation of hydrogen iodide is endothermic, whereas the formation of hydrogen chloride is exothermic
Chemistry 130 Basic properties of chemical change
For a spontaneous reaction, the chemical composition of the reaction changes smoothly and continuously to a new, constant chemical composition.
In this respect, the initial chemical composition is unstable with respect to the final composition.
This final composition is the thermodynamically most stable under the specific conditions of the reaction. We call this the thermodynamic minimum.
The speed at which a reacting chemical system achieves this new, most stable composition is not determined by the size of the stabilization that the system undergoes when the reaction takes place. Very exothermic reactions are not necessarily fast reactions.
The heat change is not automatically related to the rate of reaction.
Chemistry 130 Basic properties of chemical change
The heat change is not automatically related to the rate of reaction. 3 2Fe O Fe O H = −824.2kJmol−1 s 2 2 g 2 3 s f
Both of these reactions are the same but the rates are completely different
Chemistry 130 The rate of reaction
In both, the hydrogen and the halogen are consumed – they are reactants – and the hydrohalic acid is generated – it is a product.
H2 g I2 g 2HI g
H2 g Cl2g 2HCl g
Writing the concentration of X as [X], we can define the velocity or rate of the reaction by measuring the change in the concentrations of the reactants with time i.e.
[H2] [I2] 1 [HI] Rate = − = − = t t 2 t
note that [H2] = [H2] t − [H2] 0 Because hydrogen and iodine are both destroyed in the reaction, the rate is negative.
Chemistry 130 The rate of reaction
In general, for a reaction
a A bB cC dD
the rate of reaction is given by
1 [A] 1 [B] 1 [C] 1 [D] rate = − = − = = a t b t c t d t
where a,b,c and d are the stoichiometric coefficients for the balanced reaction.
Chemistry 130 On what does the rate of reaction depend?
The rate of reaction depends on several variables. The most basic are the temperature of the system, which is a measure of the energy content as
q = C p T and the number of particles, n.
Pressure and volume are also important 'masked' variables of the particle number.
For an ideal or perfect gas, PV = nRT n and, in general, c = V
Chemistry 130 Empirical dependencies
For a reaction a A bB cC dD
Empirically, the rate of reaction depends on the concentration of the reactants according to rate = k[A]n[B]m
where k is the rate constant and n and m are experimentally determined indices of the concentration.
n and m are not necessarily related to the stoichiometric coefficients (a,b,c and d) and can be integers, fractions or zero
Chemistry 130 Empirical dependencies
The relationship
rate = k[A]n[B]m
is the rate law and contains the concentration or 'particle number' dependency.
There is no relationship between the stoichiometric constants of a reaction and the concentration indices.
Chemistry 130 Empirical dependencies
For a general reaction a A bB cC dD
the rate law can be written in terms of the change in the concentration of the reactants by combining 1 [A] 1 [B] 1 [C] 1 [D] rate = − = − = = a t b t c t d t and
rate = k[ A]n [B]m
to give 1 [A] 1 [B] 1 [C] 1 [D] − = − = = = k[A]n[B]m a t b t c t d t
Chemistry 130 Classification of reaction rates
The complete rate law for the general reaction
a A bB cC dD is 1 [A] 1 [B] 1 [C] 1 [D] − = − = = = k[A]n[B]m a t b t c t d t
The order of the reaction with respect to A is n
The order of the reaction with respect to B is m
The overall order of the reaction is n+m
Chemistry 130 Classification of reaction rates
For the reaction
H2 g ICl g I2 g 2HCl g the rate law is given by
[H ] [ICl] rate = − 2 = − = k[H ][ICl] t t 2
The order of the reaction with respect to H2 is 1
The order of the reaction with respect to I2 is 1
The overall order of the reaction is 1+1 = 2
Chemistry 130 Classification of reaction rates
For the reaction
Cl2 g 2NO g 2NOCl g the rate law is given by
[Cl2] 1 [NO] 2 rate = − = − = k[Cl ][NO] t 2 t 2
The order of the reaction with respect to NO is 2
The order of the reaction with respect to Cl2 is 1
The overall order of the reaction is 2+1 = 3
Chemistry 130 Classification of reaction rates
For the reaction
239 239 93Np s 94Pus the rate law is given by
[239Np] rate = − 93 = k[ 239Np] t 93
239 The order of the reaction with respect to 9 3 N p is 1 and the overall reaction order is 1
Chemistry 130 Classification of reaction rates
For the reaction
H2 g I2 g 2HI g
we have already seen that the rate law is given by
[H ] [I ] 1 [HI] rate = − 2 = − 2 = = k[H ][I ] t t 2 t 2 2
It would be convenient to think that the reaction
H2 g Br2 g 2HI g
would follow the same experimental rate law......
Chemistry 130 Classification of reaction rates
However,
H2 g Br2 g 2HBr g
follows the experimental rate law
1 2 [HBr] k[H ][Br ] rate = = 2 2 t [HBr] 1k ' [Br ] 2 The details of the rate law are therefore absolutely empirical, although they can be explained by the mechanism of the reaction – the intimate changes in the arrangement of atoms during the course of the reaction
Chemistry 130 Chemistry 130 Chemistry 130
Chemical Kinetics
Dr. John F. C. Turner
409 Buehler Hall
Chemistry 130 Chemical kinetics so far
1. Chemical kinetics describes the speed at which one chemical composition transforms into another chemical composition.
2. The velocity of the chemical reaction is not related to the magnitude of the difference in enthalpy between products and reactants.
3. The experimental rate law for the general reaction a A bB cC dD
is written as 1 [A] 1 [B] 1 [C] 1 [D] − = − = = = k[A]n[B]m a t b t c t d t
where k is a constant and {a,b,c,d} are not related to {n,m}
Chemistry 130 Chemical kinetics so far
The rate of reaction depends on the path between the reactants and the products
Thermodynamics details the difference between the state function of the product and the state function of the reactant.
(State functions include
Enthalpy
Entropy
Free Energy)
Chemistry 130 Chemical kinetics so far
Because a state function is independent of the path by which the system adopts its particular state, there is no information about the path from the thermodynamics of the system.
Stoichiometry is not related to the orders of reactants in the experimental rate law.
Chemistry 130 Initial rates
The initial rate of a reaction is the rate at t = 0. It is determined from the tangent or slope of the plot of concentration vs. time:
The tangent is found in the normal manner:
y2− y1 slope = x2−x1
Note that the initial rate is related to the average rate by
[H O ] lim 2 2 t 0 { t }
Chemistry 130 Initial rates and the order of reaction
The method of initial rates is an important method for determining the order of the reaction.
The general reaction a A b B c C d D obeys the experimental rate law 1 [ A] − = k[A]n[B]m a t so if we vary the concentration of A with all other conditions fixed, the ratio of the initial rates will give us the order of the reaction with respect to A
Similarly, using the same approach with B will give us the order of the reaction with respect to B, and therefore the overall order of the reaction.
Chemistry 130 Initial rates and the order of reaction
Cl 2NO 2NOCl 2 g g g From the ratio of different concentrations of the same −5 −1 Expt [NO]0 / M [Cl2]0 / M 0 / x 10 Ms reactant, we can calculate the order of the reaction with 1 0.0125 0.0225 2.27 respect to that reactant from 2 0.0125 0.0510 4.55 the ratio of the rates. 3 0.0250 0.0225 9.08
ForCl2 g from experiments 1 and 2 When we double the concentration of chlorine, we double the rate, so as
[Cl2]0,2 0.0510 n m = = 2 = k[Cl2] [NO] [Cl2]0,1 0.0225 then n = 1 as the rate changes linearly 0,2 4.55 = = 2 with the chlorine concentration 0,1 2.27
Chemistry 130 Initial rates and the order of reaction
Cl 2NO 2NOCl 2 g g g From the ratio of different concentrations of the same −5 −1 Expt [NO]0 / M [Cl2]0 / M 0 / x 10 Ms reactant, we can calculate the order of the reaction with 1 0.0125 0.0225 2.27 respect to that reactant from 2 0.0125 0.0510 4.55 the ratio of the rates. 3 0.0250 0.0225 9.08
For NO g from experiments 1 and 3 When we double the concentration of nitric oxide, we quadruple the rate, so as
[NO]0,3 0.0250 n m = = 2 = k[Cl2] [NO] [NO]0,1 0.0125 then m = 2 as the rate changes with the 0,3 9.08 = = 4 square of the nitric oxide concentration 0,1 2.27
Chemistry 130 Initial rates and the order of reaction
In general, this method can be applied to any reaction, though it may be complicated in the case of a reaction such as
H2 g Br2 g 2HBr g 1 2 [HBr] k[H2 ][Br2] = = t [HBr] 1k ' [Br ] 2
Chemistry 130 Time dependence of the rate law
So far we have defined the rate for the general reaction
a A bB cC dD
as 1 [A] − = k[A]n[B]m a t
but we also know that the initial rate is the tangent to the concentration – time curve, implying that [ A] lim t 0 { t } This last relationship is the key to the time dependence. When t 0 , we can replace the ∆ with a 'd', the symbol for the microscopic or infinitesimal change
Chemistry 130 Time dependence of the rate law
[ A] d[A] In this case, lim = t 0 { t } dt
which is the differential change of concentration with time.
The rules of differential changes are termed the calculus and we have already used the calculus implicitly when we took the tangent to the concentration curve.
The instantaneous rate law is therefore
1 d[A] n m − = k[A] [B] a dt
for the general reaction a A bB cC dD
Chemistry 130 Time dependence of the rate law
Using the calculus, we can directly calculate the time dependence of the rate law, by integrating the differential rate law.
The results are:
Order Experimental rate law Integrated rate law
1 [A] 0 − = k [A] = −kt[A] a t t 0 1 [A] 1 − = k[A ] ln[A ] = −kt ln[A] a t t 0 1 [ A] 1 1 2 − = k[A ]2 = kt a t [ A] t [ A] 0
Chemistry 130 Time dependence of the rate law
Order Experimental rate law Integrated rate law
1 [A ] 0 − = k [A ] = −kt[A ] a t t 0 1 [A ] 1 − = k[A ] ln[A] = −kt ln [A ] a t t 0
1 [A ] 2 1 1 2 − = k[A ] = kt a t [A] t [A ] 0 The integrated rate laws for reactions of different orders allow us to calculate the concentration of any reactant at any time during the reaction.
They also allow us to determine the rate constant for the reaction from experimental results.
Chemistry 130 Halflives: first order reactions
The halflife of a reaction is the time at which half the reactant has been consumed. 1 At this time, [A] t = [A] 0 2
and when this concentration is substituted for [ A ] t in the integrated rate law, an expression for the halflife results. [A] For a first order reaction, the integrated rate equation is ln t = −kt [ A] { 0 } 1/2[ A] 1 ln 0 = ln = −ln 2 = −kt [ A] 2 1/2 { 0 } { } ln 2 and so the halflife of a first order reaction is given by t = 1/2 k
Chemistry 130 Halflives: first order reactions
ln 2 The halflife of a first order reaction is t = 0 100% 1/2 k 1 50% and is therefore independent of the quantity of reactant 2 25% present. 3 12.5% Also, if we know the halflife, we automatically know the rate 4 6.25% constant for the reaction. 5 3.125% 6 1.5625 % The halflife is a common parameter in nuclear chemistry as 7 0.78125 % radioactive decay is a first order process. ⋯ ⋯ 100% N t 238U 4.47 109 years N 1/2 92 ≃ × 2 t 239Pu 24,100 years 1/2 94 ≃ t 271Ds 210 ms 1/2 110 ≃ ≃
Chemistry 130 Halflives: second order reactions
The integrated rate equation for a second order reaction is given by 1 1 = kt [ A] t [ A] 0
1 when [ A ] = [ A ] then t 2 0 2 1 = kt [ A] 0 [A] 0 1 = kt1/2 [ A] 0 1 t1/2 = k[A] 0 and so the halflife of a second order reaction is dependent on the initial concentration Chemistry 130 The rate constant
So far, we have seen that an empirical rate law can be established for a chemical reaction that defines the rates in terms of the concentration – this is the experimental or differential rate law and is of the form
1 d[ A] n m − = k[A] [B] a dt We have also seen that this expression can be manipulated using the calculus to yield the integrated rate law, which details the time dependence of the reaction: Order Experimental rate law Integrated rate law 1 [A] 0 − = k [A] = −kt[A] a t t 0 1 [A] 1 − = k[A ] ln[A ] = −kt ln[A] a t t 0
1 [A] 2 1 1 2 − = k[A ] = kt a t [A] t [A] 0 Chemistry 130 The rate constant
We have not discussed the temperature dependence of a reaction.
The rate constant, k, is a constant only for a given temperature and in general is a function of temperature. 1 d[A] n m − = k T [A] [B] a dt
The temperature dependence of the rate law requires a theory of chemical kinetics on an intimate, microscopic level – this theory is termed transition state theory.
Chemistry 130 First Quiz
The first quiz will be on Wednesday in discussion and will cover
Chapter 12
Chapter 13 to date
Chemistry 130 Chemistry 130 Chemistry 130
Chemical Kinetics
Dr. John F. C. Turner
409 Buehler Hall
Chemistry 130 Chemical kinetics so far
1. Chemical kinetics describes the speed at which one chemical composition transforms into another chemical composition.
2. The velocity of the chemical reaction is not related to the magnitude of the difference in enthalpy between products and reactants.
3. The experimental rate law for the general reaction a A bB cC dD
is written as 1 [A ] 1 [B] 1 [C] 1 [D] = − = − = = = k[A]n[B]m a t b t c t d t
where k is a constant and {a,b,c,d} are not related to {n,m}
Chemistry 130 Chemical kinetics so far
4. The integrated rate laws for reactions of different orders allow us to calculate the concentration of any reactant at any time during the reaction.
Order Experimental rate law Integrated rate law
0 = k [A ] t = −kt[A ] 0
1 = k[A] ln[A] t = −kt ln [A ] 0
2 1 1 2 = k[A] = kt [A] t [A ] 0
From the experimental rate law, we have
● the concentration dependence of the reaction from the order of the reaction
● the time dependence from the integrated rate equation
Chemistry 130 Chemical kinetics so far
5. The order of the reaction is determined by the molecularity of the slowest elementary step in the reaction mechanism. This step is termed the Rate Determining Step (rds).
6. An elementary step of a reaction is microscopically reversible.
7. The energy barrier for the reaction is termed the activation energy, EA and the rate constant is related to the activation energy by the Arrhenius equation
−E A k = A e RT 8. The temperature dependence of the rate constant is given by
k E 1 1 ln 2 = A − k R T T 1 [ 1 2 ]
Chemistry 130 The rate constant
To understand the temperature dependence and the physical origin of the order of the reaction, we require a theory of chemical reactions on microscopic scale – and a reaction mechanism.
The first requirement for a reaction is that a collision between two reactants must take place.
Many reactions involve the transfer of an atom or a group of atoms between reactant molecules, which necessarily means that the molecules must be close.
A second requirement is that the orientation of the molecules must be correct
Chemistry 130 The rate constant
Molecules in the gas phase are moving very rapidly and are colliding continuously. The distribution of velocities is given by the MaxwellBoltzmann distribution:
3 /2 2 2 m −mv f vdv = 4 v exp dv 2 kT 2kT Chemistry 130 The rate constant
The momentum distribution is given by
3/2 2 2 1 −p f pdp = 4 p exp dp 2mkT 2mkT The individual energies are broadly distributed and only some of the collisions are result in reaction.
There is an intrinsic barrier to reaction, over and above the frequency of collision.
Chemistry 130 The rate constant
Only a proportion of the molecules have sufficient energy to react. There must be an energetic barrier to reaction.
Chemistry 130 Transition state theory
Consider the reaction between carbon monoxide and nitrogen dioxide: CO NO CO NO We know what the g 2 g 2 g g result of this reaction is:
Chemistry 130 Transition state theory
Consider the reaction between carbon monoxide and nitrogen dioxide:
We know what the result of this reaction is and we can measure the enthalpy of reaction between the two compositions – the reactants and the products
Chemistry 130 Transition state theory
We also know that not all collisions result in reaction – there is an energy
barrier; this barrier is called the activation energy, EA
Chemistry 130 Transition state theory
The point at the highest energy on the path between reactants and products is termed the transition state.
Chemistry 130 Transition state theory
In the transition state, the bonds between atoms in the reactants are beginning to break and rearrange to form the bonds that are present in the products. The transition state is occupied by the activated complex
An activated complex is not a stable species and lies part way between the reactants and the products.
It exists for approximately the time taken for a molecule to vibrate ~ 1 0 − 1 5 s and then falls apart to yield the products of the reaction.
Chemistry 130 Transition state theory
We can also think of the reverse reaction as passing through the same transition state – this is termed microscopic reversibility and there is an associated activation energy for the reverse reaction.
In this way, we can think of any chemical reaction as consisting of a forward reaction and a reverse reaction, differentiated by the activation energy for each process.
We write the reaction as ‡ CO g NO2 g [ O=C⋯O⋯N=O ] CO2 g NO g
where ‡ represents the activated complex at the transition state.
Chemistry 130 Transition state theory
For the reaction between carbon monoxide and nitric oxide, the full reaction path is
Chemistry 130 Energetics of transition state theory
Transition state theory provides a reasonable qualitative description of the reaction path.
Quantification of the reaction path was first successfully achieved by Svante Arrhenius (Nobel Prize, 1903).
The rate constant was already known to vary with temperature and the general rate law should account for this observation:
= k[A ]n [B]m
Chemistry 130 Energetics of transition state theory
Arrhenius formulated the temperature dependence of the rate constant as
−E A RT k = A e
A is termed the preexponential factor and is the product of the collision frequency and an alignment factor
EA is the activation energy
R is the universal gas constant R = 8.314 J mol−1 K−1
T is the thermodynamic or absolute temperature in K
Chemistry 130 Energetics of transition state theory
As −E A k = A e RT
then E ln k = ln A − A RT and so
k E 1 1 ln 2 = A − k R T T 1 [ 1 2 ] which is the temperature dependence of the rate constant.
Chemistry 130 Order, mechanism and rates
For an elementary reaction, i.e. a reaction that is a single intermolecular or interatomic reaction on the overall path from reactants to products, the number of molecules or atoms present in the transition state determine the order of the reaction.
When there is more than one elementary reaction, it is the slowest elementary reaction that determines the experimental rate law.
For simple reactions, there are two major types of elementary reaction:
Unimolecular – one molecule dissociates or changes before the reaction moves to products
Bimolecular – two molecules react together to form the activated complex.
(Termolecular reactions involving a simultaneous collision between three molecules are exceedingly unlikely)
Chemistry 130 Order, mechanism and rates
Elementary reactions are also microscopically reversible and the forward and back reactions are present at the same time, governed by the activation energies for both processes. It is the slowest elementary reaction along the path that determines the rate.
This is termed the rate determining step in the mechanism.
So, the molecularity of the activated complex at the transition state of the rate determining step is shown in the order of the reaction. Chemistry 130 Reaction Mechanisms
A reaction mechanism is the series of elementary steps that make up the observed, macroscopic reaction.
An acceptable mechanism must
● reproduce the rate law
● account for all of the products that are formed and the stoichiometry of the net reaction
● account for any geometrical or stereochemical features of the reaction
A mechanism is a model of the reaction and can only be supported or refuted by experimental evidence. It cannot be proved.
The two dominant elementary reactions are unimolecular and bimolecular
unimolecular 1 molecule in the rds bimolecular 2 molecules the rds Chemistry 130 Mechanism types: unimolecular
The reaction profile for a bimolecular reaction is the one that we are already familiar with.
There is a single transition state and activated complex.
Chemistry 130 Mechanism types
The rate law for the hydrolysis of methyl bromide (MeBr) by hydroxide ion is
MeBr OH MeOH Br
= k[MeBr][OH ]
Chemistry 130 Mechanism types: bimolecular
A bimolecular reaction has a slow first step followed by a fast second step.
The species in the well between E 2 the first activation barrier and A E 1 the second activation barrier is A termed an intermediate.
There are two transition states and two activated complexes and each step is an elementary reaction.
Chemistry 130 Mechanism types: bimolecular
Me C+ An example of a bimolecular reaction is the 3 hydrolysis of tertiary butyl bromide with hydroxide: Me CBr OH 3 E 2 A Me3 CBr OH Me3COH Br E A 1
= k[Me3CBr]
+ Me COH Br The intermediate in this case is Me3 C 3
Chemistry 130 Chemistry 130 Osias Beert, Flemish painter (b. ca. 1580, Antwerpen, d. 1624, Antwerpen) Chemistry 130
Chemical Kinetics
Dr. John F. C. Turner
409 Buehler Hall
Chemistry 130 Chemical kinetics so far
1. Chemical kinetics describes the speed at which one chemical composition transforms into another chemical composition.
2. The velocity of the chemical reaction is not related to the magnitude of the difference in enthalpy between products and reactants.
3. The experimental rate law for the general reaction a A bB cC dD
is written as 1 [A ] 1 [B] 1 [C] 1 [D] = − = − = = = k[A]n[B]m a t b t c t d t
where k is a constant and {a,b,c,d} are not related to {n,m}
Chemistry 130 Chemical kinetics so far
4. The integrated rate laws for reactions of different orders allow us to calculate the concentration of any reactant at any time during the reaction.
Order Experimental rate law Integrated rate law
0 = k [A ] t = −kt[A ] 0
1 = k[A] ln[A] t = −kt ln [A ] 0
2 1 1 2 = k[A] = kt [A] t [A ] 0
From the experimental rate law, we have
● the concentration dependence of the reaction from the order of the reaction
● the time dependence from the integrated rate equation
Chemistry 130 Chemical kinetics so far
5. The order of the reaction is determined by the molecularity of the slowest elementary step in the reaction mechanism. This step is termed the Rate Determining Step (rds).
6. An elementary step of a reaction is microscopically reversible.
7. The energy barrier for the reaction is termed the activation energy, EA and the rate constant is related to the activation energy by the Arrhenius equation
−E A k = A e RT 8. The temperature dependence of the rate constant is given by
k E 1 1 ln 2 = A − k R T T 1 [ 1 2 ]
Chemistry 130 Activation energy and mechanism
The rate of a reaction depends on the slowest elementary step on the path – the rate determining step. For a path with a single elementary step, we know what the path looks like: MeBr OH MeOH Br
= k[MeBr][OH ] The rate constant is determined by the activation energy EA and the order of the reaction by the molecularity of the step.
−E A RT k = A e
= k[MeBr][OH] Chemistry 130 The steady state approximation
The steady state approximation is a simple case of a kinetic path that contains more than one elementary step and shows the general approach for more complicated reaction profiles.
The reaction contains a fast step which is reversible, followed by a fast, irreversible reaction that gives the products
k1 A B C D k−1
Chemistry 130 The steady state approximation
The reaction between nitric oxide and oxygen can be described by the steady state approximation.
The reaction proceeds via
2NO g O2 g 2NO2g
2 = k[O2][NO] If this were a single elementary reaction, the activated complex would be the result of a termolecular reaction, which is vanishingly likely.
Chemistry 130 The steady state approximation
The first step of the reaction is association of two 2NO g O2 g 2NO2g NO molecules 2 = k[O2][NO]
NO g NO g O=N−N=O g
The activation energies of the forward reaction and reverse reaction are similar and so the rate constants are similar. We write this reaction as an equilibrium
k1
k−1
Chemistry 130 The steady state approximation
The second step of the reaction is the reaction of 2NO g O2 g 2NO2g
the (NO)2 molecule with oxygen 2 = k[O2][NO]
O=N−N=O O2 g 2NO2 g This reaction is fast and the activation energy is much larger for the reverse reaction than the forward reaction and is therefore essentially irreversible
Chemistry 130 The steady state approximation
2NO g O2 g 2NO2g
2 = k[O2][NO]
We can evaluate these reactions to reproduce the observed stoichiometric reaction
2NO g O=N−N=O
O=N−N=O O2 g 2NO2 g
2NO g O2 g 2 NO2 g
Chemistry 130 The steady state approximation
2NO g O2 g 2NO2g
2 = k[O2][NO]
We can also to reproduce the observed rate law
Chemistry 130 The steady state approximation
k1
k−1
Associative equilibrium: 2 forward = k1 [NO]
backward = k−1 [ONNO]
We assume that the rates are equal
2 forward = backward k1[NO] 2 [ONNO] = k NO k ONNO 1[ ] = −1[ ] k−1
Chemistry 130 The steady state approximation
The slow, irreversible step: = k2[ONNO][O2]
We know the concentration of (NO) 2 2 k [NO] [ONNO] = 1 k−1 k [NO]2 k k and so = k [ONNO][O ] = k 1 k [O ] = 2 1 [NO]2 [O ] 2 2 2 k 2 2 k 2 −1 −1 Chemistry 130 The steady state approximation
The final rate law is
k [NO]2 k k = k [ONNO][O ] = k 1 k [O ] = 2 1 [NO]2 [O ] 2 2 2 k 2 2 k 2 −1 −1 k k = 2 1 [NO]2[O ] = k'[NO]2[O ] k 2 2 −1
k k as k' = 2 1 k −1
Chemistry 130 Catalysis
A catalyst is a material that accelerates the rate of reaction but is not consumed by it and is therefore unchanged at the end of the reaction.
Catalysts work by providing a different path for the reaction, which has a lower activation energy.
~30 % of the GDP of the US depends on catalysis
Gasoline Polypropylene and polyethylene
Sulfuric acid Pharmaceuticals Fuel Cells
Fertilizers
http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Catalysis
There are two simple divisions of catalysis
Homogeneous Heterogeneous
A homogeneous catalyst is one that is in the same phase as the reactants – a solute in a liquid, a liquid in a liquid, a gas in a gas etc
A heterogeneous catalyst is one that is not in the same phase – a solidliquid system or a solidgas system
http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Catalysis
The rate is accelerated by lowering of the activation energy.
The catalyst also arranges or organizes the reactants so that they achieve the reacting configuration more efficiently. The catalyst will often change the entropy of the elementary steps along the reacting paths.
http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Catalysis
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http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Catalysis
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http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Catalysis
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http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Catalysis
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http://www.uyseg.org/catalysis/cat_contents.htm Chemistry 130 Chemistry 130 Osias Beert, Flemish painter (b. ca. 1580, Antwerpen, d. 1624, Antwerpen) http://www.uyseg.org/catalysis/ethacid/ethacid6.htm
Chemistry 130 Osias Beert, Flemish painter (b. ca. 1580, Antwerpen, d. 1624, Antwerpen)