Category Archives: Chapter 9 – Reaction Kinetics

Chapter 9 – Reaction Kinetics


Terminology and Concepts: Reaction Kinetics

Rate of reaction is the change of concentration of a reactant or a product per unit time (seconds / minutes).

Rate of reaction = rate of increase of the concentration or amount of the product / Rate of reaction = rate of decrease of the concentration or amount of the reactant.

Average rate is the change in concentration of a substance (reactant or product) over a fixed time interval.

Instantaneous rate is the rate of the reaction at a specific time (the steeper the slope, the higher the instantaneous rate).

Tangent is zero, the rate is zero / reaction has stopped.

Rate Equation or Rate Law is the rate of a reaction which is affected by the reactants concentration.

Rate = k [reactant]n ,           k is rate constant

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Nucleophile – Lewis bases / a species that attacks a positively-charged (electron deficient) carbon atom by donating an electron-pair to form a dative covalent bond.

Electrophile – Lewis acids / a species that attacks a negatively-charged (electron rich) carbon atom by accepting an electron-pair to form a dative covalent bond.

Important Notes in Organic Chemistry:

  • If the concentration of the nucleophile influences the rate of the reaction which means the rate determining step involves the nucleophile attacking the electrophile to form the transition state that evolves into product (SN2 reaction mechanism = common in organic chemistry).
  • If the concentration of the nucleophile shows no effect on the rate of reaction, the reaction is SN1 reaction mechanism.
  • Both reaction mechanisms show a rate dependence on the electrophile concentration.

Reaction Order

  • There are 3 reaction orders: zero, first and second.
  • Zero order reaction proceeds at a constant rate, independent of reaction concentration.
  • First order reaction depends only on one reactant (SN1 reaction).
  • Second order reaction depends on two reactants (SN2 reaction).
Zero order First order Second order
Rate law rate = k rate = k[A] rate = k[A]2
Half-life t1/2 = [A]o / 2k t1/2 = ln 2 / k t1/2 = 1 / k[A]o
Unit of rate constant mol dm-3 s-1 s-1 mol dm3 s-1

Reaction Mechanisms

First order Second order Second order
The slowest step involves one molecule breaking apart (its rate determining step). The slowest step involves two molecules forming a bond (its rate determining step). The slowest step involves two molecules forming a bond (its rate determining step).
A –> B + C A + B –> C 2A –> B + C
One step reactionDissociative mechanism One step reactionAssociative mechanism One step reactionAssociative mechanism
Rate = k[A] Rate = k [A][B] Rate = k [A]2

Not all reactions are concerted. There are reactants that form intermediates (or activated complexes) before the reactants form products and give a multi-step reaction.

Example 1

Reaction:

NO2(g) + CO(g) –> NO(g) + CO2(g)

Mechanism:

NO2(g) + NO2(g) –> NO(g) + NO3(g) (slow)
NO3(g) + CO(g) –> NO2(g) + CO2(g) (fast)

Which of the following options is the rate law for this reaction, assuming that this reaction mechanism is correct?

A. k (PNO2) (PCO)
B. k (PNO2)2 (PCO)
C. k (PNO2)2
D. k (PNO2)

Answer: C

Solution: The slowest step in the reaction mechanism is the rate determining step. The rate depends on the two molecules of NO2 gas and CO has no effect on the rate of this reaction which means the addition of CO does not increase the rate of reaction.

Collision Theory

  • Reaction – reactants particle must collide with one another with sufficient energy to break chemical bonds in the reactants to form product.
  • Activated complex – a very high energetic and highly unstable species is formed.
  • Chemical reaction – is the effective collisions of reactant particles.
  • Reaction rate – is the measurement of the frequency of effective collisions.
  • Activation energy (Ea) – minimum energy required to break the chemical bonds in the reactant molecules and overcome the repulsion forces of the reactants molecules.
  • Energy profile / Reaction profile – the difference in energy between the reactants and activated complex.

The rate of a reaction is affected by

  • temperature (reaction rate increases with increasing temperature)
  • physical state of reactants (gas, liquid or solid)
  • activation energy (reaction rate increases with increasing temperature)
  • catalysts (reaction rate increases with positive catalysts and reaction rate decreases with negative catalysts)
  • solvent (solvents affect the transition state stability)
  • collision frequency
  • collision orientation
  • the concentration of the reactants in the rate determining step
  • effect of pressure

Example 1

Which of the following does NOT always affect the rate of reaction?

A. Changing the temperature
B. Adding a catalyst
C. Increasing the volume by adding solvent
D. Adding a reactant

Answer: D

Solution: Changing temperature changes the reaction rate. Adding a catalyst (usually positive catalyst) lowers the activation energy which results increases the reaction rate. Increasing the volume reduces the concentration of all reagents (include the reactants in the rate determining step). Increasing volume of a gas phase reaction results in a decreased in reaction rate. Therefore, if the reactant being added is not involved in the rate determining step, then it does not influence the rate.

Rate Constant and Rate Law

Rate constant is determined by the Arrhenius constant (collision orientation and frequency take into account)

k = A e –Ea/RT

where Ea is the activation energy, R is the molar gas constant, T is the absolute temperature and A is the frequency factor.

ln k = ln A – (Ea/RT)
lg k = lg A – (Ea/2.303R) (1/T)

A plot of lg k against 1/T will be a linear graph with a slope of – (Ea/2.303R) and an intercept of lg A

First Order Reactions

The rate equation is
rate = k [A]

Example 2

Rate expression for the decomposition of N2O5,
rate = k [N2O5] or –d[N2O5]/dt = k [N2O5]1
Unit of k = mol dm-3 s-1 / mol dm-3 = s-1

ln [N2O5]t = ln [N2O5]0 – kt , where ln = natural logarithm
For the first-order reaction, a plot of ln [N2O5] against t will be linear with a slope of –k and an intercept of ln [N2O5]0.

or

ln {[N2O5]0 / [N2O5]} = kt
For the first-order reaction, a plot of ln {[N2O5]0 / [N2O5]} against t will be straight line with a slope of k and an intercept through the origin (0).

Second Order Reactions

The rate equation is
rate = k [A]2 or rate = k [A] [B]

Example 3

2NO2(g)  –> 2NO(g) + O2(g)
rate = k [NO2]2
Unit of k = mol dm3 s-1/ (mol dm3 s-1)2 = mol dm3 s-1

1/[N2O5]t = kt + 1/[ N2O5]0
For the second-order reaction, a plot of 1/[N2O5] against t will be a slope of k and an intercept of 1/[ N2O5]0

Zero Order Reaction

The rate equation is
rate = k [A]0

Example 4

Thermal decomposition of hydrogen iodide on gold:

HI(g)  –> ½ H2(g) + ½ I2(g)
rate = k [NO2]2
Unit of k = mol dm-3 s-1

[HI] = [HI]0 – kt
For the zero-order reaction, a plot of [HI] against t will be a straight line with a slope of –k and an intercept of [HI]0

Catalysis

  • only small amount of catalyst is needed for the reaction
  • catalysts lower the activation energy of the reaction
  • catalysts speed up the rate of reactions and has no effect on the yield of a reaction
  • catalysts are specific for one reaction

Homogeneous catalysis

  • catalyst that exists in the same phase as the reactant
  • an intermediate species is produced in the reaction

Example 1 (homogeneous catalyst in gas – NO)

Step 1: NO(g) + ½ O2(g) –> NO2(g) where NO2 is an intermediate compound
Step 2: NO2 (g) –> NO(g) + O (g) with sunlight
Step 3: O(g) + O2(g) –> O3(g)
Overall reaction / uncatalysed reaction: 3/2O2(g) –> O3(g)

Example 2 (homogeneous catalyst in aqueous solution – acid catalysis)

CH3COOCH3(aq) + H2O(l) –> CH3COOH(aq) + CH3OH(aq)

Example 3 (homogeneous catalyst in aqueous solution – Fe3+)

Step 1: 2Fe3+(aq) + 2I-(aq) –> 2Fe2+(aq) + I2(aq) where Fe2+ is an intermediate ion
Step 2: 2Fe2+(aq) + S2O82-(aq) –> 2Fe3+(aq) + 2SO42-(aq)
Overall reaction / uncatalysed reaction: S2O82-(aq) + 2I-(aq) –> 2SO42-(aq) + I2(aq)

Example 4 (homogeneous catalyst in aqueous solution – Br2)

Step 1: Br2(aq) + H2O2(aq) –> 2Br-(aq) + 2H+(aq) + O2(g)
Step 2: 2Br-(aq) + H2O2(aq) + 2H+(aq) –> Br2(aq) + 2H2O(l)
Overall equation / uncatalysed reaction: 2H2O2(aq) –> 2H2O(l) + O2(g)

Example 4 (homogeneous catalyst in aqueous solution – NaI)

Step 1: I-(aq) + H2O2(aq) –> IO-(aq) + H2O(l)
Step 2: IO-(aq) + H2O2(aq) –> I-(aq) + O2(g) + H2O(l)
Overall equation / uncatalysed reaction: 2H2O2(aq) –> 2H2O(l) + O2(g)

Heterogeneous catalysis

  • catalyst that exists in a different phase from the reactant
  • they are transition metals, the oxides of transition metals and the oxides of aluminium and silicon
  • adsorption process which involve formation of bonds between the reactant molecules and the atoms on the surface (active sites) of the catalyst (solid metal)
  • 4 steps in heterogeneous catalysis: reactant molecules are adsorbed on the surface, reactant molecules diffuse along the surface, reactant molecules react to form product molecules and molecules of product desorb from the surface

Example 1 (heterogeneous catalyst – gold, Au)

Decomposition of N2O
N2O(g) –Au–> N2(g) + 1/2O2(g)

Example 2 (heterogeneous catalyst – nickel, Ni)

Hydrogenation of food oils or semisolid fats
CH3(CH2)7CH=CH(CH2)7COOH + H2Ni–> CH3(CH2)7CH2CH2(CH2)7COOH

Example 3 (heterogeneous catalyst – platinum metal mixed with rhodium)

Oxidation of carbon monoxide and unburned hydrocarbon such as benzene
2CO(g) + O2(g) –Pt–> 2CO2(g)
C6H6(l) + 15/2O2(g) –Pt–> 6CO2(g) + 3H2O(l)
2NO(g) –Rd–> N2(g) + O2(g)

Example 4 (heterogeneous catalyst – V2O5)

Contact process
2SO2(g) + O2(g) –V2O5–> 2SO3(g)

Example 5 (heterogeneous catalyst – Iron)

Haber process
N2(g) + 3H2(g) –Fe–> 2NH3(g)

Example 6 (heterogeneous catalyst – Platinum)

Ostwald process
4NH3(g) + 5O2(g) –Pt–> 4NO(g) + 6H2O(g)

Example 7 (heterogeneous catalyst – Nickel, Palladium, Platinum)

Hydrogenation of alkenes (manufacture of margarine)
CH2=CH2(g) + H2(g) –> CH3CH3(g)

Effect of temperature on reaction rates and rate constants

  • Temperature increases causes the reaction rates increase
  • Reaction rate is doubled for every 10˚C rise in temperature

Kinetics Theory

  • Kinetic theory = mv2/2
  • Raising the temperature greatly increases the fraction of molecules having very high velocity and high kinetics energy.
  • Most molecules are likely to collide to react
  • Increase in the frequency of collision, this causes the fraction of effective collision increases (kinetic energy equal to or greater than the activation energy, Ea).

Arrhenius equation,

  • k = A e –Ea/RT
  • In natural logarithm, ln k = ln A – (Ea/RT)
  • The graph of ln k versus (1/T) should be linear and the slope of straight line is -(Ea/R)

Clausius-Clapeyron equation (two different temperatures, T2 and T1)

  • In natural logarithm, ln k2 – ln k1 = – (Ea/R) [(1/T2) – (1/T1)]
  • ln (k2/k1) = (Ea/R) [(1/T2) – (1/T1)]
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