# Chemical Kinetics: Mechanisms | General Chemistry 2

Mechanisms in chemical kinetics are studied in this chapter: activation energy, Arrhenius equation, elementary reactions, reversible reactions, intermediates, rate-determining step, catalysts and catalysis

## Activation Energy

Activation energy Ea (in J.mol-1):

The minimum amount of energy that must be provided to the reactants to initiate a chemical reaction. This energy corresponds to the minimum energy that the colliding molecules must have for the collision to be effective

## Arrhenius Equation

The Arrhenius equation is an equation that gives the dependence of the rate constant k of a reaction on temperature:

k = Ae-Ea/RT

ln k = - $\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}$ + ln A

k = reaction-rate constant
Ea = activation energy (in J.mol-1)
R = molar gas constant = 8.314 J.mol-1.K-1
T = temperature (in K)
A = constant which depends on the reaction

## Reaction Mechanisms

Many reactions involve more than one step and can be divided in elementary reactions

Elementary reaction:

A reaction that occurs in a single collision of the reactant molecules (single step). The reaction order of an elementary reaction is equal to the stoichiometric coefficients of the reactants ⇒ the rate law of an elementary reaction can be written directly using the stoichiometric coefficient of each reactant as exponent in the rate law

The formation of NO2 can be divided in 2 elementary steps (1) and (2):
Step (1): 2 NO → N2O2
Step (2): N2O2 + O2 → 2 NO2
Overall reaction (1) + (2): 2 NO + O2 → 2 NO2

The rate law of elementary reactions can be written directly using the stoichiometric coefficients:
rate law of (1) = k1 [NO]2
rate law of (2) = k2 [N2O2] [O2]

Reversible reaction:

A reaction in which products can react to form reactants. This type of reaction proceeds in both the forward and reverse directions. At equilibrium, the rate of the forward reaction = the rate of the reverse reaction

2 NO $⇌$ N2O4 is a reversible reaction
At equilibrium: k1 [NO]2 = k-1 [N2O4]

Intermediate vs. catalyst:

Intermediate: a species that is produced in one step and consumed in a subsequent step
Catalyst: a species that is first consumed and later regenerated
Neither intermediates nor catalysts appear in the overall balanced equation

Step (1): 2 NO → N2O2
Step (2): N2O2 + O2 → 2 NO2
Overall reaction (1) + (2): 2 NO + O2 → 2 NO2

N2O2 is an intermediate: it is produced in step (1) and consumed in the subsequent step (2)

## Rate-Determining Step

Rate-determining step:

The step in a reaction that is much slower than all the other steps. It controls the overall reaction rate

Step (1): 2 NO2 → NO + NO3   (slow)
Step (2): NO3 + CO → NO2 + CO2   (fast)
Overall: NO2 + CO → NO + CO2

NO2 + CO → NO + CO2 is a two-step reaction and (1) is the rate-determining step
Law rate of the overall reaction = law rate of (1) = k [NO2]2

## Catalysis

Catalyst:

A substance that increases the rate of a chemical reaction without being consumed during the reaction.  A catalyst speeds up the reaction by lowering the activation energy barrier to the reaction:

Catalysis:

A process by which a catalyst increases the reaction rate. Catalysis may be:

• Homogeneous: catalyst and reactants exist in the same phase
• Heterogeneous: the catalyst and the reactants exist in different phases. It is by far the most important type of catalysis in industrial chemistry

Enzymes:

Biological catalysts. They increase the rate of biochemical reactions and are also highly specific