Rate Laws of Elementary Steps

· The rate laws of the all-elementary steps determine the overall rate law of the reaction.

· The rate law of an elementary step is determined by its molecularity:

1. iMolecular processes are first order,

2. Bimolecular processes are second order, and

3. Termolecular processes are third order.

Rate Laws of Multistep Mechanisms

Rate-determining step: is the slowest of the elementary steps.

Therefore, the rate-determining step governs the overall rate law for the reaction.

For instance, the following reaction occurs in two steps:

· NO₂ (g) + CO (g) NO (g) + CO₂ (g)

Step 1. NO₂ (g) + NO₂ (g) k₁ NO₃ (g) + NO (g) (slow)

Step 2. NO₃ (g) + CO (g) k₂ NO₂ (g) + CO₂ (g) (fast)

K₂ >>>K₁ , NO₃ slowly produced in step 1 is immediately consumed in step 2

The rate determining steps is step 1 (slowest step):

R= k₁*[NO₂]² the rate law predicted by this mechanism agrees with the one observed experimentally.

Mechanisms with an Initial Fast Step

It is possible for an intermediate to be a reactant.

Consider:

2NO (g) + Br₂(g) 2NOBr(g)

The experimentally determined rate law is:

Rate = k*[NO]²*[Br₂]

The termolecular mechanism is be ruled out since it is not probable

Consider another mechanism:

k₁

Step 1: NO (g) + Br₂ (g) NOBr₂ (g) (fast)

k_-1

k₂

Step 2: NOBr₂ (g) + NO (g) 2NOBr (g) (slow)

for which the rate law is (based on Step 2):

Rate = k₂*[NOBr₂]*[NO].

The rate law should not depend on the concentration of an intermediate because intermediates are usually unstable.

Assume NOBr₂ is unstable, so we express the concentration of NOBr₂ in terms of NOBr and Br₂ assuming there is an equilibrium in Step 1

We have by definition of equilibrium:

k₁*[NO]*[Br₂] = k_-1*[NOBr₂] therefore:

[NOBr₂] = k₁/k_-1*[NO]*[Br₂

Rate = k₂*[NOBr₂]*[NO]

The overall rate law becomes:

Rate = k₂*k₁/k_-1*[NO]*[Br₂]*[NO] = k*[NO]²*[Br₂].

Catalysis

· A catalyst changes the rate of a chemical reaction by lowering the activation energy

Catalysts can operate by increasing the number of effective collisions.

That is, from the Arrhenius equation: catalysts increase k by increasing A or decreasing E_a.

k = Ae^-Ea/RT

There are two types of catalyst:

Homogeneous

Heterogeneous

Homogeneous Catalysis

The catalyst and reaction is in one phase.

Example:

Hydrogen peroxide decomposes very slowly:

2H₂O₂ (aq) 2H₂O (l) + O₂ (g).

In the presence of the bromide ion, the decomposition occurs rapidly:

2Br ^- (aq) + H₂O₂ (aq) + 2H⁺ (aq) Br₂ (aq) + 2H₂O (l)

Br₂ (aq) is brown.

Br₂ (aq) + H₂O₂ (aq) 2Br ^- (aq) + 2H⁺ (aq) + O₂ (g).

Br^- is a catalyst because it can be recovered at the end of the reaction.

The mechanism pathway with catalyst is different from that without catalyst because the catalyst (Br^-) added an intermediates (Br₂ (aq)) to the reaction.