Second Kinetics Notes

Mechanisms

Part of collision theory. A mechanism is a sequence of molecular events (called elementary steps or elementary reactions) by which a reaction occurs. A mechanism is a theory of how particles collide and produce products.

rate = k_f [N₂O₄]

The above is the theory (and an elementary reaction) of how dinitrogen tetroxide can decompose and produce 2 nitrogen dioxide molecules. The N-N bond can vibrate with the two atoms moving back and forth from each other. If the vibration is strong enough, the two N can move away and separate from each other, breaking the bond. k_f is the rate constant for the forward reaction.

If we double the concentration of dinitrogen tetroxide we will double the rate of NO₂ production. So using the elementary reaction above, we predict the forward reaction to be first order in N₂O₄. A Unimolecular reaction is an elementary reaction where a single particle reacts. A rate law can be determined from the stoichiometry of an elementary reaction. An experimental rate law cannot be determined from an given chemical reaction, because the reaction may be the sum of two or more elementary reactions, and the overall reaction does not list the individual species that react.

Now consider the reaction CH₃I + OH^- ® CH₃OH + I^-

Rate = k [OH^-] [ CH₃I]

Here we have a elementary reaction which is bimolecular, where two particles collide to produce products. Doubling [OH^-] will double the chances of hydroxide and methyl iodide colliding and reacting. And doubling the [CH₃I] will also double the chances of collision and reaction. So this reaction is first order in each reactant and 2nd order overall. You can imagine a transition state with both the OH and the I are attached to the central carbon. This transition state would lie at the peak of the energy profile.

The reaction

2 NO₂ → N₂O₄ is the reverse of the first reaction above and is a bimolecular reaction with a predicted rate law of

Rate = k_b [NO₂]²

Termolecular, reactions involving the simultaneous collision of three particles, are rare and the proposal of a termolecular mechanism would be scoffed at by cool scientists.

So far our mechanisms have involved one elementary process. Mechanisms can involve many steps. Here are two proposed mechanisms for a gas phase reaction

Mechanism 1 Step 1 NO₂ ® NO + O Rate1 = k1 [NO₂]

Step 2 NO₂ + O ® O₂ + NO Rate2 = k2 [NO₂] [O]

Net Reaction 2 NO₂ ® 2 NO + O₂

Mechanism 2 Step 1 NO₂ + NO₂ ® NO₃ + NO Rate1 = k1 [NO₂]²

Step 2 NO₃ ® O₂ + NO Rate2 = k2 [NO₃]

Net Reaction 2 NO₂ ® 2 NO + O₂

With multiple steps, one step will be slower than the other. The slow step will control the rate of the reaction and is called the rate determining step. Step 1 of Mechanism 1 produces a reactive intermediate, an oxygen atom, and this is expected to quickly react. So the first step is predicted to be a slow rate determining step and the second, fast step will have little effect on the rate. Thus the overall rate law predicts a rate that is first order in NO₂. If the first step of the second mechanism is the rate determining step, then mechanism 2 predicts second order dependence on NO₂ concentration. Experimental observations show this reaction is second order in nitrogen dioxide, so experiment supports the second mechanism.

For a mechanism to be valid,

1. the elementary reactions should sum to give the overall reaction

2. the elementary reactions must predict the experimentally observed rate law.

Remember the above reaction

CH₃I + OH^- ® CH₃OH + I^- Rate = k [OH^-] [ CH₃I]

The experimentally observed rate law supports the mechanism of these two particles colliding producing the products shown.

The following reaction is first order overall

C(CH₃)₃I + OH^- ® C(CH₃)₃OH + I^- Rate = k [ C(CH₃)₃I ]

Here H on the central C have been replaced by methyl (CH₃) groups. Evidently this reaction has a different mechanism. The following two step reaction is proposed

Rate 1 = k1 [C(CH₃)₃I ]

Rate 2 = k2 [C(CH₃)₃⁺] [OH^-]

If the first step is rate determining then the rate of this step will be the overall rate, which is what is observed. The second step, involving the reactive intermediate C(CH₃)₃⁺, is very fast and will have little effect on the rate.

This molecule with its bulky CH₃ groups , make it harder for OH^- to attack and so this molecule has a different mechanism for reaction than we saw for CH₃I. This mechanism shows how a reaction rate can be independent of a reactant concentration. This reaction is zeroth order in [OH^-] because it is used in the fast step, and its concentration does not affect the rate of the first, rate determining step.

The C(CH₃)₃+ is an intermediate. It has a longer lifetime (but still short) than a transition state.

If the second step in a two step mechanism is the rate determining step, the predicted rate law is harder to determine. An example is given in the textbook.

Catalysts

The Stratosphere is from 6 to 30 miles high. One of many reactions happening up there are

O₂ + hu (UV) ® 2 O This O atom can react with ozone

O₃ + O ® 2 O₂ This reaction has a delta H of -390. kJ and an E_a = 17.1 kJ. If chlorine atoms are present the following mechanism can also consume ozone

Step 1 O₃ + Cl ® O₂ + ClO E_a = 2.1 kJ

Step 2 O + ClO ® Cl + O₂ E_a = .4 kJ

Net Rxn. O₃ + O ® 2 O₂

Since the first step has a larger E_a, it would be expected to be the slower, rate determining step. Since the first reaction would be rate determining, you could compare the rate of this reaction versus the reaction without Cl by calculating

k₁ = A e ^{-2.1 kJ / RT}

k₂ A e ^{-17.1 kJ/RT}

This is an example of a catalyst, a substance that speeds up a reaction without being consumed. So the reaction goes much faster and the chlorine is available to destroy lots of ozone.

Enzymes are the bodies catalysts. The following chart estimated free energy of activation for decomposition of hydrogen peroxide at 20°C; catalase accelerates the rate of reaction compared to the uncatalyzed reaction by more than 10⁶ fold.

Uncatalyzed	75 kJ/mol
Catalyzed by colloidal Pt	54
Catalyzed by catalase (enzyme)	29

Compare energy profile.