We’ve pointed out that reactions go faster at higher temperature because the starting materials have more energy. But temperature is not the sole controller of rate. Two molecules might well collide with plenty of energy, but unless they are two molecules that can actually react, that energy will be lost as heat. (a reminder in the margin), it’s obvious that only collisions between ketone (A) and borohydride (B) get us any where—there will be plenty of non-productive collisions between A and A or B and B. Obviously the chance of a collision between A and B is increased the more of each you have, and especially if you have lots of A and lots of B. In fact, the chance of a successful reaction is proportional to the product of the concentration of A and the concentration of B. We can express this in a simple rate equation:

rate of reaction = k × [A] × [B]

where the value k represents the rate constant for the reaction. The value of k is different for different reactions, and it also varies with temperature. The size of k also contains information about how likely it is that the molecules will collide with the right orientation. We call this analysis of the factors affecting the rate of the reactions the kinetics of the reaction.

There is of course a link between the activation energy of a reaction and its rate, and the connection between them is known as the Arrhenius equation, after the Swedish chemist Svante Arrhenius (1859–1927) who formulated it and won the Nobel Prize in 1903.

k = Ae^−Ea/RT

where k is the rate constant for the reaction, R is the gas constant (see p. 243), T is the temperature (in kelvin), and A is a quantity known as the pre-exponential factor. Because of the minus sign in the exponential term, the larger the activation energy, E_a, the slower the reaction but the higher the temperature, the faster the reaction.

the reaction between borohydride and the ketone to make an alkoxide is only the first step of this reaction. Since ethanol likewise has to collide with the alkoxide for this second step to take place, you might very reasonably ask yourself why the rate of forma tion of the alcohol product does not also depend on [EtOH]: 

rate of reaction = k × [ketone] × [borohydride] × [EtOH] ?

The answer is hinted at in the energy profile diagram you saw on p. 253, which is repro duced below. The activation energy for the proton transfer step is lower than for the addition step, so it happens faster. It fact, it can happen fast whatever the concentration of ethanol, so ethanol does not appear in the rate equation. The overall rate of any reaction is determined only by what happens in the mechanistic step that is slowest, known as the rate-determining step or rate-limiting step. This is a general point about anything that happens in several steps: if you want to empty a football stadium through a set of turnstiles, it is only the rate at which the turnstiles operate that limits the emptying speed—it doesn’t matter how quickly or slowly people walk away after they are through.

Now you know why: proton transfers between N and O atoms are fast, and other steps are almost always rate determining. It doesn’t really matter how you get a proton from one electronegative atom to another—in reality it will be flitting all over the place and any reasonable route is just as correct as any other.

● Proton transfers, particularly between O or N, are always fast and only rarely rate determining.

مواضيع ذات صلة

Protons on saturated carbon atoms Chemical shifts are related to the electronegativity of substituents

Regions of the proton NMR spectrum

Integration tells us the number of hydrogen atoms in each peak

The differences between carbon and proton NMR

Kinetic versus thermodynamic products

Catalysis in carbonyl substitution reactions

What does third-order kinetics mean

Catalysis

Reaction intermediates

Why some reactions are done at low temperature

The route from reactants to products: the transition state

How fast do reactions go? Activation energies