Rate Determining Step

rate determining step title image

What is the Rate Determining Step?

The rate determining step in a reaction is the step which will take the longest time in a reaction. It is the slowest part of the reaction mechanism and will determine how fast the overall reaction will take place. The step may be slower than the others for a variety of reasons, including activation energy.

Energetic Favorability

The concentration of the reactants is always important, particularly the reactants in the rate determining step. Reactions proceed when it is energetically favorable to do so. In equilibrium reactions, the concentration of reactants to products changes the G of the reaction; when the ratio of reactants to products is imbalanced, with more reactants per products, the G is lowered by entropy.

Though it is important to note that chemists will say these factors drive reactions, energetic favorability has nothing to do with the rate determining step. G isn’t able to tell us anything about the rate of a reaction. At the same time, it can’t tell us anything about its rate limiting step.

A reaction may be energetically favorable, but still be the rate determining step.

Relationship Between Rate Determining Step and Activation Energy

How do you determine the rate determining step? For all reactions to occur, the reactants must overcome an activation energy. This activation energy is equivalent to the amount of energy required to break the bond needed to form the product or key intermediate. The rate determining step is the reaction with the highest activation energy in a reaction mechanism.

Activation energy within an energy profile of a spontaneous reaction. The rate determining step is that which the highest energy
To go from A+B to C the energy of reaction increases. This increase is the activation energy.

There are only a few factors which influence activation energy. As noted above, the energy needed to break the bonds is the primary factor in activation energy. In addition, when we break stable bonds to form unstable bonds, we will form unstable intermediates. The formation of these unstable intermediates is energetically unfavorable and will usually have the most activation energy.

However, steric hinderance can also affect the activation energy of a reaction. Steric hinderance is the idea that atoms within a molecule will repel each other, as well as atoms from other molecules. In essence, the presence of other bonds to the less electronegative molecule partially blocks the antibonding orbital. As labeled by collision theory, if the anti bonding orbital is partially blocked, the reaction will proceed slower in the presence of the steric hinderance.

Several activation energies

Within organic chemistry, we learned the curved arrow mechanisms of many reactions. These curved arrows indicate the intermediates a molecule will form for a reaction to take place. As we saw in organic chemistry, most reactions don’t have concerted arrows like the Diels-Alder reaction. Instead, most reactions will form one or many intermediates before it arrives at its product. The formation of each of these intermediates have their own respective activation energies.

s1 reaction with a notable rate determining step
Here we see the activation energy for a reaction may change depending on the reaction environment

Above is an energy profile of an SN1 reaction. As one can see, the formation of the carbocation intermediate has its own activation energy, apart from the reaction which forms the product. Coincidentally, this step of the reaction is also the rate limiting step because it has the highest activation energy in the energy profile.

Rate Determining Step in Energy Profiles

The rate determining step in energy profiles is that which has the highest activation energy. Energy profiles will yield this step by giving the activation energies for the formation of all intermediates and products. Generally speaking, the steps which form the most unstable intermediate determines the reaction rate.

Rate Determining Step Examples

Formation of intermediates such as carbocations or enolates (without the use of LDA) are incredibly energetically unfavorable and typically proceed only under very specific conditions. Generally, any half reaction or part of a reaction mechanism which produces a good nucleophile or electrophile as the product is the rate limiting step.

Rate Determining Step in Half Reaction

In half reactions, many times courses will describe a half reaction as “slow”. This slow reaction is the rate determining step. Another option is to break apart the curved arrow mechanisms. Then identify where the unstable intermediate is produced, this reaction is likely the rate limiting step.

Rate Determining Step and Reaction Rates

Once the rate determining step is identified, the reactants involved in the step are the molecules in the rate law equation. Chemists are only able to experimentally calculate and determine the rate law equation of a reaction. There is no identifier of the order of a reactant. To know the rate law equation, run 3 reactions with varying concentrations and measure their half lives.

In addition, it is important to note that the rate constant is specific to the experimental conditions, such as temperature. Changes in these environmental factors will affect the rate constants of a reaction.