The Rate-Determining Step
• Chemical reactions can occur in multiple steps. Many reactions don't actually occur all in one go as it might look from a chemical equation, they often occur in multiple steps.
• Usually the steps involve dependency. The reactant of one step is the product of the previous step, so each new step can't take place until the one before it has.
• Only the slowest step of the reaction limits reaction rate. The rate-determining step is the slowest step of all of the steps of a reaction, it is also sometimes known as the rate-limiting step. The rate- determining step governs the overall rate of the reaction as it is the slowest. Any step that follows the rate-determining step will not affect the rate of the reaction, as long as it is faster than the rate-determining step.
• The reaction mechanism can be used to derive the rate equation.
The total number of moles of the substances in the slowest step and preceding it, will be the same as the order of reaction for each substance in the rate equation. Any reactant involved in a step that follows the rate-determining step will not be involved in the rate equation.
• Intermediates are not part of the rate equation. They must be replaced by the reactants which make it up.
• Catalysts can be part of the rate equation. They can therefore be part of the rate limiting step.
Worked Example:
F + G + H → A + B
This reaction may occur in these separate steps:
1. F + G→C (first intermediate) FAST
2. C →D (second intermediate) SLOW
3. D + H → A + B
Determine the overall rate equation.
Answer:
• Step 2 is the slowest step, so it is the rate-determining step.
• Step 1 is faster than step 2, the rate-determining step, however step 2
depends on the product of step 1.
• This means that step 1 also has an effect on the rate of the reaction because the rate-determining step depends on it.
• Therefore all of the reactants of both step 1 and step 2 will need to be
included in the rate equation.
The rate equation for the reaction of F + G + H→ A + B is:
Rate ∝[F][G][H]
Using the Order of a Reaction to find the Rate-Determining Step
The overall reaction for C4H9Br reacting with alkali is:
C4H9Br + OH− → C4H9OH + Br−
But there are two possible mechanisms for this reaction:
• A two-step mechanism - The C-Br is broken in the slow step and the fast step is two oppositely charged ions interacting.
1. C4H9Br →C4H9+ + Br− SLOW
2. C4H9+ + OH− → C4H9OH FAST
• A one-step mechanism - The C-Br bond is broken while the C-OH is formed.
C4H9Br + OH− → C4H9OH + Br− SLOW
C4H9Br exists as 3 different isomers and experiments have found that the
isomer 1-bromobutane has a second order mechanism when involved in
this reaction. The rate equation is:
rate = k[CH9Br][OH−]
This shows that the rate is dependent upon the concentration of bromobutane and the hydroxide ions, which suggests the mechanism is the second one we looked at, the one step reaction, as this contains both the bromobutane and the hydroxide ions in the slow step, the rate-determining step.
Worked example:
The rate equation for a reaction is:
r = k [NO]2[H2]
The overall reaction is:
2NO(g) + 2H2(g) →N2(g) + 2H2O(g)
The following three step mechanism is suggested for the reaction.
Determine the rate-determining step.
Step 1: 2NO → X
Step 2: X + H2 → Y
Step 3: Y + H2 → N2 + 2H2O
Answer:
As the rate equation contains NO and is second order, this suggests that
two moles of NO are used. This means that rate determining step could
be step 1.
However, H2 is also included. This means the rate determining step is step 2.
It can’t be step three, as the reaction is first order with respect to hydrogen, but not second order. If step 3 were involved, then there would be 2 moles of hydrogen.
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