Reaction Kinetics (5) Kinetics and Mechanism

Reaction kinetics are determined by experiment. 

If we can determine how the rate varies with concentration of a reactant [A] then we can begin to build a mathematical model of the reaction kinetics.

These three graphs demonstrate three different possible orders of reaction.

But you should not think of them as exhaustive.

There is no reason why there cannot be a reaction in which the order with respect to one reactant is not fractional: say ½

But if we can only have access to information that relates concentration of a reactant [A] to the time the reaction takes then the graphs for zero, first and second order look like this

The zero order plot has a reducing half life, the first order graph has a constant half life and the second order plot has a half life inversely proportional to the initial concentration of the reactant. 

Let’s express these plots mathematically:

1. Zero Order Reactions

Zero order plot show that the rate  =  k (the rate constant)

Rate = ∆[A]   = k

             ∆t

which on integration gives

[A]= [A_o] –kt

which is of the form y=mx +c so that a plot of [A] vs time t is a straight line and the negative gradient is the rate constant k and the intercept on the [A] axis is the initial concentration of A

2. First order reactions

Here the first order plot shows that the rate = k[A]

Rate = ∆[A]   = k[A]

             ∆t

which on integration gives

[A]  =  [A_o]e^–kt   or taking natural logs ln[A] =  ln[A_o] – kt

This second expression is of the form y=mx+c so that a plot of ln[A] vs t should give a straight line in which the negative gradient is the rate constant –k and the intercept on the ln[A] axis is ln[A_o] the natural log of the initial concentration of A.

The beauty of these integrated rate equations is that they avoid you having to draw tangents to a curve, a very unreliable method of determining order. 

3. Second order reactions

Here the second order plot shows that rate = k[A]²

This is the simpler form of the second order plot. 

Rate = ∆[A]   = k[A]²

             ∆t

which on integration gives

  1       =     1     +  kt

[A]          [A_o]

This second expression is of the form y=mx+c so that a plot of l/[A] vs t should give a straight line in which the gradient is the rate constant k and the intercept on the l/[A] axis is l/[A_o] the inverse of the initial concentration of A.

The discussion above is summarised in the schematic below:

How is rate related to mechanism?

The assumption here is that many reactions we study have multistep structures.

The other assumption is that these different steps do not all work at the same rate.

Therefore, the slowest step will be the one that determines how fast the reaction can go.

The analogy might be that in the dinner queue in your college dining hall the process that makes getting your lunch slow is the time you have to spend at the till paying for lunch. 

That’s where the queue is the longest.

That one step is rate determining.

So it stands to reason that in the rate equation the species involved will be in the rate determining step.

Take the iodination of propanone as the classic example.

The equation for the reaction is

CH₃COCH₃   +   H⁺   +  I₂    =     CH₂ICOCH₃   +   HI   +    H⁺

But the rate equation is

Rate   =  k[H⁺].[CH₃COCH₃].[I₂]^o

Showing that the iodine concentration has no effect on the reaction rate.

Therefore, the other two reactants, hydrogen ions and propanone molecules, are involved in a rate–determining step as this mechanism shows: 

There are many other examples of where kinetics has shown the mechanism of reactions to be especially in organic chemistry.