*INSERT HUMOROUS BUT RELEVANT TITLE HERE*

I thought the title "The Hammett Equation" was a little bland for our blog, so I've left it up to your imaginations. Considering our last Friday meeting, I figured it would be a good idea to a little reading on the Hammett Equation.


Basically, the equation expresses an approximately linear relationship between the equilibrium constants and reaction rates of certain types of reactions, marrying up chemical equilibrium and kinetics quite nicely. Recall that the equation is as follows:

        or     

(where 'K' is the equilibrium constant for an equilibrium reaction where the substituent is R, 'Ko' is a reference constant where the substituent R is a hydrogen atom,  σ is the substituent constant, and where ρ is the reaction constant [which depends only on the type of reaction]. The lower case 'k' and 'ko' are the analogues for a reaction which uses benzene derivatives.) 


Hammett's paper entitled: "Some relations between reaction rates and equilibrium constants" has useful information and examples regarding the equation. (1)


There is no known universal relation that ties up both rate and equilibrium, but Hammet's does come close regarding acid/base reactions and those involving benzene derivatives. There are other relations that depend on rate and concentration terms, for example: 

log(k) = x log(K) + log(G)

where, G and x are constants, k is the rate constant, and K is the constant of ionization.  This relation is relevant to the following type of reaction: 

HA + S ---> Products +HA 

which can be seperated into the steps: 

1. HA + S <--> SH+ + A-   and

2. SH+ + A- ---> Products + HA. (where 2 is a rapid step). 

Since 2. is so rapid, the measured rate is that of 1. 


An example reaction is: 

RCOOCH3 + N(CH3)3 ---> RCOO- + N(CH3)4+

The paper shows that plotting log(k), rate constant, against log(K), the ionization constant of N(CH3)3, somewhat linear behaviour is observed. Reactions showing the hydrolysis of para/meta ethyl benzoate derivatives and the hydrolysis of para ethyl phenylacetate derivates also show linear curves when the data is plotted. The rates of the aforementioned two reactions differ due to the steric hindrance in para ethyl phenylacetate. 


The paper ends discussing the following reaction: 

AB + C ---> A + BC

A theory was proposed by London et al (1929) suggesting simultaneous proceeding of combining C and B with the dissociation of A and B. The height of the potential energy peak must be overcome while the kinetic energies of AB and C combined, must decrease. This process is a function of the dissociation energies. A relation between the height of the potential energy peak and the dissociation energies has not be established according to the paper. (Hammett, 1935). 


Quite some time has passed since the paper was written but it raises some interesting points regarding reaction types and where or not they follow the Hammett equation. 

References:
(1). Hammett, Louis (1935) "Some relations between reaction rates and equilibrium constants". Dept of Chemistry, Colombia University. American Chemical Society, pp.125-136.