Hammett equation
The Hammett equation establishes a quantitative relationship between the structure of chemical reactants and their reactivity. It is a linear free energy relationship (Linear Free Energy Relationships, LFER ). It applies generally, but is parameterized differently for different reactions or reactants. The equation falls into the sub- field of physical organic chemistry.
- 3.1 Mechanistic effects
- 3.2 conjugative
General
The American chemist Louis Plack Hammett developed this relationship for substitution reactions of second- substituted benzenes. Considering in the alkaline hydrolysis of substituted benzoic acid esters, the relative rate constants based on the unsubstituted esters and the relative pKa value of the ester, based on the appropriately substituted benzoic acid, is obtained in double-logarithmic representation of the graph of a linear function. An exception is ortho-substituted benzoic acids, as with them entropic effects due to the proximity of the ester group and the Zweitsubstituenden play a role in the reactivity.
The general form of the equation is:
With
K: rate constant
K: equilibrium constant
The influence of the substituents can be described by the difference in the free Gibbs enthalpy of the different reactions. x denotes an indefinite substituent H represents a hydrogen Referenzsubstituenten:
Additionally, it should:
And
It can be seen that also can be applied to. In addition, it adds a proportionality factor, so as to obtain the above-mentioned general form of the Hammett equation.
So you correlate a kinetic size with a thermodynamic to close on a correlation of reactivity and structure. So you use the relationship between reactivity and kinetics, as well as between structure and thermodynamics in order to establish a quantitative relationship between reactivity and structure of the third joint of kinetics and thermodynamics in the Hammett relationship.
The side chain of reactions of ortho -and para- substituted benzene derivatives of the following two of the Hammett equation are based on the reaction rates and equilibria.
Log ( Co ) or log ( Co ) are in this case the Achsenabschitte when the log ( k) and log ( K) against the substituent constant σ ρ applying a constant reaction rate constant.
Selected substitution constants of substituted benzoic acids:
Parameter
Is called Substituentenparameter, postulating that he is independent of, the reaction parameters. This is only an approximation, because a reaction with different substituents never by exactly the same route runs. For substituents in the para or meta position, this assumption is, however, permitted. Qualitatively it can be stated that the reaction parameter represents the sensitivity of a reaction to substituent effects.
Substituentenparameter
Since the size of Substituentenparameters also on other reaction conditions such as, for example, depends on the solvent to be used is generally standardized Substituentenparameter, averaged over many reactions. The amount of the size characterized by the ability of a substituent to interact with the electron distribution in the transition state. The values are tabulated, and for each reaction, as well as the position and nature of the substituent different.
There are two different substituent effects, which lead to a Substituentenparameter.
- Resonance or Mesomerieeffekt (R or M)
- Inductive Effect ( I)
I effect only of alkyl radicals, - about Hyperconjugation - or substituents, which are more electropositive than carbon, for example, Silicon or boron - are triggered. Unless Inductive and Mesomeric effects are in opposite directions so dominated the Mesomeric effect in general. So you can find essentially four types of substituents:
- Alkyl groups,- SiR3, - BR2 I
- - Acceptor -R -I
For example, carbonyl, nitro, nitrile and sulfate groups
- Groups with unbound electron pairs R, -I
For example, sec. Amine, ether, thioether, halide
- Cationic groups -I
For example,- NR3 or -PR3
Nonlinearity
Mechanistic effects
Mechanistic effects are the cause of a change in the reaction parameters. Under certain circumstances, two different reaction mechanisms, compete with each other which have a similar activation energy, but very different electron demand. This can lead to a non-linear curve of the Hammett graph. In the case of the change of the reaction mechanism, the graph can be divided into linear sub-regions. So there exist linear sections with different slopes and hence different reaction parameters.
Furthermore, mechanisms with intermediate steps can lead to non-linear behavior. Generally the slowest reaction step, in a sequence is responsible for the overall speed. By changing the substituents of the rate-determining step of the reaction sequence may change, and consequently, there is the non-linear curves. If necessary. is no longer a function also of linear partial areas if the exchange vonstattengeht slowly and continuously. In this case, one obtains a graph of curvature.
Conjugative
Conjugation effects lead to a variation in Substituentenparameter. When a substituent is in the para position with a second substituent, there may be in the transition state to a conjugated system which includes both of the substituents. This effect is to be distinguished from the normal Mesomerieeffekt, and also acts on the reactivity. This leads to a non-linear curve. To counter this, they developed more and substituent. The former for donors, the latter for acceptors. You put the two cases set a benchmark reaction to obtain the relative sizes.
This fact may help in the elucidation of the mechanism of a reaction. If one finds a correlation with parameters or rather, there is probably a durchkonjugierter transition state.
As reference reactions for values, the hydrolysis of substituted cumyl chloride used. For values using the dissociation of substituted aniline.
Despite these three possible parameter systems may lead to non-linear behavior. In this case perform an additional parameter r a, the group consisting of a weighting factor for a sum - and values used. If the value is one, the curve correlates with only, it is zero only. Thus, reactions that lie between these extremes can be mapped.
Extension to the Taft
In aliphatic systems are substituent and reaction center usually closer together so that steric effects must be taken into account. Further separating the parameters and their components according to I- and R - effect. For example, consider the hydrolysis of an aliphatic ester, and makes the following assumptions:
Generally leaves the Linear free Enthalpiebeziehung for this case up: With the assumptions (1) and (3) the following: (*) In addition, give the assumptions (2) and (3): With the last two equations to a set of new parameters define, so that the steric parameter just picks: If one takes for a value from the Hammett parameters, so can the new parameters can be calculated. Thus, the Taft equation can be set up: The steric parameter can be calculated from (*), as a reference for the rate constants of the methyl substituent is selected. The Taft equation thus provides a formalism ready to quantify systems in which steric effects in the course of the reaction play a role.