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Grunwald-Winstein Plots

In physical organic chemistry, Grunwald-Winstein Plot is a linear free energy relationship between relative rate constants and the ionizing power of various solvent systems, describing the effect of solvent as nucleophile on different substrates. The equation, which was developed by Ernest Grunwald and Saul Winstein in 1948, could be written as equation 1.

$$\log \frac{k_{x,sol}}{k_{x,80\% EtOH}} = mY $$  (1)

Where the $k_{x, sol}$ and $k_{x, 80% EtOH}$ are the solvolysis rate constants for a certain compound in different solvent systems and in the reference solvent, 80% aqueous ethanol, respectively. The m is a parameter of the compound measuring sensitivity of solvolysis rate to Y, the measure of ionizing power of the solvent.

=Backgroud= Hammett equation(Equation 2) provides us the relationship between the substituent on the benzene ring and the ionizing rate constant of the reaction. Hammett use the ionization of benzoic acid as the standard reaction (Fig. 1) to define a set of substituent parameters σX, and then generate the ρ values, which represent ionizing abilities of different substrate, through Hammett Plot.

$$\log \frac{k_X}{k_H} = \sigma_X\rho $$    (2)



However, If the solvent of the reaction is changed, but not the structure of the substrate, the rate constant may change too. Following this idea, a plot of relative rate constant vs. the change of solvent system can be generate through an equation, which is Grunwald-Winstein Plots. Since it has the same pattern with Hammett equation but dealing with the change of solvent system, we can also consider it as a supplement of Hammett Equatoin

=Definition=

Reference Compound
The Substitution reaction of tert-Butyl chloride (Fig. 2) was chosen as reference reaction. The first step, ionizing step, is the rate determining step, SO stands for the nucleophilic solvent. The reference solvent is 80% Ethanol and 20% water by volume. Both of them can carry out the nucleophilic attack on the carbocation.

The SN1 reaction is performed through a stable carbocation intermediate, the more nucleophilic solvent can stabilize the carbocation better, thus the rate constant of the reaction could be larger. Since there’s no sharp line between SN1 and SN2 reaction, a reaction goes through SN1 mechanism more is preferred to achieve a better linear relationship, that’s why t-BuCl was chosen.

Y values
$$\log \frac{k_{t-BuCl, sol}}{k_{t-BuCl, 80\% EtOH}} = Y $$      (3)

In equation 3, kt-BuCl, 80% EtOH stands for the rate constant of t-BuCl reaction in 80% aqueous Ethanol, it is a constant. kt-BuCl, sol. stands for the k of the same reaction in different solvent system, such as ethanol-water, methanol-water, and acetic acid-formic acid. Thus Y reflects the ionizing power of different nucleophile solvents.

m values
The equation parameter, sensitivity factor of solvolysis, m describes the compound’s ability to form the carbocation intermediate in certain solvent system. It is the slop of the plot of log(ksol/k80%EtOH) vs Y values. Since the reference reaction has little solvent nucleophilic assistance, the reactions with m equal to 1 or lager than 1 have almost full ionized intermediate. If the compounds are not so sensitive to the ionizing ability of solvent, then the m values are smaller than 1. That is:

1. m ≥ 1, the reactions go through SN1 mechanism.

2. m < 1, the reactions go through the mechanism between SN1 and SN2.

=Disadvantage= 1. This equation could not fit into all different kind of solvent mixtures. The combinations are restrained in only certain systems and only the nucleophilic solvents.

2. Relationships between many reactions and nucleophilic solvent systems are not linear. This derives from the growing SN2 reaction character within the mechanism.

=reference=