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.^[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.^[2]

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 σ_X, 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)

**Fig. 1** Dissociation of substituted benzoic acids.

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.^[3] ^[4]

**Fig. 2** S_N1 mechanism of substitution reaction

The S_N1 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 S_N1 and S_N2 reaction, a reaction goes through S_N1 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, k_{t-BuCl, 80% EtOH} stands for the rate constant of t-BuCl reaction in 80% aqueous Ethanol, it is a constant. k_{t-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.

solvent, %by vol.	Y	solvent, %by vol.	Y	solvent, %by vol.	Y
EtOH-H₂O		25	2.908	30	2.753
100	-2.033	20	3.051	20	3.025
98	-1.681	15	3.189	10	3.279
95	-1.287	10	3.312	AcOH-HCOOH
90	0.747	5	3.397	100	-1.639
80	0	H₂O	3.493	90	-0.929
70	0.595	MeOH-H₂O		75	-0.175
60	1.124	100	-1.09	50	0.757
50	1.655	90	-0.301	25	1.466
45	1.924	80	0.381	10	1.862
40	2.196	70	0.961
37.5	2.338	60	1.492
35	2.473	50	1.972
30	2.721	40	2.391

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(k_sol/k_80%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 S_N1 mechanism.

2. m < 1, the reactions go through the mechanism between S_N1 and S_N2.

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 S_N2 reaction character within the mechanism.

reference

^ Eric Anslyn, E.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science Books, 2006, p 456.
^ Fainberg, A.H.; Winstein,S. (1956). "Correlation of Solvolysis Rate III. t-Butyl Chloride In a Wide Range of Solvent Mixtures". J. Am. Chem. Soc. 78 (12): 2770–2777. doi:10.1021/ja01593a033.
^ Grunwald, E.; Winstein,S. (1948). "The Correlation of Solvolysis Rates". J. Am. Chem. Soc. 70 (2): 846–854. doi:10.1021/ja01182a117.
^ Winstein,S.; Grunwald, E.; Jones, H.W. (1951). "The Correlation of Solvolysis Rates and the Classification of Solvolysis Reactions into Mechanistic Catogories". J. Am. Chem. Soc. 73 (6): 2700–2707. doi:10.1021/ja01150a078.

[1] Eric Anslyn, E.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science Books, 2006, p 456.

[Grunwald56-2] Fainberg, A.H.; Winstein,S. (1956). "Correlation of Solvolysis Rate III. t-Butyl Chloride In a Wide Range of Solvent Mixtures". J. Am. Chem. Soc. 78 (12): 2770–2777. doi:10.1021/ja01593a033.

[Grunwald48-3] Grunwald, E.; Winstein,S. (1948). "The Correlation of Solvolysis Rates". J. Am. Chem. Soc. 70 (2): 846–854. doi:10.1021/ja01182a117.

[Grunwald51-4] Winstein,S.; Grunwald, E.; Jones, H.W. (1951). "The Correlation of Solvolysis Rates and the Classification of Solvolysis Reactions into Mechanistic Catogories". J. Am. Chem. Soc. 73 (6): 2700–2707. doi:10.1021/ja01150a078.

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