Grunwald-Winstein equation
Encyclopedia
In physical organic chemistry
, the Grunwald–Winstein equation 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)
Where the and 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.
(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 to define a set of substituent parameters σX, and then generate the ρ values, which represent ionizing abilities of different substrate, through Hammett Plot.
(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 the Grunwald-Winstein Equation. 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 Equation.
of tert-Butyl chloride
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, hence t-BuCl was chosen.
(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.
1. m ≥ 1, the reactions go through SN1 mechanism.
2. m < 1, the reactions go through the mechanism between SN1 and SN2.
Physical organic chemistry
Physical organic chemistry is the study of the interrelationships between structure and reactivity in organic molecules. It can be seen as the study of organic chemistry using tools of physical chemistry such as chemical equilibrium, chemical kinetics, thermochemistry, and quantum chemistry...
, the Grunwald–Winstein equation is a linear free energy relationship between relative rate constants and the ionizing power of various solvent
Solvent
A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...
systems, describing the effect of solvent as nucleophile
Nucleophile
A nucleophile is a species that donates an electron-pair to an electrophile to form a chemical bond in a reaction. All molecules or ions with a free pair of electrons can act as nucleophiles. Because nucleophiles donate electrons, they are by definition Lewis bases.Nucleophilic describes the...
on different substrates. The equation, which was developed by Ernest Grunwald and Saul Winstein
Saul Winstein
Saul Winstein was the Canadian chemist who discovered the Winstein reaction, in which he argued a non-classical cation was needed to explain the stability of the norbornyl cation. This fueled a debate with Herbert C. Brown over the existence of delocalized cations such as this. Richard F...
in 1948, could be written as equation 1.
(1)Where the and are the solvolysis rate constants for a certain compound in different solvent systems and in the reference solvent, 80% aqueous ethanol
Ethanol
Ethanol, also called ethyl alcohol, pure alcohol, grain alcohol, or drinking alcohol, is a volatile, flammable, colorless liquid. It is a psychoactive drug and one of the oldest recreational drugs. Best known as the type of alcohol found in alcoholic beverages, it is also used in thermometers, as a...
, respectively. The m is a parameter of the compound measuring sensitivity of solvolysis rate to Y, the measure of ionizing power of the solvent.
Background
Hammett equationHammett equation
The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with just two parameters: a substituent constant and a...
(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
Benzoic acid
Benzoic acid , C7H6O2 , is a colorless crystalline solid and the simplest aromatic carboxylic acid. The name derived from gum benzoin, which was for a long time the only source for benzoic acid. Its salts are used as a food preservative and benzoic acid is an important precursor for the synthesis...
as the standard reaction to define a set of substituent parameters σX, and then generate the ρ values, which represent ionizing abilities of different substrate, through Hammett Plot.
(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 the Grunwald-Winstein Equation. 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 Equation.
Reference compound
The Substitution reactionSubstitution reaction
In a substitution reaction, a functional group in a particular chemical compound is replaced by another group. In organic chemistry, the electrophilic and nucleophilic substitution reactions are of prime importance...
of tert-Butyl chloride
Tert-Butyl chloride
tert-Butyl chloride is a colorless, liquid organic compound at room temperature. It is sparingly soluble in water, with a tendency to undergo spontaneous solvolysis when dissolved into it...
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
SN1 reaction
The SN1 reaction is a substitution reaction in organic chemistry. "SN" stands for nucleophilic substitution and the "1" represents the fact that the rate-determining step is unimolecular...
is performed through a stable carbocation
Carbocation
A carbocation is an ion with a positively-charged carbon atom. The charged carbon atom in a carbocation is a "sextet", i.e. it has only six electrons in its outer valence shell instead of the eight valence electrons that ensures maximum stability . Therefore carbocations are often reactive,...
intermediate, the more nucleophilic solvent can stabilize the carbocation
Carbocation
A carbocation is an ion with a positively-charged carbon atom. The charged carbon atom in a carbocation is a "sextet", i.e. it has only six electrons in its outer valence shell instead of the eight valence electrons that ensures maximum stability . Therefore carbocations are often reactive,...
better, thus the rate constant of the reaction could be larger. Since there’s no sharp line between SN1 and SN2 reaction
SN2 reaction
The SN2 reaction is a type of nucleophilic substitution, where a lone pair from a nucleophile attacks an electron deficient electrophilic center and bonds to it, expelling another group called a leaving group. Thus the incoming group replaces the leaving group in one step...
, a reaction goes through SN1 mechanism more is preferred to achieve a better linear relationship, hence t-BuCl was chosen.
Y values
(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
Acetic acid
Acetic acid is an organic compound with the chemical formula CH3CO2H . It is a colourless liquid that when undiluted is also called glacial acetic acid. Acetic acid is the main component of vinegar , and has a distinctive sour taste and pungent smell...
-formic acid
Formic acid
Formic acid is the simplest carboxylic acid. Its chemical formula is HCOOH or HCO2H. It is an important intermediate in chemical synthesis and occurs naturally, most notably in the venom of bee and ant stings. In fact, its name comes from the Latin word for ant, formica, referring to its early...
. 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(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
- 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.
- Relationships between many reactions and nucleophilic solvent systems are not linear. This derives from the growing SN2 reaction character within the mechanism.