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| In [[physical organic chemistry]], the '''Grunwald–Winstein equation''' is a [[linear free energy relationship]] between relative [[rate constant]]s 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<ref>Eric Anslyn, E.; Dougherty, D. A. ''Modern Physical Organic Chemistry''; University Science Books, 2006, p 456.</ref><ref>{{cite journal | doi = 10.1021/jo990588w | title = Correlation of Solvolysis Rates 50 Years Later | year = 1999 | last1 = Catalán | first1 = Javier | last2 = Díaz | first2 = Cristina | last3 = García-Blanco | first3 = Francisco | journal = The Journal of Organic Chemistry | volume = 64 | issue = 17 | pages = 6512–6514}}</ref>
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| :<math>\log \frac{k_{x,sol}}{k_{x,80% EtOH}} = mY </math>
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| where the {{math|<VAR>k<sub>x, sol</sub></VAR>}} and {{math|<VAR>k<sub>x, 80% EtOH</sub></VAR>}} 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.<ref name=Grunwald56>{{cite journal| title = Correlation of Solvolysis Rate III. ''t''-Butyl Chloride In a Wide Range of Solvent Mixtures | journal= [[J. Am. Chem. Soc.]]|year = 1956 | volume = 78 | pages = 2770 | author1 = Fainberg, A.H. | author2 = Winstein,S.| doi = 10.1021/ja01593a033| issue = 12}}</ref>
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| ==Background==
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| [[Image:Benzoicacid.png|thumbnail|right|350px |Dissociation of substituted benzoic acids.]]
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| [[Hammett equation]] (Equation '''1''') provides 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 σ<sub>X</sub>, and then generate the ρ values, which represent ionizing abilities of different substrate, through Hammett Plot.
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| :<math>\log \frac{k_X}{k_H} = \sigma_X\rho </math> ('''1''')
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| 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.
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| ==Definition==
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| ===Reference compound===
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| [[Image:TBuCl.jpg|thumbnail|right|350px |S<sub>N</sub>1 mechanism of substitution reaction]]
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| The [[Substitution reaction]] 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.<ref name=Grunwald48>{{cite journal| title = The Correlation of Solvolysis Rates | journal= [[J. Am. Chem. Soc.]]|year = 1948 | volume = 70 | pages = 846 | author1 = Grunwald, E. | author2 = Winstein, S. | doi = 10.1021/ja01182a117| issue = 2}}</ref><ref name=Grunwald51>{{cite journal| title = The Correlation of Solvolysis Rates and the Classification of Solvolysis Reactions into Mechanistic Categories | journal= [[J. Am. Chem. Soc.]]|year = 1951 | volume = 73 | pages = 2700 | author1 = Winstein, S. | author2 = Grunwald, E. | doi = 10.1021/ja01150a078 | author3 = Jones, H.W.| issue = 6}}</ref>
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| The [[SN1 reaction|S<sub>N</sub>1 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<sub>N</sub>1 and [[SN2 reaction|S<sub>N</sub>2 reaction]], a reaction goes through S<sub>N</sub>1 mechanism more is preferred to achieve a better linear relationship, hence ''t''-BuCl was chosen.
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| ===Y values===
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| :<math>\log \frac{k_{t-BuCl, sol}}{k_{t-BuCl, 80% EtOH}} = Y </math> ('''2''') | |
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| In equation '''2''', k<sub>t-BuCl, 80% EtOH</sub> stands for the rate constant of ''t''-BuCl reaction in 80% aqueous Ethanol, it is a constant. k<sub>t-BuCl, sol</sub>. 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.
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| {| class = "wikitable" style="text-align:center"
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| |-
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| ! solvent, %by vol.
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| ! Y
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| ! solvent, %by vol.
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| ! Y
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| ! solvent, %by vol.
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| ! Y
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| |-
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| | EtOH-H<sub>2</sub>O
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| | 25
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| | 2.908
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| | 30
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| | 2.753
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| |-
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| | 100
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| | -2.033
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| | 20
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| | 3.051
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| | 20
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| | 3.025
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| |-
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| | 98
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| | -1.681
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| | 15
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| | 3.189
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| | 10
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| | 3.279
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| |-
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| | 95
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| | -1.287
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| | 10
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| | 3.312
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| | AcOH-HCOOH
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| |-
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| | 90
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| | -0.747
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| | 5
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| | 3.397
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| | 100
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| | -1.639
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| |-
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| | 80
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| | 0
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| | H<sub>2</sub>O
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| | 3.493
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| | 90
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| | -0.929
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| |-
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| | 70
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| | 0.595
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| | MeOH-H<sub>2</sub>O
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| | 75
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| | -0.175
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| |-
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| | 60
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| | 1.124
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| | 100
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| | -1.09
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| | 50
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| | 0.757
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| |-
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| | 50
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| | 1.655
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| | 90
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| | -0.301
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| | 25
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| | 1.466
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| |-
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| | 45
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| | 1.924
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| | 80
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| | 0.381
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| | 10
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| | 1.862
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| |-
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| | 40
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| | 2.196
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| | 70
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| | 0.961
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| |-
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| | 37.5
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| | 2.338
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| | 60
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| | 1.492
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| |-
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| | 35
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| | 2.473
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| | 50
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| | 1.972
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| |-
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| | 30
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| | 2.721
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| | 40
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| | 2.391
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| |}
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| ===m values===
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| 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 slope of the plot of log(k<sub>sol</sub>/k<sub>80%EtOH</sub>) 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:
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| 1. m ≥ 1, the reactions go through S<sub>N</sub>1 mechanism.
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| 2. m < 1, the reactions go through the mechanism between S<sub>N</sub>1 and S<sub>N</sub>2.
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| ==Disadvantage==
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| # 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.
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| # Relationships between many reactions and nucleophilic solvent systems are not linear. This derives from the growing S<sub>N</sub>2 reaction character within the mechanism.
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Grunwald-Winstein equation}}
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| [[Category:Physical organic chemistry]]
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| [[Category:Equations]]
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I am Yukiko from Horsforth. I love to play Harp. Other hobbies are Inline Skating.
Take a look at my homepage: Diễn Đàn Sinh Viên Hutech