# Classification of Solvents

Solvents are integral part of chemical reactions and it is difficult to imagine reactions without solvents. Although advancement of chemistry has led to the development of many solvent-free reactions, most of the common reactions practised in laboratory invariably involve the use of solvents. In many cases, reactions are solvent-selective, i.e., certain reactions occur in certain solvents only. Further, physical properties of many compounds are studied in solvents. Thus, it is essential to develop a feeling for the properties of solvents and how these properties manifest in the outcome of certain reactions or physical properties of a compound. Given that molecules can be either inorganic or organic in nature and that they vary widely both in physical and chemical properties, it is not an easy task to categorize different solvents. Attempts have been made to classify solvents based on their

1. chemical constitution
2. physical constants (physical properties)
3. chemical properties
4. polarities and so on

The solvents are also classified based on their chemical constitutions. Thus, depending on the characteristic bonds that are present in the solvents, they can be of three types:

a. molecular liquids
b. ionic liquids
c. atomic liquids

All common organic solvents, i.e., aliphatic and aromatic hydrocarbons and their halo and nitro derivatives, alcohols, carboxylic acids, carboxylic esters, ethers, ketones, aldehydes, nitriles, amines, solphoxides, sulphones, etc. belong to this category. The study of their properties reveals that they always prefer to solvate molecules of related functional groups and similar physical properties; this is often stated as: like dissolves like. Further, proper knowledge of their properties derived from functional groups present in them helps in choosing a proper solvent for a particular reaction. For example, if we carry out a condensation reaction, we will never choose a solvent like acetone, which itself has the potential to participate in such a reaction.

Water is the universal solvent, and of course, belongs to this category. Use of water as a molecular liquid in contemporary chemistry has found renewed interest due largely to its environmentally benign attributes and capability to solvate apolar solutes to some degree through hydrophobic hydration; the latter originates from extensive van der Waals interactions at the expense of partially broken H-bonded networks present in the solvent, that is, water. Perfluorohydrocarbons that are non-polar, hydrophobic, chemically inert and non-toxic in nature are mostly used for spectroscopic measurements and various kinds of organic reactions. They are known to form biphasic systems in the presence of other common organic solvents. The differential solubilities of the starting materials and products in the biphasic solvent systems with “fluorous phase” facilitate isolation of the products from a complex reaction mixture.

Liquid crystals that are long, rigid and flat in general have the following structure:

The degree of ordering present in a liquid crystal is in general in between that present in isotropic liquids and crystals and is strongly dependent on the nature of bridges and terminal substituents. Liquid crystals are further classified into lyotropic and thermotropic crystals depending on their nature of origin. In a polar solvent, if the liquid crystal is generated upon controlling the concentration of the amphiphilic solute, then it is called lyotropic liquid crystal. On the other hand, if the variation of temperature generates the liquid crystal it is called thermotropic liquid crystal. Thermotropic liquid crystals are further sub-categorized as nematic, smectic, and cholesteric liquid crystals based on their molecular arrangements.

There is a surge of interest in the applications these solvents as applied to organic and inorganic reactions in the last few decades. High thermal stability, excellent electrical conductivity, large liquid range thus providing a possibility for use at high reaction temperatures, low vapor pressure along with their excellent capability to dissolve a wide range of metals and salts make them extremely useful reaction media. The low vapor pressures of these solvents are enormously advantageous from the point of view of environmentally benign nature. In addition, they can be easily recycled. Since they are viscous, they have excellent ability to stabilize transition states in which reactant molecules come closer together. Examples of ionic liquids are:

Liquid atoms with potential of being used as solvents have been categorized under this class. Liquid mercury and sodium were used as atomic solvents in primitive days of chemistry. Given that sodium is highly reactive and mecury is highly poisonous, it is not difficult to predict that these solvents were used with intent to study something very specific which is otherwise not accessed from the use of other solvents. Unless inevitable, i.e., if and only if and when no other alternatives are available, they are not employed as solvents simply because they are not good choices. That is precisely why they have never been paid much attention to by the chemists.

As mentioned at the outset, solvents play an important role in organic and inorganic reactions and in physical studies. The role of solvent is so critical that certain reactions proceed only in specific solvents. Further, certain physical properties exist only in certain solvents. In the following, we shall focus on how solvents play pivotal role in different chemical and physical processes.

Solvents play an important role in determining the acid-base equilibria. This is true not only when they themselves are acidic or basic, but also when they are neutral in nature; the observed effects are guided by solvation effects. It is said that benzoic acid is a stronger acid than acetic acid. However, there is an element of incompleteness in the statement unless we specify the solvent. The true statement indeed should be “benzoic acid is stronger acid than acetic acid in water”. This is because they ionize to different extents to give different amounts of the active acid species, that is, hydronium ions. This ionization, however, becomes equal when the solvent is changed from water to say, ammonia. Ammonia is sufficiently basic in nature such that both the acids are completely ionized and they appear equally strong acids in ammonia. This simple illustration points to the very fact that solvents play crucial role in controlling the position of acid-base equilibria.

Gas-phase acidities and basicities of organic compounds are different from those in their solution phases. This is because the gas-phase acidity or basicity reflects the intrinsic property of the molecule, whereas the solution phase acidity or basicity reflects the combined effect of molecule itself and the solvent, their nature of interaction and influence of solvent on the molecule. For example, the basicities of substituted amines in gas phase run as: R3N > R2NH > RNH2 > NH3. This is expected considering the inductive effect (+I) of the alkyl (R) group(s). However, the effect of solvent becomes vivid when we consider the basicity order of the same species in aqueous medium, which runs as: NH3 < RNH2 < R2NH > R3N. If the inductive effect were the only factor operative in controlling their basicities, the order should have been exactly the same as that in the gas phase. However, higher basicity of R2NH over R3N emphasizes that solvent molecule, i.e. water has a crucial role in determining the basicities. In reality, it is understood in terms of a competition between inductive effect and solvation. When an alkyl group is introduced, the inductive effect is, of course, increased, but at the expense of energy loss in the form of one hydrogen bonding, as one hydrogen atom is replaced by an alkyl group. This trade-off between the inductive effect and hydrogen bonding determines the aqueous-phase basicity trend of the differently substituted amines.

As can be seen in the above scheme, when lesser number of alkyl groups are present, more the stabilization of the reactive acid, that is, ammonium ion, occurs due to greater solvation by hydrogen bonding with solvent (water) molecules.

Similar example is the following:

In gas phase:

In solution phase:

Similar explanation as above is applicable to this example too. The gas phase basicity, however, needs little attention. The incipient ammonium ion would be more stable, if alkyl groups shield the nitrogen center and provide electron density by +I effects.

The solution and gas-phase acidities of C-H bonds are interesting. In gas phase the C-H acidities have the following order:

CH4 < H2O < CH3OH < C6H5CH3 < HCCH < CH3SOCH3 < CH3CN < CH3COCH3 < CH3CHO < C6H5COCH3 < CH3NO2 < Cyclopentadiene < CH3COOH.

It is compelling to note that toluene is more acidic than water in gas phase. Thus if we add OH- to toluene we expect acid base reaction to get water and C6H5CH2-. This is rather surprising at a first glance.

The gas phase acidity order of the haloacetic acid X-CH2COOH is H < F < Cl < Br < I, i.e. the order is reversed in comparison to that in aqueous solution. This immediately puts a lot of emphasis on the solvent effects and in fact solvation plays more important role than the inductive effects. If the inductive effect was the sole reason for the acidities in the aqueous phase, then the same trend would be retained in the gas phase. This points to the fact that the solvation effect in fact dominates over the inductive effect in the aqueous phase to determine the acidity orders of the halo-acids.

α-Amino acids are known to be present in zwitterionic form. Actually, there exists an equilibrium between neutral and zwitterionic form in them. However, the gas-phase acidity measurement data show that these species exist in neutral form. This means that it is not the intramolecular acid-base reaction between amine and carboxylic acid groups; rather it is the solvation that causes amino acids to exist in zwitterionic forms. Moreover, It has been found that, the amount of zwitterions present in DMSO is significantly lower than that present in aqueous solution which can be explained only if we invoke the concept of better solvation and hence stabilization carboxylate group in aqueous medium.

Tautomers are isomers of a compound and are interconvertible into each other by simple chemical manipulations. The tautomers are often found to exist in equilibrium. This kind of isomerism is known as taumerism. Solvents influence tautomeric equilibrium too. Presumably, this has to do with the extent to which the tautomers are solvated in the solvent under consideration. This is not thus surprising that the shift in the tautomeric equilibrium occurs to different extents in different solvents.

The following data are available for the above equilibria:

For both molecules, the keto form is more polar than the enol form. Thus, on going from gas phase (where auto-solvation is possible) to cyclohexane, the molecules are separated from each other by the non-polar cyclohexane molecules and hence auto-solvation is not possible. Thus the amount of more polar keto form is decreased in a non-polar environment. Thus amount of enol content is greater in cyclohexane than in gas-phase. Also, it is noteworthy that the amount of enol form for B in all medium is greater than that of A; this is primarily because of greater acidity of enolic proton of B when compared to that of A. The higher acidity of B is attributed to the presence of two keto groups in the molecule in comparison to one ester and one keto group as in A; of course, carbonyl functionality has greater electronic withdrawing effect than alkoxycarbonyl functionality. Further, it should be noted that the amount of enol form decreases in a polar protic media as in EtOH or H2O. Now the question arises what does this trend point to? If carefully looked at, it is seen that there exists intramolecular hydrogen bonding in the enol forms that presumably stabilizes these non-polar entities in nonpolar solvents. Now, if nonpolar solvents are replaced with polar protic solvents such that the enol forms can establish intermolecular hydrogen bonding with the solvents, then there is no reason as to why the enol form should be predominant. This is exactly what happens and this explanation nicely correlates to the data presented above. Thus, with the increase in polarity and hydrogen bonding ability of the solvents the amount of enol form decreases for both the compounds.

Let us exemplify the effect of solvents on tautomerism with another example:

The above chart gives the ratio of enol and keto form of the compound in three different solvents. As can be perused from the above chart, increase in polarity and hydrogen bonding capability of the solvent brings down the amount of enol form.

Hydrogen bonding is crucial in some cases to determine the relative amounts of the tautomers. Let us consider the following two examples:

Example 1:

In chloroform and water, no enol form is detectable, but in solvents such as DMSO and acetonitrile the enol form has been found to be exclusive. This observation immediately draws attention to the hydrogen bonding capabilities of the solvents that presumably control the relative amounts. The enol form is hydrogen donor and thus solvents that are hydrogen acceptors would stabilize the former maximum; thus, the enol form is exclusive in solvents such as acetonitrile and DMSO. On the other hand, solvents such as water, chloroform, dichloromethane, etc., which are hydrogen bond donors, would preferentially stabilize the keto form which is a hydrogen bond acceptor.

Example 2:

The argument–the H-bonding capabilities of solvents control the relative amounts of keto and enol form–as advanced in the last example holds true in this example also. The keto form which is polar as well as hydrogen bond acceptor will be predominant in nonpolar and in hydrogen donor solvents. Conversely, the enol form will be favored if the solvent is hydrogen acceptor. Thus, in hydrogen acceptor solvents such as DMF, pyridine, DMSO, etc., the enol form is exclusive. Thus, it has been noticed that the addition of triethylamine to a benzene solution of 9-anthrone leads to a gradual shift of equilibrium towards the enol form.

There are countless examples of above kinds wherein the H-bonding capabilities and/or polarity have been tweaked to control the equilibrium in keto-enol tautomerism. The role of solvents, however, is not limited to keto-enol tautomerism described above, but extends to several other systems. Let us take some examples:

i)

It has been found that increase in solvent polarity shifts the equilibrium towards right, i.e., more towards the keto form. This is because this form is dipolar in nature and is more dipolar than the hydroxyl-form; this is due to the presence of a charge separated mesomeric form that makes the keto form dipolar in nature. It is needless to mention that H-bonding plays important role in this case also (please refer to the explanations described earlier).

ii)

The structure at the left hand side is colorless form and the one at the right is colored. In presence of hydrogen bond acceptor solvents, the color intensity increases. This suggests that the equilibrium shifts towards right. Conversely, in hydrogen bond donor solvents the solution becomes colorless; the equilibrium stays in favor of the species in the left. The reason is obvious and is traceable to the H-bonding capabilities of the solvents under consideration.

Solvents can also influence the conformational existence of a molecule. It is known that a molecule can exist in several conformations that lie on plateaus of an energy profile diagram. The equilibrium is established between different conformations of a molecule in a solvent if the solvation energies are such that they can promote interconversion between different conformations. If the solvation energies with different conformations are vastly different and are of the order of the energy barrier of different conformations, then solvents show huge impact on the relative amounts of the different conformations. This is why it has been often observed different conformations exist in different solvents. Let us illustrate with couple of examples.

Example 1:

The conformation at the left has a net zero dipole moment and the one at the right has a net positive dipole moment. Thus, it is expected that in a more polar solvent the conformer with higher dipole moment will be more stable. The data in following table support the premise.

Example 2:

For the conformational equilibrium in the phencyclidine system, as shown above, the following information is available:

Intuitively, steric and electronic factors can be put forward to explain the above observation. From the steric point of view, both A and B are of similar energy. On the other hand, a simple qualitative treatment based on stereoelectronic considerations (the C-H bond being antiperiplanar to the polar C-N bond) imply that (A) is more stable than (B). Thus, in solvents such as dichloromethane and other non-polar solvents, which do not have much solvation effects, (A) is the major conformer. However, if there is possibility of hydrogen bonding, the scenario can change a lot. When the equilibrium is studied in a hydrogen bond donor solvent the equilibrium lies far toward (B). This is because hydrogen bonding increases the crowding around N center. Thus the conformer with axial piperidine ring will become more destabilized when compared to the case where the piperidine ring is situated equatorially as in (B). Consequently, (B) is almost exclusive in CD2Cl2/CD3OD (1:2), wherein CD3OD functions as hydrogen bond donor solvent. Further, in CD3COCD3 and CD3CN, which are polar but not hydrogen bond donor solvents, almost equal population of two conformations is observed.

Solvent effects on electron-transfer equilibria: Solevnt has been found to play important role electron-transfer equilibrium too. Let us take the following example:

Following information are available for the above equilibrium:

As expected, the equilibrium shifts towards right with the increase in solvent polarity. More polar solvents result in better solvation of the ion pair when compared to the neutral radical species.

Solvent has impact on the isomerization equilibrium also. Valence isomers are isomers that are related by simple reorganization of bonding electrons without migration of any atoms. They have different properties since they have different structures and thus we can expect that solvents will have an impact in their equilibrium too. Let us consider the following example:

The isomer in the left has smaller dipole moment (µ = 5.2 $\times$ 10 − 30 Cm) than the one in the right (µ = 13.7 $\times$ 10 − 30 Cm). In gas phase and in other non-polar solvents such as carbon tetrachloride and benzene, the left isomer is more stable and is the major isomer. However in polar solvents such as DMSO and HMPA, the bicyclic valence isomer is the predominant species.

Qualitative Classification of Reaction Types and Solvent Effects on them

Organic Chemistry deals with organic reactions that can be qualitatively categorized into three groups based on the nature of the activated complex, i.e., transition state through which reactions proceed.

1. dipolar reactions
2. isopolar reactions

Dipolar reactions: Almost all ionization, displacement, fragmentation, elimination reactions come under this category and are usually associated with large difference in polarities between the activated complex and the reactants. Thus they show pronounced solvent effects. This is due differential stabilization of the transition states and starting materials in different solvents. The nature of the starting materials and transition states determine whether a certain solvent would facilitate/hinder the reaction.

Ionization reactions:

In ionization reactions, starting materials are usually neutral and the products are ionic in nature; consequently, the transition state has some product-like character and is thus charge separated. As shown in the above scheme, the ionization reactions display maximum solvent effects since maximum charge separation takes place on going from reactants to the activated complex.

Displacement reactions:

In displacement reactions, partial charge separation takes place and thus solvent effect is expected, but to a lesser extent when compared to the ionization reactions; this is due largely to the fact that the developed charged is dispersed over a larger area. In other words, the charge density of the activated complex is much lesser and consequently solvation will not be profound.

Elimination reactions:

In elimination reactions as shown in the scheme, solvent effect is observed. However, here the charges are further dispersed and solvent effect depends on the amount of charge separation in the activated complex.

Isopolar reactions: In this kind of reactions, polarity seldom changes on going from reactants to the TS and hence solvent effect is lesser here. However, in a seemingly isopolar reaction, if the solvent effect becomes prominent then it gives insight as to the mechanism of the reaction. In situation like this, it is better to think of an alternative pathway for the reaction whereby charge separation is possible in the TS. The very fact that solvent effect exists in certain isopolar reaction, is an clue of operation of alternative mechanism leading to the product. Thus change of solvent system and study of the rates of the reaction scan sometimes help us to investigate the mechanism in detail. Most of the pericyclic reactions fall under this category. The nature of the TS in electrocyclic, cycloaddition, chelotropic and sigmatropic reactions can be studied by performing the reactions in different solvents.

Radical-like reactions: As the name implies, here the reaction proceeds via radical intermediates. Following Hammond’s postulate, we can infer that the TS will also be radical-like. Since the polarity does not alter dramatically upon forming radicals, solvent effect is not also pronounced here. However, when the radical becomes either heteroatom assisted or conjugated then sometimes effect of solvents turns out to be important.

Solvent Effect Exemplified: Before we look at the examples, let us acquaint ourselves to the so-called Hughes-Ingold rule that governs the solvent effect to predict the reaction rate. It should be emphasized that this rule only deals with the kinetics of the reaction and it does not affect the equilibrium.

Hughes-Ingold rules: The rules have been summarized below:

When TS is more charged than the starting materials, then a more polar solvent will stabilize the TS to a greater extent than starting materials. Thus the net result is lowering of activation energy and a concomitant increase of rate. By the same token, a non-polar solvent will destabilize the TS more than the starting materials. Consequently, a higher activation energy and slow reaction rate will be the outcome. Similarly, the effects of polar and nonpolar solvents are reversed in rule 2, where the TS is a less charged species when compared to the starting materials. Of course, when there are no significant changes in the charge of the TS on going from the starting materials, there will be no alteration in the activation energies and hence no rate change is observed. Having familiarized ourselves with the Hughes-Ingold rules, we are now equipped with knowledge's to explain observation of reaction rates in some examples. Of course, to apply this rule, it is prerequisite that we have sufficient knowledge on solvent polarity.

Example 1:

For this reaction charge separation occurs in the TS and the TS is more charged species than the reactant. Thus following Hughes-Ingold rule, we predict that increase in the reaction rate in a more polar solvent. The following table is in conformity with our prediction:

Example 2:

In the above example, the starting material is ionic and is more stable in the polar medium. It is expected that the starting material is at a lower energy in the energy profile diagram. In a polar solvent, the TS will be less solvated when compared to the reactants due to the dispersion of charge in the TS. The TS, however, will still be of lower energy in the energy profile diagram in a polar solvent in comparison to that in non-polar solvent. This is because of the fact that the charged species is anyway more stable than a neutral molecule in a polar solvent irrespective of the amount of charge. As it turns out, the relative energy difference between the reactant and the TS is lesser in a non-polar solvent leading to lowering of activation energy in a nonpolar medium. Thus, a relatively nonpolar medium will favor this reaction. Chloroform being the least polar amongst the solvents listed in the chart below, the reaction rate is the highest in this medium.

Example 3:

This example is similar to the one described above and the following data are in accordance with the mechanism.

Example 4:

For the ionization reaction as depicted above, charge separation occurs on moving from reactant to TS. Thus a polar solvent will stabilize the TS to a greater extent. Thus the reaction is expected to be more facile in a polar solvent.

Example 5:

In this reaction, the charge density decreases as one moves from the reactant stage to the TS. Thus a more polar solvent will cause reduction in the reaction rate. So, if the water content is increased in a mixture of ethanol and water, then we expect the reaction rate to decrease. The following table supports our premise:

Example 6:

This is a traditional Michael addition reaction. The transition state has developed charge and hence would be better solvated by a polar solvent. Thus a polar solvent would, as expected, expedite the reaction as is evident from the data given in the table below:

Example 7: The study of the effect of solvents in a reaction can often provide insight towards the actual events during the reaction course, the nature of TS, etc. For the reaction outlined below, a simple [2+2] cycloaddition reaction between ketene and vinyl ether is expected. Thus, classical cyclic TS can be delineated:

However, things would have remained unravelled unless people studied the reaction in different solvents. Let us look at what happens to the relative rates for the reaction in different solvents:

The model of simple neutral and cyclic TS is not able to explain the differences in rates in solvents with different polarities. The model of a charge separated TS was thus introduced to explain the reaction. This is quite logical in light of the fact that the electron demands are quite matched as we move the arrows and thus leading to a charge separated TS.

Example 8:

For this cycloaddition reaction, the following data are available:

The data point to the fact that the above cycloaddition reaction has neutral (apolar) and cyclic TS and marginally affected by solvents effect is observed. This is an example of isopolar reaction.

Example 9:

Similarly, for this isopolar Claisen rearrangement reaction also, no solvent effect is expected as the TS is apolar and the following table is at par with our expectation:

Example 10:

For the cleavage of the peroxo compound under thermal condition, two probable transition states are possible. In the transoid TS, the two dipoles are almost anti-parallel to each other and hence the resultant dipole moment of the TS will be very low; a less polar solvent would preferentially lead the reaction through this TS. On the other hand, the cisoid TS will have significant dipole moment as the two dipoles do not cancel each other, rather reinforce. This TS is expected to be achieved if the reaction is carried out in a sufficiently polar solvent. The following sets of data support our premise, we have following observation:

$\left ( \dfrac{k_{water}}{k_{toluene}} \right )_{cisoid}$ = 5 9

$\left ( \dfrac{k_{water}}{k_{toluene}} \right )_{transoid}$ = 7

Conclusion: Solvents play pivotal role in many chemical as well as physical processes. Study of reactions in different solvents helps to develop insights into the mechanism of the reaction. Thus, it is highly sought after and recommended that reactions be investigated in many solvents that are widely different in polarities before coming to any sort of conclusions with regard to the mechanism operative in a reaction.

Solvent Effect Indices: Now that we are convinced that solvent is indeed important in several important equilibria and deciphering reaction mechanisms, it is important to put them in a scale so that we have easy access to the data associated with the solvents. This would allow us to choose solvents judiciously rather than operating in a foolish manner and just trying our lucks. Thus, attempts have been made to categorize solvents in terms of some indices based on their properties. Consequently, to understand those in a qualitative manner a number of physical constants have been assigned. These assignments are based on physical properties, chemical reactions (kinetics), spectroscopic properties, etc.

Dielectric constant (ε): In a qualitative manner, it is the ability of the medium to conduct electricity. Rigorously, the dielectric constant (or static relative permittivity) of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. It is the ratio of the amount of stored electrical energy when a potential is applied, relative to the permittivity of a vacuum.

Organic chemists have tried to correlate dielectric constant of a solvent to its polarity. For example, for a simple alkane, ε ~ 2 and that for water is ~ 80. This result immediately indicates that a solvent with higher polarity should possess higher ε value.

For the following reaction,

the transition state is more polar as compared to both the reactants; so increase in solvent polarity should result in higher rate of the reaction. Thus if we assume ε as measure of polarity, then we expect a linear plot when lnkobs is plotted against ε. However, the observation is not at par with our assumption. The irregularity (the dots that do not lie on the straight line) of actual plot clearly suggests that ε is a very poor measure of polarity.

It was thus surmised that though ε is related to polarity, it’s not a direct measure of polarity. Thus, it was assumed that energy associated with a dipole in a medium is a function of ε. Thus Kirkwood and Onsager gave a relation known as Kirkwood-Onsager Function.

f $({\varepsilon})$ = ⁡ $\dfrac{\varepsilon-1}{2\varepsilon+1}$

A better correlation was observed when lnkobs was plotted against f (ε). Later, it has been found that correlation may become very good in a mixture of solvents instead of a single solvent. The advantage of this nice correlation is that it helps to find out course of reactions (kinetics) or equilibria by extrapolation.

Chemical reaction kinetics (Y): This index was proposed by Winstein and Grunwald in 1951.

The reaction was chosen in such a way there is very little chance of SN2 reaction that might take place with the nucleophilic solvent molecules. Based on the above ionization, the Y parameter is defined as:

Y = log ksolv (t-BuCl) - log k80%EtOH (t-BuCl)

= log $\frac{k_{solv}^{t-BuCl}}{k_{80%EtOH}^{t-BuCl}}$

Y is a measure of how facile the ionization is in a solvent as compared to the standard solvent system comprising of 20% EtOH and 80% water. Thus, it was decided that the solvents that facilitate the ionization of tert-butyl chloride a high value of Y will be assigned for that solvent. The more facile the ionization, the higher is the value of Y for that solvent. Thus, water has the highest value of Y in the list given below. It implies that SN1 reaction of tert-butyl chloride is favored by a factor of 103.49 in comparison to that observed in 80% Ethanol:

The above data give a feeling of polarity with respect to the ionization of tert-butyl chloride in 80% ethanol. However, this method of ionization that follows SN1 pathway is valid only in polar protic solvents. Thus, kinetic measurements based on the ionization of tert-butyl chloride cannot generate solvent effect indices in a wide range of solvent. Thus, a different attempt was made later:

Ionization of X was similarly followed as above and a term (≡ T) was obtained, which is defined as follows:

log⁡ $\frac{k_{solv}^X}{k_{80%EtOH-water}^X}$

If T is plotted against Y, a linear plot is obtained.

This linear correlation is expected since both the reactions are of similar types (ionization). The slope (m) of the plot would reflect how facile the ionization of X in comparison to t-BuCl is in a given solvent. In a similar manner, ionization of other compounds can be followed by similar studies. Thus, a series of compounds were prepared and their ionizations were studied in different solvents. The ‘m’ value gives insight towards the relative rate of ionization of the compounds with respect to that of t-BuCl in a given solvent.

Thus, the compound fluorotriphenylmethane ionizes better than the other compounds listed in the above table.

Z parameter (Kosower, 1958): The following compound, namely, 1-ethyl-4-methoxycarbonyl pyridinium iodide was taken as a reference for the development of this very popular solvent index:

The compound exhibits a charge transfer band. The absorbance of the compound in different solvents was plotted against wavelength to find out the λmax of charge transfer band. The wavelength is finally converted to energy and thus Z scale is created. In short, Z parameter is the excitation energy of the charge transfer band expressed in kcal/mole. The formula used to calculate the Z value is given by the formula:

Z = 2.859 $\times$ 104

where, Z is in kcal/mol and λ is in nm.

λmax has been found to vary in different solvents. This is because of the presence of the following equilibrium:

As can be seen, there occurs an electron transfer from the negative part (iodide) to the positive part (pyridinium ion) resulting in the formation of radicals in the excited state. Clearly, the ground state is more polar than the excited state and thus, the former is more susceptible to change of solvent polarity. A more polar solvent will stabilize the ground state effectively and destabilize the excited state to some extent. Therefore, the band gap of this charge transfer transition varies with solvent polarity. Thus, this variation in λ is converted into Z-scale, which now is a very precise measure of solvent polarity as this method deals with spectroscopic techniques. In addition, for the same reason the method is very rapid and allows for assigning Z value very quickly.

However, this method is fraught by a serious disadvantage. This has to do with the fact that assigning Z value is possible only in solvents of medium polarity and the method fails in highly polar as well as nonpolar solvents. In a highly polar solvent, the species in the left would be so stable that a large hypsochromic shift is expected and the charge transfer band gets buried under the strong ππ* transition. This is why Z parameter cannot be employed in case of a highly polar solvent. On the other hand, the compound, which is ionic in nature, suffers from insolubility in a highly non-polar solvent restricting its application in those kinds of solvents.

Reinchardt-Dimmorth Et Scale:

Reinchardt and Dimmorth developed Et scale based on the same concept that led to the development of Z-scale. A different dye, namely, betaine dye was chosen for the development of this parameter.

In this molecules also, the ground state is highly polar and the excited state has reduced dipole moment. Thus, ground state will be solvated effectively by a more polar solvent whereas excites state is destabilized to some degree. However, it was observed that this compound nicely responded to the solvent variations. The added advantage is the larger separation of charge transfer band from the π - λ* band that allows the compound to be studied for the measurement of solvent index (Et) in highly polar solvents. However, the applicability in highly nonpolar solvent should still be a concern as the compound is ionic in nature. Let us look at some of the data for different solvents:

As can be seen water is the most polar solvent amongst others listed in the above table. However, one has to keep in mind that this method deals with only how solvent influences the charge transfer bands of certain dyes and does not consider any other properties of the solvents that might affect the charge transfer bands.

Taft-Kamlet π* Scale: Taft and co-workers made a general approach for studying the solvatochromic shift of π - π* transition for different dyes in different solvents. The scale is name such a way because it deals with the absorption data that promote the electron in the π*orbital. This method is based on the different polarities of the ground state and the excited state and how they are stabilized in different solvents. However, this calculation excludes the H-bonding interaction ability of the solvents.

Taft α and β Scale: Taft and co-workers later extended their work and introduced α and β scales for the hydrogen bond donating and accepting ability of the solvents, respectively. A high value of α is assigned for solvents with greater H-bond donor capacity and a high value of β implies that the solvent is efficient H-bond acceptor. A value of zero for either α or β implies that the solvent is neither H-bond donor nor an acceptor.

AN and DN Numbers: Gutman developed this scale to measure the ability of the solvents to interact with specific substances. AN numbers refer to the ability of the solvent to accept electrons from electron rich centers and DN Numbers reflect the e-donating capability of solvent to electron deficient centers. AN number is defined as the negative of enthalpy change in the reaction between a solvent with SbCl5 in dilute dichloroethane. On the other hand, DN Number is defined as the relative shift in the 31P NMR of (C2H5)3PO in the solvent under study and in hexane.