March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Chapter 8. Acids and Bases

8.C. Measurements of Solvent Acidity¹²⁴

When a solute is added to an acidic solvent it may become protonated by the solvent. This effect can lead to an enhancement of acidity, as in the effect of using formic acid rather than methanol.¹²⁵ An acidity scale has been reported for ionic liquids¹²⁶ (see Sec. 9.D.iii for a discussion of ionic liquids), and the Lewis acidity of ionic liquids has been established using IR.¹²⁷ If the solvent is water and the concentration of solute is not very great, then the pH of the solution is a good measure of the proton-donating ability of the solvent. Unfortunately, this is no longer true in concentrated solutions because activity coefficients are no longer unity. A measurement of solvent acidity is needed that works in concentrated solutions and applies to mixed solvents as well. The Hammett acidity function¹²⁸ is a measurement that is used for acidic solvents of high dielectric constant.¹²⁹ For any solvent, including mixtures of solvents (but the proportions of the mixture must be specified), a value H₀ is defined as

H₀ is measured by using “indicators” that are weak bases (B) and so are partly converted, in these acidic solvents, to the conjugate acids BH⁺. Typical indicators are o-nitroanilinium ion, with a pK in water of −0.29, and 2,4-dinitroanilinium ion, with a pK in water of −4.53. For a given solvent, [BH⁺][B] is measured for one indicator, usually by spectrophotometric means and with the known pK in water () for that indicator, H₀ can be calculated for that solvent system. In practice, several indicators are used, so that an average H₀ is taken. Once H₀ is known for a given solvent system, pK_a values in it can be calculated for any other acid–base pair.

The symbol H₀ is defined as

where is the activity of the proton and f_I and are the activity coefficients of the indicator and conjugate acid of the indicator,¹³⁰ respectively. The parameter H₀ is related to H₀ by

so that H₀ is analogous to pH and H₀ to [H⁺], and indeed in dilute aq solution H₀ = pH.

The parameter H₀ reflects the ability of the solvent system to donate protons, but it can be applied only to acidic solutions of high dielectric constant, mostly mixtures of water with acids (nitric, sulfuric, perchloric, etc.). It is apparent that the H₀ treatment is valid only when is independent of the nature of the base (the indicator). Since this is so only when the bases are structurally similar, the treatment is limited. Even when similar bases are compared, many deviations are found.¹³¹ Other acidity scales¹³² have been set up, including a scale for C–H acids,¹³³ among them H₋ for bases with a charge of −1, H_R for aryl carbinols,¹³⁴H_C for bases that protonate on carbon,¹³⁵and H_A for unsubstituted amides.¹³⁶ It is now clear that there is no single acidity scale that can be applied to a series of solvent mixtures, irrespective of the bases employed.¹³⁷

Although most acidity functions have been applied only to acidic solutions, some work has also been done with strongly basic solutions.¹³⁸ The H₋ function, which is used for highly acidic solutions when the base has a charge of −1, can also be used for strongly basic solvents, in which case it measures the ability of these solvents to abstract a proton from a neutral acid (BH).¹³⁹ When a solvent becomes protonated, its conjugate acid is known as a lyonium ion.

Another approach to the acidity function problem was proposed by Bunnett et al.,¹⁴⁰ who derived the equation

where S is a base that is protonated by an acidic solvent. Thus the slope of a plot of log ([SH⁺]/[S]) + H₀ against H₀ + log [H⁺] is the parameter ϕ, while the intercept is the pK_a of the lyonium ion (SH⁺, referred to infinite dilution in water). The value of ϕ expresses the response of the equilibrium

to changing acid concentration. A negative ϕ indicates that the log of the ionization ratio [SH⁺]/[S] increases, as the acid concentration increases, more rapidly than −H₀. A positive ϕ value indicates the reverse. The Bunnett–Olsen equation given above is a linear free–energy relationship (see Sec. 9.C) that pertains to acid–base equilibria. A corresponding equation that applies to kinetic data is

where k_ψ is the pseudo-first-order rate constant for a reaction of a weakly basic substrate taking place in an acidic solution and is the second-order rate constant at infinite dilution in water. In this case, ϕ characterizes the response of the reaction rate to changing acid concentration of the solvent. The Bunnett–Olsen treatment has also been applied to basic media, where, in a group of nine reactions in concentrated NaOMe solutions, no correlation was found between reaction rates and either H₋ or stoichiometric base concentration, but where the rates were successfully correlated by a linear free energy equation similar to those given above.¹⁴¹

A treatment partially based on the Bunnett–Olsen treatment is that of Bagno et al.,¹⁴² which formulates medium effects (changes in acidity of solvent) on acid–base equilibria. An appropriate equilibrium is chosen as reference, and the acidity dependence of other reactions compared with it, by use of the linear free energy equation

where the K values are the equilibrium constants for the following: K for the reaction under study in any particular medium; K′ for the reference reaction in the same medium; K₀ for the reaction under study in a reference solvent; for the reference reaction in the same reference solvent; and m^∗ is the slope of the relationship [corresponding to (1 − ϕ) of the Bunnett–Olsen treatment]. This equation has been shown to apply to many acid–base reactions.

Another type of classification system was devised by Bunnett¹⁴³ for reactions occurring in moderately concentrated acid solutions. Log k_ψ + H₀ is plotted against log , where K_ψ is the pseudo-first-order rate constant for the protonated species and is the activity of water. Most such plots are linear or nearly so. According to Bunnett, the slope of this plot w tells something about the mechanism. Where w is between −2.5 and 0, water is not involved in the rate-determining step; where w is between 1.2 and 3.3, water is a nucleophile in the rate-determining step; where w is between 3.3 and 7, water is a proton-transfer agent. These rules hold for acids in which the proton is attached to oxygen or nitrogen.

A new acidity scale has been developed based on calorimetric measurement of N-methylimidazole and N-methylpyrrole in bulk solvents.¹⁴⁴ A revised version of this method was shown to give better results in some cases.¹⁴⁵Another scale of solvent acidities was developed based on the hydrogen-bond donor acidities in aq DMSO.¹⁴⁶ Note that bond energies, acidities, and electron affinities are related in a thermodynamic cycle, and Fattahi and Kass¹⁴⁷show that by measuring two of these quantities the third can be found.