Abstract

Collection of interesting and stimulative data led us to construct Hammett plots for different properties like proton affinities, gas phase basicities, solvation free energies of free and protonated benzenes (I), pyridines (II) and phosphorines (III), and for pK_a values of protonated pyridines and phosphorines. Trends in Hammett reaction constants (ρ) for all these processes were discussed.

1. Introduction

Acuity of work in chemical education and chemical research that took a shape from literature reported data on several chemical and physical aspects like phase transition temperatures, dipole moments, surface tensions, attenuation effect, associative and non-associative behavior of liquids, stability and lifetimes of reactive intermediates, LFER, effect of hybridization of carbon on Hammett (ρ) and Taft (ρ*) reaction constants, prediction of pK_a values of unstable arenium ions and benzenes, from our group has been ever increasing in recent times ^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63}. In the present work to go a step ahead we have tried the comparison of substituent effects on pK_a, proton affinities, gas phase basicities, solvation free energies in benzenes (C₅H₆C), pyridines (C₅H₅N) and phosphorines (C₅H₅P) and their protonated species.

2. Methods

All the linear correlations were done using the KaleidaGraph software, Reading, PA, USA. All chemical structures were drawn using chemdraw software. All Hammett σ values are from reference 64.

3. Discussion

Hammett reactions constants (ρ) and pK_a data of arenium, pyridinium and phosphorinium ions are given in Table 1. The corresponding plots are shown in Figure 1, Figure 2 and Figure 3.

Since the Hammett ρ can not be determined for the dissociation equilibriums of arenium ions XC₆H₆⁺ ⇌ XC₆H₅ + H⁺ as they are highly unstable, an alternate and lucid method was adopted by us based on the attenuation effect ²⁶. Figure 1 shows the determination of the Hammett ρ for the dissociation equilibriums of arenium ions XC₆H₆⁺ ⇌ XC₆H₅ + H⁺ from the study of attenuation effect of methylene group (-CH₂-) on the dissociation equilibriums of anilinium ions, benzyl ammonium ions and 2-phenylethyl ammonium ions ²⁶ and using the Andrew Williams’ empirical equation ρ = m1^{(2 – i) 65} where m1 is an arbitrary constant “i” is the number of atoms between ionizable proton and the ring carbon.

Figure 2 shows the determination of the Hammett ρ for the dissociation equilibriums of pyridinium ions XC₅H₅N⁺ ⇌ XC₅H₄N + H⁺ from the plot of pK_a versus Hammett σ.

Figure 3 shows the determination of the Hammett ρ for the dissociation equilibriums of phosphorinium ions XC₅H₅P⁺ ⇌ XC₅H₄P + H⁺ from the plot of pK_a versus Hammett σ. The pK_a values of the equilibriums XC₅H₅N⁺ ⇌ XC₅H₄N + H⁺ and XC₅H₅P⁺ ⇌ XC₅H₄P + H⁺ are from reference 66.

The negative Hammett ρ values for the equilibriums XC₅H₅N⁺ ⇌ XC₅H₄N + H⁺ and XC₅H₅P⁺ ⇌ XC₅H₄P + H⁺ are from the plots of pK_a versus Hammett σ to be taken as positive for the plots of log K_a (since -log K_a = pK_a) versus Hammett σ. Therefore the three Hammett ρ values of the three equilibrium reactions are 14.3, 6.48 and 7.73 respectively. It is to be noted that there is a large difference of nearly 7.8 and 6.6 units between Hammett ρ of the equilibrium XC₆H₆⁺ ⇌ XC₆H₅ + H⁺ and of the equilibriums of XC₅H₅N⁺ ⇌ XC₅H₄N + H⁺ and XC₅H₅P⁺ ⇌ XC₅H₄P + H⁺. This is mainly due to the loss of energy of the highly unstable and energetic intermediate arenium ions to drive back to the highly stable and less energetic benzene molecule. And this involves the restoration of the aromaticity due to the relief of unit positive charge on the arenium ions. And the small difference of 1.25 units of Hammett ρ between the equilibriums of XC₅H₅N⁺ ⇌ XC₅H₄N + H⁺ and XC₅H₅P⁺ ⇌ XC₅H₄P + H⁺ is due to only the difference of the occupancy of the lone pairs of electrons of N and P. The lone pair of electrons of N is in the p orbital and that of P is in the d orbital. In spite of the fact that the p orbital is more electronegative than d orbital the tendency towards retention of aromaticity of both the molecules even on protonation is a prime reason. There are several arguments about the aromaticity of phosphorine based on many theoretical calculations. And it is believed to have the 88-96% of aromaticity of that of benzene ⁶⁷. Such a high aromaticity of phosphorine is reflected from the well matched electronegativities of phosphorous (2.1) and carbon (2.5) ⁶⁷.

Hammett reactions constants (ρ) and proton affinity data of benzenes, pyridines and phosphorines are given in Table 2. The corresponding Hammett plots are shown in Figure 4, Figure 5 and Figure 6.

Figure 4 shows the determination of the Hammett ρ for the proton affinities (PA) of benzenes from the plot of PAs versus Hammett σ.

Figure 5 shows the determination of the Hammett ρ for the proton affinities (PA) of pyridines from the plot of PAs versus Hammett σ.

Figure 6 shows the determination of the Hammett ρ for the proton affinities (PA) of phosphorines from the plot of PAs versus Hammett σ.

Figure 7 gives the Hammett ρ for the proton transfer reaction of protonated benzene to substituted benzenes.

Figure 8 gives the Hammett ρ for the gas phase basicities of pyridines.

Figure 9 gives the Hammett ρ for the gas phase basicities of phosphorines.

Figure 10 gives the Hammett ρ for the ΔG_solv versus Hammett σ of free benzenes.

Figure 11 gives the Hammett ρ for the ΔG_solv versus Hammett σ of protonated benzenes.

Figure 12 gives the Hammett ρ for the ΔG_solv versus Hammett σ of free pyridines.

Figure 13 gives the Hammett ρ for the ΔG_solv versus Hammett σ of protonated pyridines.

Figure 14 gives the Hammett ρ for the ΔG_solv versus Hammett σ of free phosphorines.

Figure 15 gives the Hammett ρ for the ΔG_solv versus Hammett σ of protonated phosphorines.

The trends in the Hammett ρ values of the proton affinities (PA) and gas phase basicities (GB) of benzenes, pyridines and phosphorines are again in the same order of that observed for pK_as (Table 5). At this point it is worth to discuss little about the proton affinities and gas phase basicities. Though they look same in brief but they differ thermodynamically. Proton affinity of a species A^- is defined as the negative value of the enthalpy change (ΔH) of the process shown in the following reaction.

(1)

And gas phase basicity is defined as the negative value of the corresponding Gibbs free energy change (ΔG) of the same reaction ^{68, 69}. It is known that ΔG = ΔH - TΔS. Therefore it is clear that both ΔG and ΔH differ by an amount of TΔS. And ΔH values are always higher by an amount of TΔS than the values of ΔG (Table 2 and Table 3). From the trends of Hammett ρ for PAs and GBs the same explanations offered hold good on Hammett ρ for pK_as given on page 5.

Effect of substituents on the trends in the Hammett ρ values of ΔG_solv of the free and protonated benzenes, pyridines and phosphorines are rather complex. It is reported that there were two ways of approach of the addendum solvent molecule on to the benzene as shown below in A and B ⁷⁰.

The solvation process is a result of a competition between π-electron interaction as shown in A and H-interaction of X-H bond (X = C or N or P) as shown in B with the approaching solvent molecule. From the negative Hammett ρ value of -3.75 (Table 5, Figure 10) of the correlation of ΔG_solv values with Hammett σ values in the present work for benzene clearly indicates that the interaction shown in A of scheme 1 may be predominant over the interaction shown in B. This is because the electron donating substituents are o,p-directing and they make the benzene molecule more electron rich at two ortho and at one para positions thus making the π-electron system of benzene more nucleophilic ⁷¹. This makes easy for the positive part of addendum molecule to be attracted more by the benzene molecule. In the case of protonated benzenes high negative value of Hammett ρ of -289 (Figure 11) is at present unexplainable. Probably one needs some more data of ΔG_solv for other substituents.

In the case of pyridines the Hammett ρ value is positive and it is 3.23 (Table 5, Figure 12). Here the solvation process is a result of a competition between H-interaction of N-H bond and π-electron interaction with the approaching solvent molecule. In this process from the positive Hammett ρ value of 3.23 suggests that the interaction of the type shown in B of scheme 1 is more favorable. This is because the electron withdrawing substituents at para position in pyridine moiety makes H of N-H bond more electrophilic hence the negative part of addendum molecule to be attracted more by the pyridine molecule.

In the case of protonated pyridines the whole process is just reversed as it can be seen from the negative Hammett ρ value of -10.3 (Table 5, Figure 13).

And the same observations hold well for free and protonated phosphorines (Table 5, Figure 14 and Figure 15).

4. Conclusions

Trends in Hammett reaction constants (ρ) on pK_as, proton affinities (PA), gas phase basicities (GB) and free energy of solvation (ΔG_solv) of benzenes (XC₅H₅C), pyridines (XC₅H₄N) and phosphorines (XC₅H₄P) and their protonated species were discussed.

References