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ATTENUATION EFFECT IN ALIPHATIC ACIDS EXTENDED TO ALKANES THE CARBON ACIDS VIA THE ALIPHATIC ALCOHOLS: AN EDUCATIONAL PERSPECTIVE IN CHEMISTRY
Резюме. A simple, new, lucid and an improved version of a protocol over Andrew William’s treatment is presented in this article for the evaluation of the attenuation effect of methylene group on the deprotonation process of aliphatic acids \(\mathrm{RCOOH}-\mathrm{RCOO}^{-}+\mathrm{H}^{+}\)and extended to aliphatic alcohols and alkanes; the carbon acids.
Ключови думи: attenuation effect; methylene group; aliphatic acid dissociation equilibriums, Taft r*
Introduction
Aliphatic acid dissociation equilibriums and their chemical reactivity is well explained on the basis of well established acid and base catalyzed hydrolysis of substituted aliphatic ester derivatives by Taft equation (Taft, 1952a; 1952b; 1953) in terms of two parameters the Taft substituent constant (s*) and the Taft reaction constant (\(\mathrm{r}^{*}\) ). Thus the Taft equation in terms of only polar sensitivity factors in aliphatic acid dissociation equilibriums is:
(1)\[ \log K_{\mathrm{x}}=\log K_{\mathrm{CH}_{\mathrm{s}}}+\rho^{*} \sigma^{*} \]
\(K_{\mathrm{X}}\) and \(K_{C \mathrm{H}} \quad K_{C \mathrm{H}}\) are the acid dissociation constants of substituted acids and acetic acid respectively. The Taft reaction constant (\(\mathrm{r}^{*}\) ) is a measure of the magnitude of the polar effect of structure on the aliphatic acid dissociation equilibriums. The steric effects are assumed to be negligible because the distance between the dissociable hydrogen and the substituent is quite appreciable.
Methods
All calculations and curve fittings were done by KaleidaGraph software version 4.1 supplied by Synergy Software INC., Reading, PA, USA. All chemical structures were drawn using “Chemdraw” software.
Discussion
The attenuation effect may be explained as a systematic depletion of the transmitting power of a polar effect through increasing number of methylene groups between the dissociable hydrogen and the substituent. On this aspect few publications have appeared in literature from our group (Jagannadham, 2009; Sanjeev & Jagannadham, 2017; Sanjeev et al., 2014; 2020).
Owing to his observations and formulation of a strong empherical relation that explains the attenuation effect in aromatic systems, Andrew Williams (2003) has come up with another empherical equation for aliphatic systems, Eq. (2).
(2)\[ \rho^{*} \sim 0.8(2.0)^{(2-i)} \]
Here"\(i\)"is the number of methylene groups or the number of carbon atoms between the atom bearing the dissociable hydrogen and the substituent \(\mathrm{R}\left(\mathrm{R}-(\mathrm{C})_{\mathrm{i}}-\mathrm{XH}\right)^{1)}\) (Williams, 2003). Here one must bear in mind that the number "\(i\)"is not the number of methylene groups between the dissociable proton and the substituent as mentioned above in the first paragraph of our “discussion”, but in the contention of Williams it is the number of the methylene groups or the number of carbon atoms between the atom bearing the dissociable hydrogen that is the “oxygen” in red in the structures I and II and the substituent R (R-(C)ituent \(\mathrm{R}\left(\mathrm{R}-(\mathrm{C})_{\mathrm{i}}-\mathrm{XH}\right)^{1}\) (Williams, 2003). Using Eq. (2), the predicted values of Taft \(\mathbf{r}^{*}\) for substituted acetic acids \(\left(\mathrm{RCH}_{2} \mathrm{CO}_{2} \mathrm{H}, \mathrm{i}=2\right.\), the blue carbons in the structure I and formic acids \(\left(\mathrm{RCO}_{2} \mathrm{H}\right), \mathrm{i}=1\), again the blue carbon in the structure II) are 0.8 and 1.6 respectively. And these values are well agreed with the observed values of 0.67 and 1.62, respectively (Perrin et al., 1981).
Making Taft plots for substituted acetic acids, \(\mathrm{RCH}_{2} \mathrm{CO}_{2} \mathrm{H}\) and formic acids, \(\mathrm{RCO}_{2} \mathrm{H}\), we found that the Taft \(\mathrm{r}^{*}\) values 0.75 and 1.6 respectively (present work). William’s treatment is good as long as these two examples are used. But Eq. (2) fails when the treatment is extended to alcohols and the alkanes, the carbon acids and with higher"\(i\)"values.
Different Taft plots including alcohols with \(\mathrm{i}=1\) and alkanes with \(\mathrm{i}=0 ; \mathrm{p} K_{\mathrm{a}}\) versus Taft s* were made and presented in Tables 1-7 and Figures 1-7. Applying William’s empherical equation, Eq. (2), a plot of Taft r* versus i is shown in figure 8 with the corresponding data in table 8 with the inclusion of aliphatic alcohols and the alkanes (the carbon acids). The correlation is very poor (\(\mathrm{r}=0.4757\) ).
In the present work William’s treatment is further extended by including aliphatic alcohols and the alkanes (the carbon acids) with a different but modified equation, Eq. (3).
(3)\[ \rho^{*}=m 1+m 2^{*} e^{-m 3^{*} i} \]
Here \(\mathrm{m} 1, \mathrm{~m} 2\) and m3 are arbitrary constants. And “i” is as usual the number of methylene groups or the number of carbon atoms between the dissociable hydrogen (not the atom to which dissociable hydrogen attached) and the substituent. With this new definition "\(i\)"would be 3 for acetic acid as an example, as shown in structure III.
Table 1. Taft s* and pK data of substituted carbon acids, i = 0
A plot of Taft r* versus i is shown in Fig. 9 with the corresponding data in table 8 with the inclusion of aliphatic alcohols (\(\mathrm{i}=1\) ) and the alkanes (\(\mathrm{i}=0\), the carbon acids). The correlation is very good (\(\mathrm{r}=0.9989\) ). A similar study was manifested by one of the authors (VJ) earlier (Jagannadham, 2009) in the study of attenuation effect in benzoic acids and was extended to benzenes, the aromatic carbon acids (in the present work it is alkanes, the aliphatic carbon acids) itself via phenols (in the present work it is alcohols).
Figure 1. Plot of pKa vs. Taft σ*
The attempt in the present work on the evaluation of attenuation effect in aliphatic systems gave an encouragement for studying attenuation effect in different proton dissociation equilibriums to be brought on one rope which includes the nitrogen acids and sulfur acids and even the molecules containing the carbons with different hybridizations other than sp3.
Table 2. Taft s* and pK data of substituted aliphatic alcohols, i = 1, blue oxygen
Table 3. T a ft \(\mathrm{s}^{*}\) and \(\mathrm{p} K_{\mathrm{a}}\) data of substituted formic acids, \(\mathrm{i}=2\), one blue carbon and one blue oxygen
Figure 2. Plot of pKa vs. Taft s*, i =1
Figure 3. Plot of pKa vs. Taft s*, i = 2
Table 4. Taft \(\sigma^{*}\) and \(\mathrm{p} K_{\mathrm{a}}\) data of s* and pKa cetic acids, \(\mathrm{i}=3\), two blue carbons and the blue oxygen
Figure 4. Plot of pKa vs. Taft s*, i=3
Table 5. T a ft \(\mathrm{s}^{*}\) and \(\mathrm{p} K_{\mathrm{a}}\) data of substituted propionic acids, \(\mathrm{i}=4\), three blue carbons and one blue oxygen
Figure 5. Plot of pKa vs. Taft s*, i=4
Table 6. Taft \(\mathrm{s}^{*}\) and \(\mathrm{p} K_{\mathrm{a}}\) data of substituted butyric acids, \(\mathrm{i}=5\), four blue carbons and one blue oxygen
Figure 6. T a ft \(\mathrm{s}^{*}\) and \(\mathrm{p} K_{\mathrm{a}}\) data of substituted butyric acids, \(\mathrm{i}=5\), four blue carbons and one blue oxygen
Table 7. T a ft \(\mathrm{s}^{*}\) and \(\mathrm{p} K_{\mathrm{a}}\) data of substituted pentanoic acids, \(\mathrm{i}=6\), five blue carbons and one blue oxygen
Figure 7. Taft s* and pKa data of substituted butyric acids, i = 6
Table 8. Data of ‘i’ and Taft r*
(#)From the plots of pKa versus Taft s* the slopes are all negative. Yet taking the positive sign for Taft r* values is justified because pKa = - log Ka.
Figure 8. Plot of Taft ρ* vs. i using Eq. (2)
Figure 9. Plot of Taft ρ* vs. i
The decrease in Taft r* value is more pronounced with increase in the number of atoms between the ionizable proton and the first carbon atom of the substituent when compared to that in aromatic systems (Jagannadham, 2009; Sanjeev & Jagannasdham, 2020). Here it decreased from a value of 12.1 with one atom to 0.275 to 0.18 with five and six atoms. After the number atoms become 5 the Taft \(r^{*}\) is approaching zero, Fig. (9). In the aromatic systems the gradual decrease in Hammett \(r\) is only by a factor of 2 each time as a function of each methylene group (Jagannasdham, 2009). But in aliphatic systems as in the present work the decrease is \(3-4\) each time and finally approaches zero as ‘x’ approaches 8 (Fig. (9)). This may be because of the larger distance between the substituent attached to aromatic system and the ionizable proton compared to the smaller distance in the aliphatic systems. Hence the attenuation effect of substiuents is not much pronounced in aromatic systems compared to that in aliphatic systems.
NOTES
1. The readers are requested to make a note in Eq. (2) that it is not the equality sign it is “~” and reflects its meaning as not exactly the same.
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