Figure 3 The relationship between the pKa3 with the inverse temperature of the studied amines. ●: n-2AOE13PDA; ▼: DMAPAPA; ○: DAOMDPA
All amines were ranked in terms of pKa
Equation 7 is the van’t Hoff equation and is used for determining the standard state entropy change (ΔS0, kJ·mol-1·K-1) and enthalpy change (ΔH0, kJ·mol-1). In the equation, the slope and intercept of the plots in Figures 1 to 3 represent\(\frac{-\Delta H^{0}}{R}\) and \(\ \frac{\Delta S^{0}}{R}\), respectively with R being the Universal gas constant (8.3145x10-3kJ·mol-1·K-1). Furthermore, the standard state Gibbs free energy change (ΔGo, kJ·mol-1) of the reaction can be calculated using Equation 8. The values of ΔHo, ΔSoand ΔGo for the studied amines are summarized in Tables 5 to 10.
\begin{equation} \ln\left(K_{a}\right)=\ -\ln\left(10^{{pK}_{a}}\right)=\ \frac{S^{o}}{R}+\ \frac{-H^{o}}{\text{RT}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (7)\nonumber \\ \end{equation}\begin{equation} G^{o}=R.T.\ln\left(10^{pK_{a}}\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8)\nonumber \\ \end{equation}
Table 5 Standard state enthalpy and entropy changes of the first pKa of the eight studied amines