## 3 Results and Discussion
### Density and Excess Molar Volume of the Binary Mixtures
The calculated \(V^{E}\) for MDEA + H\({}_{2}\)O mixtures showed the lowest deviation for the range of amine concentrations compared to DMEA + H\({}_{2}\)O and DEEA + H\({}_{2}\)O mixtures. The largest deviation for \(V^{E}\) was observed in DEEA + H\({}_{2}\)O mixtures, indicating the existence of strong intermolecular interactions and efficient molecular packing in the mixtures. Compared to \(V^{E}\) of MDEA, a significant deviation was reported with DMEA (\(\approx\)1.4 times) and DEEA (\(\approx\)1.6 times) at the minimum point of 293.15 K. The substitution of one methyl (-CH\({}_{3}\)) group for one ethanol (-CH\({}_{2}\)CH\({}_{2}\)OH) group in MDEA might results an increase of intermolecular interactions especially the H-bonding between N and OH in amine and H\({}_{2}\)O or increase of packing efficiency. Two ethyl groups (-CH\({}_{2}\)CH\({}_{3}\)) in DEEA compared to two methyl (-CH\({}_{3}\)) groups in DMEA further negatively contributed to \(V^{E}\). The introduction of methyl (-CH\({}_{3}\)) or ethyl (-CH\({}_{2}\)CH\({}_{3}\)) groups increases the hydrophobicity of amine [19]. As explained by [PERSON] et al. [23], the H\({}_{2}\)O molecules restructure around the hydrophobic part of the organic solute forming a cage-like structure. Accordingly, more structured H\({}_{2}\)O molecules around the hydrophobic groups (-CH\({}_{3}\)) and (-CH\({}_{2}\)CH\({}_{3}\)) in DMEA and DEEA, respectively, might explain the reported volume contraction in the mixtures. A Redlich-Kister [28] type polynomial as given in the Equation (3) was proposed to fit calculated \(V^{E}\) for all aqueous mixtures. The measured densities at low amine concentrations (\(<30\%\) mass) presented in literature for MDEA + H\({}_{2}\)O mixtures from [PERSON], [PERSON], [PERSON], and [PERSON] [17], DMEA + H\({}_{2}\)O mixtures from [PERSON] et al. [18], and DEEA + H\({}_{2}\)O mixtures from [PERSON] et al. [20] were adopted for this work to improve the accuracy of data fitting into the proposed correlation. A temperature dependency for the Redlich-Kister coefficients (\(A_{i}\)) was suggested as given in Equation (4) to determine optimum values for (\(A_{i}\)) at each temperature. Table 4 lists the parameters for temperature dependency of the Redlich-Kister coefficients (\(A_{i}\)) for \(V^{E}\) of different mixtures. \[Y^{E}=x_{1}x_{2}\sum_{i=0}^{i=n}A_{i}(1-2x_{2})^{i} \tag{3}\]  
\[A_{i}=\sum_{i=0}^{i=n}a_{i}T^{i} \tag{4}\]  
The partial molar volume of each component \(\overline{V_{i}}\) is defined as shown in Equation (5)  
\[\overline{V_{i}}=\left(\frac{\partial V}{\partial n_{i}}\right)_{T,\ P,n_{j}} \tag{5}\]  
For a binary mixture, partial molar volume \(\overline{V_{i}}\) can be determined by the following equations [29]:  
\[\overline{V_{1}}=V^{E}+V_{1}^{0}-x_{2}\left(\frac{\partial V^{E}}{\partial x_ {2}}\right)_{p,T} \tag{6}\]  
\[\overline{V_{2}}=V^{E}+V_{2}^{0}+(1-x_{2})\left(\frac{\partial V^{E}}{ \partial x_{2}}\right)_{p,T} \tag{7}\]  
Equations (8) and (9) can be derived by differentiating Equation (3) for \(V^{E}\) with respect to \(x_{2}\) and combining it with Equations (6) and (7). \[\overline{V_{1}}=V_{1}^{0}+x_{2}^{2}\sum_{i=0}^{i=n}A_{i}(1-2x_{2})^{i}+2x_{2} ^{2}(1-x_{2})\sum_{i=0}^{i=n}A_{i}(i)(1-2x_{2})^{i-1} \tag{8}\]  
\[\overline{V_{2}}=V_{2}^{0}+(1-x_{2})^{2}\sum_{i=0}^{i=n}A_{i}(1-2x_{2})^{i}-2x _{2}(1-x_{2})^{2}\sum_{i=0}^{i=n}A_{i}(i)(1-2x_{2})^{i-1} \tag{9}\]  
The partial molar volume of amines at infinite dilution in H\({}_{2}\)O \(\overline{V_{1}^{\infty}}\) can be determined by considering the scenario of \(x_{2}=1\) as given in the Equation (10) and partial molar volume of H\({}_{2}\)O at infinite dilution in amines \(\overline{V_{2}^{\infty}}\) can be found by considering the scenario of \(x_{2}=0\) as shown in Equation (11).