## 3 Results and Discussions
### Density Studies  
Density is an important concept because it allows one to determine whether a substance with a specified density will float/sink in a liquid. Specifically, substances with a lesser density than the density of the liquid will float in that liquid. Also, it is an important physical property used in calculating the acoustic and physical properties of a substance such as the molar refraction, dipole moment, boiling temperature and superficial tension. The density of the binary liquid mixtures, taken for the present study, was calculated using the [PERSON] model (\(\rho_{\text{MNM}}\)) [31], [PERSON] and [PERSON] model (\(\rho_{\text{HT}}\)) [32], [PERSON] and Gunn model (\(\rho_{\text{YG}}\)) [33] and [PERSON] et al. model (\(\rho_{\text{R}}\)) [34] as given by the following details:  
Mchaweh-Nasrifar-Mashfeghian model (\(\rho_{\text{MNM}}\)) [31]  
[PERSON], [PERSON] and [PERSON] reported the following correlation:  
\[\rho_{mix}=\rho_{cmix}\rho_{0 mix} \tag{10}\]  
where \(\rho_{\text{mix}}\) is the density of the mixed solution, and \(\rho_{\text{cmix}}\) is the critical density of the mixture. The critical density of the mixture is calculated with the following equation:  
\[\rho_{cmix}=[\sum_{i=1}^{N}x_{i}\rho_{ci}^{-3/4}]^{-4/3} \tag{11}\]  
where \(\text{x}_{i}\) is the mole fraction, and \(\rho_{\text{ci}}\) is the critical density of the ith component. \[\rho_{0 mix}=1+1.169\tau_{mix}^{1/3}+1.818\tau_{mix}^{2/3}-2.658\tau_{mix}^{3/ 3}+2.161\tau_{mix}^{4/3} \tag{12}\]  
where the temperature-dependent variable \(\tau_{\text{mix}}\) is calculated by the following expression:  
\[\tau_{mix}=1-T_{matrix}/\alpha_{SRK} \tag{13}\]  
In the above equation, \(T_{\text{mix}}\) is the reduced temperature of the mixed solution and \(\alpha_{\text{SRK}}\) is the term from the original Soave Redlich-Kwong equation of the state. The reduced temperature of the mixture is defined as  
\[T_{mix}=T/\sum_{i=1}^{N}x_{i}T_{ci} \tag{14}\]  
where \(T_{\text{ci}}\) is the critical temperature of the ith component. The parameter \(\alpha_{\text{SRK}}\) is defined in terms of the reduced temperature (\(T_{\text{r}}\)):  
\[\alpha_{SRK}=\Big{[}1+m\Big{(}1-\sqrt{T_{mix}}\Big{)}\Big{]}^{2} \tag{15}\]  
\[m=0.480+1.574\omega_{mix}-0.176\omega_{mix}^{2} \tag{16}\]  
The acentric factor of the solution \(\omega_{\text{mix}}\) is calculated with the following expression:  
\[\omega_{mix}=\sum_{i=1}^{N}x_{i}\omega_{i} \tag{17}\]  
where \(\omega_{i}\) is the acentric factor of the ith component. The acentric factor is a measure of the complexity of the molecule as formed in relation to a molecule with spherical symmetry of a simple fluid for which \(\omega=0\). [PERSON] and Thomson model (\(\rho_{\text{HT}}\)) [32]  
The Hankinson-Thomson model (H-T) [21] is based on the corresponding state principle and is valid for \(0.25<T_{\text{r}}<0.95\). The density of the pure compound is defined by  
\[\rho=\rho_{c}/\Big{[}V^{(0)}\Big{(}1-\omega V^{(1)}\Big{)}\Big{]} \tag{18}\]  
\[V^{(0)}=1-1.5281\Big{(}1-T_{r})^{1/3}+1.4390\Big{(}1-T_{r})^{2/3}-0.8144(1-T_{r })+0.19045\Big{(}1-T_{r})^{4/3} \tag{19}\]  
\[\rho_{cmix}=[\sum_{i=1}^{N}x_{i}\rho_{ci}^{-3/4}]^{-4/3} \tag{11}\]0  
The reduced temperature of the component is defined as \[\rho_{cmix}=[\sum_{i=1}^{N}x_{i}\rho_{ci}^{-3/4}]^{-4/3} \tag{11}\]1  
Yamada and Gunn model (\(\rho_{\rm YG}\)) [33]  
The Yamada-Gunn model extended the Racket equation and requires the molecular weight M, the critical density \(\rho_{c}\), the reduced temperature T\({}_{r}\) and the acentric factor \(\omega\):  
\[\rho_{cmix}=[\sum_{i=1}^{N}x_{i}\rho_{ci}^{-3/4}]^{-4/3} \tag{11}\]2  
[PERSON] et al. model (\(\rho_{\rm R}\)) [34]  
The [PERSON] et al. model proposed an equation also based on the molecular weight, critical density, reduced temperature and acentric factor:  
\[\rho_{cmix}=[\sum_{i=1}^{N}x_{i}\rho_{ci}^{-3/4}]^{-4/3} \tag{11}\]3  
The density values calculated using the Mchaeweh-Nasrifar-Mashfeghian model, Hankinson and Thomson model, Yamada and Gunn model and [PERSON] et al.