## 3 Results and Discussions
### Molecular Interaction Properties  
From the experimental values of density, viscosity and ultrasonic velocity [27], various molecular interaction parameters like adiabatic compressibility, intermolecular free length, free volume, internal pressure, and viscous relaxation time were determined and are presented in Table 8.  
Normally, a decrease in adiabatic compressibility indicates closed packing and decreased ionic repulsion. In the present study, the adiabatic compressibility for both systems (Ethanol + 1-Hexanol and Ethanol + 1-Octanol) increases with an increase with the concentration of ethanol. This indicates that the molecules are loosely packed in the solution. The adiabatic compressibility shows an inverse behaviour when compared to ultrasonic velocity. This indicates that there is a significant interaction between the binary liquids. This increasing trend suggests a moderate strong electrolytic nature in which the solutes tend to attract the solvent molecules. The intermolecular free length shows a similar behaviour to adiabatic compressibility. From Table 8, the free volume shows an increasing trend with the increase in the concentration of ethanol. This may be compactness due to association at a higher concentration [54]. This increasing trend is due to stronger intramolecular interaction than intermolecular interaction which can be attributed to the loose packing of molecules inside the shield, which suggests a weak molecular interaction in the components of mixtures [55]. The internal pressure is a measure of cohesive forces between the constituent molecules in liquids. It is also defined as the energy required to vaporize a unit volume of a substance. The values of internal pressure increase with an increase in  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Mole Fraction** \\ **of Ethanol** \\ **Values** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Ultrasonic** \\ **Velocity** \\ **(Experimental Values) m/s** \\ \end{tabular} } & \multicolumn{4}{c}{**Theoretical Ultrasonic Velocity (m/s)**} \\ \cline{3-6}  & & **[PERSON]** & **[PERSON]** & **Impedance** & **Rao’s Specific** & **Junjie** \\  & **Nomoto** & **[PERSON]** & **Relation (U\({}_{\text{IR}}\))** & **Velocity** & **Relation (U\({}_{\text{R}}\))** & **Relation (U\({}_{\text{J}}\))** \\ \hline
0.00 & 1327.5 & 1234.6 & 1327.5 & 1327.5 & 1235.3 & 1327.3 \\ \hline
0.13 & 1316.6 & 1224.8 & 1183.1 & 1303.1 & 1210.9 & 1314.1 \\ \hline
0.24 & 1307.6 & 1214.8 & 1109.1 & 1281.8 & 1190.0 & 1300.9 \\ \hline
0.33 & 1298.6 & 1205.5 & 1070.4 & 1264.4 & 1173.3 & 1289.0 \\ \hline
0.55 & 1264.0 & 1177.5 & 1028.9 & 1223.1 & 1134.7 & 1255.1 \\ \hline
0.70 & 1239.7 & 1150.2 & 1032.9 & 1193.7 & 1108.1 & 1224.3 \\ \hline
0.81 & 1200.4 & 1123.5 & 1053.4 & 1171.6 & 1088.6 & 1196.3 \\ \hline
0.89 & 1167.8 & 1097.6 & 1081.0 & 1154.5 & 1073.9 & 1170.9 \\ \hline
0.96 & 1146.8 & 1073.3 & 1110.7 & 1141.3 & 1062.7 & 1148.5 \\ \hline
1.00 & 1133.3 & 1056.1 & 1133.3 & 1133.3 & 1055.9 & 1133.3 \\ \hline APD from experimental values & 6.79\% & 10.10\% & 1.66\% & 8.60\% & 0.33\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Experimental and Theoretical Ultrasonic velocity of Binary liquid system of Ethanol + 1-Octanol at 303.15 K.  
the mole fractions of ethanol. The value of internal pressure was found to be greater for the Ethanol+1-hexanol than Ethanol+1-octanol liquid system. This suggests that there is a strong interaction between the solute and solvent molecules or that there is an increase in the extent of complexation with the increase in concentration [55]. The internal pressure of a liquid reflects the molecular interaction. The dispersion of the ultrasonic speed of sound in the binary system gives information about the characteristics of relaxation time (\(\tau\)), which explains the cause of dispersion. The decreasing trend of relaxation time was observed in the present case. It may be due to the structural changes occurring in the mixtures resulting in the weakening of intermolecular forces [56].