Question $2$

The interfacial energy $Y_{\text{o}\text{i}\text{l}-\text{w}\text{a}\text{t}\text{e}\text{r}}$ of an oil $-$ water interface at $25C$ is $53m\frac{J}{m^2}.$ The surface tension of the

oil is $25m\frac{N}{m}$ and that of water is $72\mathrm{.}5m\frac{N}{m}$ at $25C.$

$($a$)$ Calculate the spreading coefficient. Does the oil spread on water at $25C?$

$($b$)$ When carboxylic acid is dissolved in the oil, Yoil$-$water is reduced. We may assume that acid

addition only affects ${}_{\text{o}\text{i}\text{l}-\text{w}\text{a}\text{t}\text{e}\text{r}\text{,}}$ which decreases linearly with acid concentration $($dilute solution$).$ It

is observed that spreading of the oil occurs when the acid concentration in greater than $0\mathrm{.}005$

$mo\frac{l}{L}.$ Calculate the adsorption isotherm $$ versus $C$ for adsorption of acid at the interface, and

the area occupied by each acid molecule at the interface at the onset of spreading.