The interfacial energy $\backslash$gamma oil$-$water of an oil $$ water interface at $25$ oC is $53$ mJ$/$m$2$

$.$ The surface tension of the

oil is $25$ mN$/$m and that of water is $72\mathrm{.}5$ mN$/$m at $25$ oC$.$

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

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

addition only affects $\backslash$gamma oil$-$water, which decreases linearly with acid concentration $($dilute solution$).$ It

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

mol$/$L$.$ Calculate the adsorption isotherm $\backslash$Gamma 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.