(c) The data set below represents the surface tension data for aqueous solutions of CTAB, cetyl trimethyl ammonium bromide also referred to as hexadecyltrimethylammonium bromide [CH$_3$(CH$_2$)$_{15}$N(CH$_3$)$_3$Br] at 25°C.
C[mol.dm$^{-3}$] 0.0001 0.0002 0.0004 0.0008 0.0010 0.0020
y [mN.m$^{-1}$] 65.0 55.0 45.0 35.0 34.0 33.0
(i) Estimate the critical micelle concentration of this surfactant, commenting briefly on your estimate.
(ii) Calculate the surface excess of CTAB (in mol.m$^{-2}$)
(iii) Hence estimate the molecular cross-sectional area (in nm$^2$) for CTAB
(iv) Compare your estimate with the molecular cross-sectional one might expect for the corresponding carboxylic acid, hexadecenoic acid, CH$_3$(CH$_2$)$_{14}$COOH and account for the difference, if any, between the two surface active molecules.
[22 marks]