The surface tension of aqueous SDS solutions at was measured as follows

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Amphiphiles and self-assembly

Problem

The surface tension γ\gamma of aqueous SDS solutions at 25∘C25^\circ\mathrm{C} was measured as follows. Data: at c=1,2,4,6,8,8.2,10,15,20 mMc = 1, 2, 4, 6, 8, 8.2, 10, 15, 20\,\mathrm{mM} the surface tension is γ=65,60,52,45,40,38,38,38,38 mN m−1\gamma = 65, 60, 52, 45, 40, 38, 38, 38, 38\,\mathrm{mN\,m^{-1}} respectively. ((a)) Read off the CMC of SDS (C12\mathrm{C_{12}} sulfate) from this table. ((b)) For sodium alkyl sulfates, log⁡10(CMC)\log_{10}(\mathrm{CMC}) falls by about 0.30.3 per extra carbon in the tail. Use the CMC found in part (a) to estimate the CMC of sodium hexadecyl sulfate (C16\mathrm{C_{16}} sulfate), four carbons longer.

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