Micellisation is found to be spontaneous i.e. $\Delta G < 0.$ It's found that $\Delta S > 0,$ which was intuitive since, solvated molecules are released. And, it may be most loosely started that $\Delta H > 0$ i.e endothermic at low temperature and exothermic ($\Delta H<0$) at higher temperatures. Guess why?
Hint, derive that $\Delta H^\circ=-RT^2 \dfrac{\mathrm d(\ln{\text{CMC}})}{\mathrm dT}$. And CMC may be defined as CMC as the point corresponding to the maximum change in gradient in an ideal property–concentration $(\phi$ against $S_\mathrm{tot})$ relationship $\dfrac{\mathrm d^3\phi}{\mathrm dS^3_\mathrm{tot}} = 0.$
(emphasis mine)
Why was most loosely stated term used in the text? Isn't it true? Excluding non-dressed micelle model, $\Delta G$ can be shown to be approximately $(1 + \beta)\ln{\text{CMC}}$.
Writing $\Delta H^\circ = \Delta G^\circ + T\Delta S^\circ$ and plugging in the values I couldn't get the desired term. Is my process correct?
Also, what's the meaning of “ideal property–concentration”?
