Question

Calculate the surface charge density of the SDS micelle assuming that the particles have a radius of 20 nm, and contain 100 molecules of SDS and 20 molecules of lauric acid. Do the calculation at the pKa of lauric acid (where half the molecules are ionized and the other half unionized). Use your knowledge of surface area of a sphere and relate this to number of molecules.

Answer 1

Ans: Micelle is a defined as an amphipathic molecule which has polar part on the surface and non polar part at the core, examples: lipid molecules.

In the question it is given that the surface charge density is calculated at pKa of lauric acid and the radius of the particle is 20 nm. Since micelle is of spherical shape its surface area will be 4πr2. Putting the value of r in this formula we get 5024 nm².

Now one molecule of SDS contains net charge of -2 and one molecule of lauric acid at its pKa contains net charge of -1 and it’s also given that at its pKa half molecules of lauric acid will be charged and half will be neutral. So net charge on the surface of SDS micelle is 100*2+10= 210.

Now surface charge density= Total charge/surface area (Coulomb/m2); 210*1.6*10^-19C/5024*10^-18m²

( 1 electron= 1.6*10^-19 C charge and 1 m= 10⁹ nm)

=> 336/50240= 0.0062.

So the surface charge density is 0.0062 C/m²