# Diffusion constant

Phosphatidylcholine is a lipid that can be found in egg yolk. When phosphatidylcholine is mixed with water it will form micelles – spherical particles.

Molecular weight (Mw) for the particles is 97*000 g/mole
Density for the particles is 1.018 g/cm3
The temperature is 25°C

a) What is the radius for the particles?

Assume that the particles are not hydrated.
The viscosity of water (eta) at the given temperature is 0,9 mPa·s (milliPascal second)
Boltzmann constant: 1,38 ´ 10-23 J/K
(Pa=kg/ms2 and J=kgm2/s2)

b) What is the diffusion coefficient (D) for the particles in water?

a) One particle has the mass m = (97 000 g/mol)/6.02E23 = 1.61E-19 g.

This gives V = 1.58E-25 m3, and since the volume of a sphere is given by (4/3)*pi*r^3, the radius for the particles is 3.35 nm.

b) Stokes-Einstein: $$D = \frac{k_B T}{6 \pi \eta R_s} = \frac{1.38E-23 \cdot 298}{6 \pi \cdot 0.9E-3 \cdot 3.35E-9} = 7.24E-11$$

What's wrong here?

## Answers and Replies

V = 1.58E-25 m3 is correct

3.35 nm is wrong... u key the values wrongly.