Can anyone explain this? How and why does the chain length of surfactants affect CMC? How and why does the addition of a salt (eg., NaCl) affect the CMC?

Increasing the chain length decreases the CMC by increasing the hydrophobic nature of the surfactant.

Adding a salt decreases the CMC by decreasing repulsions between the charged heads of the surfactant molecules.

A surfactant (surface active agent or SAA) has a polar head and a nonpolar tail.

At low concentrations, the SAA molecules tend to arrange themselves on the surface with their tails in the air.

As the concentration of SAA increases, more SAA molecules accumulate on the surface, which eventually becomes saturated with SAA molecules.

The addition of more SAA then leads to the formation of micelles.

The concentration at which micelles start to form is called the Critical Micelle Concentration (CMC).

For most ionic SAAs, such as sodium alkyl sulfates, the CMC is usually between 10⁻² and 10⁻³ mol/L.

Increasing the chain length increases the hydrophobic character of the SAA and causes micelles to form at a lower concentration.

In general, the CMC is halved when the chain length increases by one CH₂ group.

The addition of salts decreases the CMC.

The charged heads of the SAAs repel each other, and this works against micelle formation.

Adding salt ions decreases the repulsions, so micelles can form at a lower SAA concentration.