What is it that the molecules are trying to achieve as a result of passive
transport?

The molecules are trying to achieve equilibrium.

Explanation

In cells, molecules will migrate through the phospholipid bilayer during passive transport, a form of simple diffusion that does not use the energy currency, ATP.

This layer serves as a selectively-permeable membrane; its hydrophilic heads are drawn to water (seen looking outward), while its hydrophobic water-repellent tails face each other, allowing water molecules to diffuse down the concentration gradient through the membrane.

This typcally continues til the molecules gain equilibrium or balance. At equilibrium, molecules neither enter nor leave the cell through passive transport.