# Why does the time to reach equilibrium across a membrane decrease with concentration?

We're learning about flux and Fick's law and there's one point I'm having trouble understanding. Assuming we have a higher concentration of a species on one side of a membrane, I understand that increasing the concentration will increase the flux (net particle movement/(time*area)). We were told as well that increasing the concentration also decreases the time it takes to reach equilibrium. Why would that be?

Rephrased: If you have 10 particles on one side of the membrane and 0 on the other, it takes X amount of time to reach equilibrium (~ 5 particles on each side). If you have 10 million particles, why would it take <X amount of time to reach equilibrium (~5M particles on each side).

Thanks

Considering Fick's first law, there must have been a misunderstanding between you and your teacher. where

• J is the diffusion flux, of which the dimension is amount of substance per unit area per unit time. J measures the amount of substance that will flow through a unit area during a unit time interval.
• D is the diffusion coefficient or diffusivity. Its dimension is area per unit time.
• φ (for ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume.
• x is position, the dimension of which is length.

As you can see, flux is proportional to concentration, meaning equilibrium time is not affected by concentration. Possibly, your teacher meant that either (1.) an absolute increase in concentration on both sides of the membrane (by the same offset) decreases the equilibrium time or (2.) that a proportional increase in concentration by down-scaling of the containers (x; length) would also shorten the equilibrium time.

• +1, though this is relevant when you get closer to real world demonstrations: 1[ncbi.nlm.nih.gov/pmc/articles/PMC6648224/]. Where absolute concentrations can effect your lattice walking. I agree that this is more likely a misunderstanding. Sep 17, 2021 at 3:16
• I agree; it's definitely more complicated than that, including considerations like viscosity or temperature and Boltzmann distribution of corresponding velocities. Sep 17, 2021 at 13:55