concentration gradients

Meaning: A concentration gradient is a difference in the concentration of a species between two regions. Particles move randomly, but more of them leave the crowded region than the sparse one, so net movement is down the gradient, from high to low concentration. This is spontaneous because it increases entropy. Across a semipermeable membrane, water moves toward the region of higher solute concentration (osmosis).

Equation: J = −D(ΔC/Δx), where J is flux in mol/(m²·s), D is the diffusion coefficient in m²/s, ΔC is the concentration difference in mol/m³, and Δx is the distance in m. The minus sign means flux points down the gradient. A steeper gradient gives a larger flux.

On the MCAT: Expect concentration cells. Both half-cells have the same electrode and the same ions at different concentrations, so E° = 0, but the Nernst equation gives a nonzero voltage. The dilute half-cell is the anode and the concentrated half-cell is the cathode, so the two concentrations move toward each other. In biology-style passages, passive transport follows the gradient and active transport spends energy to go against it.

Common confusion: At equilibrium the gradient is gone, but particles still cross in both directions at equal rates, so movement does not stop. For charged ions, the electrical potential also matters, so direction follows the electrochemical gradient, not the concentration difference alone.