Fick's first law relates diffusion flux to the concentration gradient. Which expression is correct?

• A. J = -D (dC/dx); J is diffusion flux, D is diffusion coefficient, dC/dx is concentration gradient.
• B. J = D (dC/dx); J is current density, D is density, dC/dx is concentration.
• C. J = -D (dT/dx); J is heat flux, D is diffusion coefficient, dT/dx is temperature gradient.
• D. J = -D (dC/dx^2); J is diffusion flux, D is diffusion coefficient, dC/dx^2 is curvature.

Answer: (A)

Diffusion flux is driven by concentration differences, with particles moving from high to low concentration. Fick's first law expresses this as J = -D dC/dx in one dimension: J is the amount diffusing through unit area per unit time, D is the diffusion coefficient that captures how easily particles move in the medium, and dC/dx is the spatial rate of change of concentration. The negative sign is essential—it points the flux down the concentration gradient, so when concentration increases with x (positive dC/dx), the flux is in the negative x direction, and vice versa.

If you tried a positive sign, it would imply flow toward higher concentration, which is not how diffusion operates. Using a temperature gradient would describe heat conduction (Fourier’s law), not mass diffusion. Using the second derivative, dC/dx^2, would involve curvature and does not correspond to the basic diffusion flux relation. In more general terms, J = -D ∇C in three dimensions, with D potentially a tensor if diffusion is anisotropic.