Question

The unit of diffusion coefficient is

• A. mol m$^{-2}$ s$^{-1}$
• B. mol m$^{-3}$
• C. m$^{2}$ s$^{-1}$
• D. kJ mol$^{-1}$

Hint:

The diffusion coefficient always has the dimension of {area per unit time}, so its SI unit is {m$^{2}$ s$^{-1}$}.

Answer 1

The Correct Option is C

Step 1: Fick's first law states \( J = -D \dfrac{dC}{dx} \), where flux \( J \) has units of mol m\(^{-2}\) s\(^{-1}\) and the concentration gradient \( \dfrac{dC}{dx} \) has units of mol m\(^{-4}\) (concentration per unit distance).
Step 2: Rearranging for \( D \) gives \( D = \dfrac{J}{dC/dx} \).
Step 3: Substituting the units, \( D \) has units of \( \dfrac{\text{mol m}^{-2}\text{s}^{-1}}{\text{mol m}^{-4}} \), and the mol terms cancel while the metre powers combine.

\[ D = \text{m}^{2}\,\text{s}^{-1} \]

Answer 2

Checking each option against a physical quantity it is known to represent is a quick way to confirm which one belongs to the diffusion coefficient.

1. mol m\(^{-2}\) s\(^{-1}\): This combination of units describes flux, the amount of a substance passing through a unit cross-sectional area each second, a quantity distinct from the diffusion coefficient.
2. mol m\(^{-3}\): This is simply concentration, amount of substance per unit volume, and carries no time dependence at all, so it cannot describe a rate-of-spreading coefficient.
3. m\(^{2}\) s\(^{-1}\): This combination, an area divided by a time, is the unit assigned to any transport coefficient describing how a length-squared quantity evolves with time, which is exactly the physical role the diffusion coefficient plays in Fick's law.
4. kJ mol\(^{-1}\): This unit belongs to molar energy quantities such as activation energy or enthalpy, unrelated to spatial transport.

Matching each set of units to the physical quantity it actually represents leaves area-per-time as the only one consistent with the diffusion coefficient.

Therefore, the correct answer is m\(^{2}\) s\(^{-1}\).