Diffusion coefficient is exponentially dependent on which variable?

• A. Pressure
• B. Time
• C. Concentration
• D. Temperature

Answer: (D)

Diffusion involves atoms or molecules jumping over energy barriers, so the rate at which they diffuse depends on an activation energy. This leads to an Arrhenius-type relation for the diffusion coefficient: D = D0 exp(-Ea/(RT)). Here Ea is the activation energy for the diffusion mechanism, R is the gas constant, and T is temperature. As temperature increases, the exponent becomes less negative, causing D to rise very quickly—in other words, D grows exponentially with temperature. This is why heating speeds up diffusion a lot.

Pressure, time, and concentration don’t set D through this exponential temperature dependence in the standard diffusion description. Pressure mainly shifts diffusion behavior in gases inversely with pressure at a fixed temperature, time controls how far diffusion progresses given D, and concentration can affect diffusion in non-ideal systems but not through the same exponential temperature factor.