Which statement about the Arrhenius form for diffusion is correct?

• A. D = D0 exp(+Q/RT); increasing temperature increases D.
• B. D = D0 exp(-Q/RT); as temperature rises, D increases exponentially.
• C. D = D0 exp(-Q/RT); as temperature rises, D decreases.
• D. D = D0 exp(-Q/RT^2); temperature effect is not exponential.

Answer: (B)

Diffusion obeys an Arrhenius form because it involves overcoming an energy barrier to move from one site to another. The relation D = D0 exp(-Q/(RT)) captures that idea, where Q is the activation energy, R is the gas constant, T is the absolute temperature, and D0 is a pre-exponential factor setting the scale.

As temperature rises, the ratio Q/(RT) becomes smaller in magnitude since 1/T decreases. The negative sign in the exponent means the exponent is less negative, so the exponential factor exp(-Q/(RT)) grows. Put another way, higher temperature makes it more likely that atoms have enough energy to surmount the barrier, so diffusion accelerates, often very rapidly with temperature.

If the exponent carried a plus sign, exp(+Q/(RT)), increasing temperature would reduce the exponent, which would decrease D, contradicting observed behavior. If the temperature dependence were not exponential in 1/T or involved an incorrect form like RT^2, it would fail to describe the typical temperature-activated diffusion behavior.