At 500oC, the diffusion coefficient of Cu in Ni is 1.3 x 10-22 m2/s, and the activation energy for diffusion is 256,000 J/mol. From this information, determine the diffusion coefficient of Cu in Ni at 900 oC. (R = 8.314 J / (mol K)) 0oC = 273 K

the diffusion coefficient at 900°C is D₂=8.9*10⁻¹⁸ m²/s

Explanation:

The dependence of the diffusion coefficient is similar to the dependence of chemical reaction rate with respect to temperature, where

D=D₀*e^ (-Q/RT)

where

D₀ = diffusion energy at T=∞

Q = activation energy

T = absolute temperature

D = diffusion coefficient at temperature T

R=ideal gas constant

for temperatures T₁ and T₂

D₁=D₀*e^ (-Q/RT₁)

D₂=D₀*e^ (-Q/RT₂)

dividing both equations and rearranging terms we get

D₂=D₁*e^[-Q/R (1/T₂-1/T₁) ]

replacing values

D₂=D₁*e^[-Q/R (1/T₂-1/T₁) ] = 1.3*10⁻²² m²/s*e^ (-256,000 J/mol/8.314 J / (mol K) * (1/1073K-1/773K) = 8.9*10⁻¹⁸ m²/s