Question

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

Answer 1

Answer:

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