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
