Question

The diffusion coefficient for O^-2
in Cr2O3 is 4 × 10-15 cm^2 /s at 1150°C and 6 ×10-11 cm^2 /s at 1715°C. Calculate (a) the activation energy and (b) the constant Do.

Answer 1

Recall the equation

D=D0 e^(q/RT)

where R is gas constant

Q is activation energy

at, 1150 C =1423 K

4x10^-15 cm²/s= D0*exp(- q/R*1423 ))

at 1715=1988K

6x10^-11 cm^2/s= D0e^(- q/R*1988))

dividing both equations we get

(4x10^-15)/(6x10^-11)=e^(-q/r(1/1423 -1/1988))

6.6x10^-5= e^(-q/r(1/1248-1/1913))

-9.61= -Q/r (1.99*10^-4)

Q = (9.61*8.314)/(1.99*10^-4)

Q= 401495.17 = 401.5 kJ/mol

For D0

D0= 4x10^-15 cm²/s= D0*e^(- q/R*1423 ))=4x10^-15 /9.92x10^-13

D0=4.03x10^-3 cm²/s