Nitrogen from a gaseous phase is to be diffused into pure iron at 700°C. If the

Question

Nitrogen from a gaseous phase is to be diffused into pure iron at 700°C. If the surface concentration is maintained at 0.16 wt% N, what will be the concentration (in weight percent) 2.2 mm from the surface after 8.1 h? The diffusion coefficient for nitrogen in iron at 700°C is 1.1 x 10 10 m2/s. 0.00 0.0000 0.55 0.5633 1.3 0.9340 0.025 0.0282 0.60 0.6039 1.4 0.9523 0.05 0.0564 0.65 0.6420 1.5 0.9661 0.10 0.1125 0.70 0.6778 1.6 0.9763 0.15 0.1680 0.75 0.7112 1.7 0.9838 0.20 0.2227 0.80 0.7421 1.8 0.9891 0.25 0.2763 0.85 0.7707 1.9 0.9928 0.30 0.3286 0.90 0.7970 2.0 0.9953 0.35 0.3794 0.95 0.8209 2.2 0.998 0.40 0.4284 1.0 0.8427 2.4 0.9993 45 0.4755 1.1 0.8802 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999 weight percent

Explanation / Answer

Recall that:

(Cx-Co)/(Cs-Co) = 1- erf(x/2sqrt(Dt))

so

x = 2.2 mm = 2.2*10^-3

D = 1.1*10^-10

t = 8.1 h = 8.1*3600 = 29160 s

1-erf( (2.2*10^-3) / (2*sqrt((1.1*10^-10)*29160))

1-erf ( 0.614)

erf(0.614) = 0.6040 approx

so

1-0.6040 = 0.396

(Cx-Co)/(Cs-Co) = 1- erf(x/2sqrt(Dt))

(Cx-Co)/(Cs-Co) =1-0.396

Cx-0)/(0.16 - 0) = 0.604

Cx = 0.16*0.604

Cx = 0.09664 wt%N

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