Question

Nitrogen from gaseous phase is to be diffused into pure iron at 973 K. Surface is maintained at 0.1 wt% N, what will be the concentration 1 mm from the surface after 10 hours? diffusion coefficient at 700 C is 2.5E-11 m^2/s

Please show your work!

A) 0.46 wt%
B) 0.010 wt%
C) 0.1 wt%
D) 0.046 wt%

Answer 1

You are actually missing some important data to do this. I need the table of the erf argument to finish solve this. Use the following equation:

Cx - Co / Cs - Co = 1 - err[x/2(Dt)^1/2]

Now, Like I said, you miss some data, but let me help you as what are you going to do next.

first convert x from mm to m (1 mm is 0.001 m). then the time of hour to seconds (10 h is 36000 s) and calculate the factor:

0.001 / 2 * (2.5x10^-11 * 36000)^1/2 = 0.5270

With this value and with the reported value of erf (is a table) all you have to do then, is solve for Cx and assume that Cs is 0. let's suppose that the obtained value, after look in a table is 0.51

Cx - 0.1 / 0 - 0.1 = 0.51

Cx - 0.1 / -0.1 = 0.51

Cx - 0.1 = 0.51*0.1

Cx = -0.051 + 0.1

Cx = 0.049 %

This is something really close to one of the option, however, like I told you before, you need the value of the erf function to do this.

Hope this guide, helps.