Homework Help: Chemistry

Posted by Joel on Friday, December 14, 2012 at 5:52am.

You wish to increase the carbon content of a slab of steel by exposing it to a carburizing atmosphere at elevated temperature. The carbon concentration in the steel before carburization is 379.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 6910.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 13.0 x 10-2 cm is one half the value of the carbon concentration at the surface. The diffusion coefficient of carbon in steel is 3.091 x 10-7 cm2/s at the carburizing temperature. Express your answer in hours.

DATA: Error Function Values
erf(ξ 0.6), use the approximation erf ξ = ξ
erf(1.0) = 0.84
erf(2.0) = 0.998

Chemistry - anonymous, Friday, December 14, 2012 at 6:04am
Please indicate the method of solving it. Not just the answer.
Chemistry - MIT2, Saturday, December 15, 2012 at 5:50am
CHEAT!

Do NOT help this person. They are trying to cheat in a midterm exam.
Chemistry - Ling, Saturday, December 15, 2012 at 6:14am
Step 1:

(0.5*6910.0 - 6910.0)/ (379.0 - 6910.0)= erf(ξ)

Step 2:
erf(ξ < 0.6), use the approximation erf ξ = ξ

Step 3:

t= d^2/4*D*ξ^2

d=13.0 x 10-2 cm
D=3.091 x 10-7 cm2/s

Step 4:
t in sec -> hours
Conversion seconds to hours is total/(60x60)
Chemistry - JoeBob, Saturday, December 15, 2012 at 3:34pm
I did it with this formula 3 times. I still did not get it.
Chemistry - qpt, Saturday, December 15, 2012 at 4:57pm
ξ= (0.5 * carbon concentration at the surface of the steel - carbon concentration at the surface of the steel)/ (carbon concentration in the steel before carburization - carbon concentration at the surface of the steel)

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