Homework Help: Chemistry

Posted by Odesa on Saturday, December 15, 2012 at 8:30am.

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 211.5 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 6155.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 26.5 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 - Odessa, Saturday, December 15, 2012 at 8:32am
how to find erf??? ??? error function(z)
Chemistry - qwerty, Saturday, December 15, 2012 at 3:19pm
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)
Chemistry - Odesa, Saturday, December 15, 2012 at 4:40pm
Step 1:

(0.5* 6155.0 - 6155.0)/ ( 211.5 - 6155.0)= erf(ξ)

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

Step 3:

t= d^2/4*D*ξ^2

d=59.0 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 - jjj, Sunday, December 16, 2012 at 4:00am
how to do step 2??

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