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Posted by on Saturday, December 15, 2012 at 4:19pm.

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 299.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 8655.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 20.5 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 - , Saturday, December 15, 2012 at 4:49pm

    Step 1:

    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)

    (0.5* 8655.0 - 8655.0 )/ ( 299.0 - 8655.0 )= erf(ξ)

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

    Step 3:

    t= d^2/4*D*ξ^2

    d=20.5 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 - , Saturday, December 15, 2012 at 5:33pm

    I'm getting:

    d = 0.205

    D = 0.0000003091

    0.205 / 0.0000003091 = 663215.78777094791329666774506632

    663215.78777094791329666774506632 / 60 / 60 = 184.22660771415219813796326251842

    I'm putting 184 in but it's wrong...any ideas where my math is going wrong?

  • Chemistry - , Saturday, December 15, 2012 at 10:24pm

    184 hours = 7.6 days ==> 1 week? The steel industry will collapse if this is the answer. LOL! Just by seeing the figure one can tell this does not make sense.

  • Chemistry - , Sunday, December 16, 2012 at 11:31am

    Someone please help!

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