Carbon is allowed to diffuse through a steel plate 13-mm thick. The concentrations of carbon at the two faces are 0.654 and 0.377 kg C/m3 Fe, which are maintained constant. If the preexponential and activation energy are 6.5 * 10-7 m2/s and 82 kJ/mol, respectively, calculate the temperature (in K) at which the diffusion flux is 3.2 * 10-9 kg / (m2-s).

Question

Maeve Henderson

Chemistry

19 May, 13:44

Carbon is allowed to diffuse through a steel plate 13-mm thick. The concentrations of carbon at the two faces are 0.654 and 0.377 kg C/m3 Fe, which are maintained constant. If the preexponential and activation energy are 6.5 * 10-7 m2/s and 82 kJ/mol, respectively, calculate the temperature (in K) at which the diffusion flux is 3.2 * 10-9 kg / (m2-s).

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Clarissa Holmes · Answer 1

T = 1177.95 K

Explanation:

Equation for diffusion flux is given as;

J = D (ΔC/Δx) e^ (Qd/RT)

Where J = 3.2 * 10^ (-9) kg/m². s

Qd = 82Kj/mol = 82,000 J/mol

D = 6.5 * 10^ (-7) m²/s

ΔC = 0.654 - 0.377 = 0.277 kg. C/m³

Δx = 13mm = 0.013m

R = 8.314 J/mol. k

Let's make T the subject of the equation;

T = Qd / (R In D (ΔC/JΔx))

T = 82,000 / (8.314 In 6.5 * 10^ (-7) (0.277 / (3.2 * 10^ (-9) x 0.013))

T = 82000 / (8.314In 4328.125) = 1177.95 K