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31 August, 20:05

Calculate the diffusion coefficient for magnesium in aluminum at 500oC. Pre-exponential and activation energy values for this system are 1.2 x 10-4m2/s and 144,000 J/mole respectively. R = 8.314 J/mol K

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  1. 31 August, 23:14
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    The diffusion coefficient for magnesium in aluminum at the given conditions is 2.22x10⁻¹⁴m²/s.

    Explanation:

    The diffusion coefficient represents how easily a substance (solute, e. g.: magnesium) can move through another substance (solvent, e. g.: aluminum).

    The formula to calculate the diffusion coefficient is:

    D=D₀. exp ( - EA/R. T)

    Each term of the formula means:

    D: diffusion coefficient

    D₀: Pre-exponential factor (it depends on each particular system, in this case the magnesium-aluminium system)

    EA: activation energy

    R: gas constant

    T: temperature

    1st) It is necessary to make a unit conversion for the temperature from °C to K, because we need to solve the problem according to the units of the gas constant (R) to assure the units consistency, so:

    Temperature conversion from °C to K: 500 + 273 = 773 K

    2nd) Replace the terms in the formula and solve:

    D=D₀. exp ( - EA/R. T)

    D=1.2x10⁻⁴m²/s. exp[ - 144,000 J/mole / (8.314 J/mol K. 773K) ]

    D=1.2x10⁻⁴m²/s. exp (-22.41)

    D=1.2x10⁻⁴m²/s. 1.85x10⁻¹⁰

    D = 2.22x10⁻¹⁴m²/s

    Finally, the result for the diffusion coefficient is 2.22x10⁻¹⁴m²/s.
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