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

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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