Answer:
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.
