What Does Delta Gn Represent in the MIT Chemistry Course Equation?

[guiromero]

Homework Statement

Assume that a material has an activation energy for substitutional self diffusion migration energy of 250 kJ/mol and a Do prefactor of 100 mmm2/s. Calculate the following quantities for this material (express all your answers in units of mm2/s):
a) Calculate the vacancy diffusion coefficient at 750°C"

Relevant Equations

D = Do * exp(-Ea/RT)

Hello,

I have a doubt in a question from a chemistry MIT course:

My attempt is attached. The formula given in the lecture is D = Do * exp(-Ea + Delta Gn)/RT
However, they don't explain what Delta Gn is, I suppose it is Gibbs free energy, but as the statement doesn't give any other extra energy value despite of the activation energy (Ea), I didn't include Gn in the equation.

The correct answer is: 5.5e-8 mm2/s.

Does anyone have knowlege about this subject and would be able to help me?

Thanks a lot.

 

[Steve4Physics]

Homework Statement: Assume that a material has an activation energy for substitutional self diffusion migration energy of 250 kJ/mol and a Do prefactor of 100 mmm2/s. Calculate the following quantities for this material (express all your answers in units of mm2/s):
a) Calculate the vacancy diffusion coefficient at 750°C"

Not really familiar with this stuff but (in the absence of other replies) this might help a bit…

The question asks for the “vacancy diffusion coefficient”. It’s asking about how fast vacancies, not atoms, diffuse.

It seems that you have calculated the ‘usual’ diffusion coefficient (for atoms).

Maybe more information is needed to answer the question. Check that you have the complete/accurate question.

Also, a few other points which are worth noting:

Exponential terms are dimensionless (have no units) so there was no need to convert from mm²/s to m²/s and then back again to mm²/s.

You converted 1.7x10⁻¹⁷ m²/s to 1.7x 10⁻¹⁴ mm²/s. That’s incorrect.

The symbol for ‘kilo’ is lower case ‘k’. So kilojoule is kJ not KJ.

 

[Lord Jestocost]

If the diffusion occurs by a vacancy mechanism, the self-diffusion coefficient is given by the product of the vacancy diffusivity $D_V$ and the vacancy concentration $[V]: D_{self}=[V]D_V$