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

• Chemistry
• guiromero
In summary: So the self-diffusion coefficient for a material with an activation energy of 250 kJ/mol and a Do concentration of 100 mm²/s is: ##D_{self} = D_V*(250*100)/(RT*100)##. So the self-diffusion coefficient at 750°C is: ##D_{self} = D_V*(750*100)/(RT*100)##.
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.

Thanks a lot.

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guiromero said:
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).

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.

BvU
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##

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