Solve Diffusion Homework Problem: Vacancy Concentration at 687K

[ScareCrow271828]

Homework Statement

The activation energy of vacany formation in Zinc is 72kj per mole. What is the vacancy concentration at 687k

Homework Equations

Nv=Nexp(-Q/kt)
N=p(Na/A)

The Attempt at a Solution

Seems very straight forward.
Although I keep getting zero for the exponent term.
Nv=(7,14g/cm^3)(6.02e23 atom/mole)/(65.382g/mol)xEXP((-72000J/mol/((1.3807E-23 J/k)(687k)=0

Something is definately fishy with the units. What am I missing? If I convert the Qv into eV/atom and use 8.61 eV/K I can get a number.

Thanks for your time.

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[TSny]

I believe that Q in the formula needs to be expressed as activation energy per vacancy rather than activation energy per mole of vacancies.

 

[ScareCrow271828]

I believe that Q in the formula needs to be expressed as activation energy per vacancy rather than activation energy per mole of vacancies.

Thanks for the response. would dividing Q by Avogadro's number to get Q (kJ/atom) work? Boltzman constant is actually j/k*atom right? so the units would match then.

 

[TSny]

Thanks for the response. would dividing Q by Avogadro's number to get Q (kJ/atom) work? Boltzman constant is actually j/k*atom right? so the units would match then.

Yes.