Solve Diffusion Homework Problem: Vacancy Concentration at 687K

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Homework Help Overview

The discussion revolves around calculating the vacancy concentration in Zinc at a temperature of 687K, using the activation energy for vacancy formation. The original poster presents an equation for vacancy concentration but encounters issues with the exponent term resulting in zero.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the formula for vacancy concentration but questions the validity of their unit conversions and the expression of activation energy. Other participants suggest that the activation energy should be expressed per vacancy rather than per mole, and they discuss the implications of unit consistency.

Discussion Status

Participants are exploring different interpretations of the activation energy's units and how they relate to the formula. There is a suggestion that dividing the activation energy by Avogadro's number could resolve the unit mismatch, and some participants confirm this approach.

Contextual Notes

The original poster is working under the constraints of a homework assignment, which may impose specific requirements for unit usage and calculations. There is an ongoing examination of the assumptions regarding the activation energy's expression.

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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 definitely 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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I believe that Q in the formula needs to be expressed as activation energy per vacancy rather than activation energy per mole of vacancies.
 
TSny said:
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? Boltzmann constant is actually j/k*atom right? so the units would match then.
 
ScareCrow271828 said:
Thanks for the response. would dividing Q by Avogadro's number to get Q (kJ/atom) work? Boltzmann constant is actually j/k*atom right? so the units would match then.
Yes.
 

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