How do you calculate activation energy per vacancy?

[ENgez]

the question is like this:
Calculate the activation energy needed to create a single vacancy in aluminium, given:
T= 500 Celsius
Density (500 Celsius) = 2.62 gr/cm³
n = 7.57e23 m^-3
Mw (Al) = 26.98 gr/mol

I know these Formulas:
n = N*exp (Q/kT) (k = boltzmann's constant)
N = Na*Density/Mw (Na = avogardo's number)

 

[drizzle]

Hey ENgez, welcome to PF

It seems like a direct question with a direct answer, just find Q [the activation energy required to create one vacancy].

 

[ENgez]

I did Find Q and it turned out to be 1.053 ev/mole or 16.85e-20 Joule/mole, but according to the answer sheet its supposed to be 72.33 kJoule/mole. Is it possible for the answer to be so big or is there a mistake in the sheet? And if there isn't, what am i doing wrong?

Btw, thanks drizzle :)

 

[Astronuc]

An energy value like 1.053 ev, should be on the basis of an atom.

 

[drizzle]

Did you convert Celsius to kelvin?

 

[ENgez]

I solved it :). Thank you Astronuc and drizzle. Astronuc, your post made me see that i had actually found the energy per atom, so all i had to do was to multiply it by avagardo's number to get it per mole.