How do you calculate activation energy per vacancy?

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Discussion Overview

The discussion revolves around calculating the activation energy required to create a single vacancy in aluminium, with specific parameters provided, including temperature, density, and molecular weight. The focus is on the application of relevant formulas and the interpretation of results.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem and relevant formulas for calculating activation energy.
  • Another participant suggests that the question has a straightforward answer, indicating the need to find the activation energy Q.
  • A participant reports their calculated value of Q as 1.053 eV/mole but questions the discrepancy with an answer sheet that states 72.33 kJoule/mole.
  • There is a suggestion that the reported energy value should be based on an atom rather than a mole.
  • A participant prompts a check on the conversion from Celsius to Kelvin as a potential source of error.
  • A later reply indicates that the participant resolved their issue by realizing they had calculated energy per atom and needed to multiply by Avogadro's number to convert to per mole.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the calculated activation energy and the answer sheet's value. The discussion reflects uncertainty regarding the calculations and the appropriate units.

Contextual Notes

Limitations include potential confusion over unit conversions and the distinction between energy per atom versus energy per mole, which remains unresolved in the discussion.

ENgez
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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)
 
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Hey ENgez, welcome to PF :smile:

It seems like a direct question with a direct answer, just find Q [the activation energy required to create one vacancy].
 
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 :)
 
An energy value like 1.053 ev, should be on the basis of an atom.
 
Did you convert Celsius to kelvin?
 
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.
 

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