The energy of vacancy formation in palladium (Pd) is 1.5 eV. At 888C there is one vacancy for every million (106) atom sites. What temperature would be necessary to achieve a vacancy fraction of one for every thousand (10 3) atom sites?
Express your answer in degrees C:
1882
Thank you!
it's wrong....
Correction, it's right. WHY it is right though, that is the question. After all, who would want to know how to do a similar question where internet access is disallowed? Anyone who hasn't just stumbled onto the question, or already knows how, that's who.
To determine the temperature necessary to achieve a vacancy fraction of one for every thousand atom sites, we can use the concept of equilibrium vacancy concentration.
The equilibrium vacancy concentration (Cv) can be calculated using the Arrhenius equation:
Cv = Cexp(-Qv / (k * T))
Where:
- Cv is the equilibrium vacancy concentration
- C is a constant related to the number of vacancies produced per atom
- Qv is the energy of vacancy formation in electron volts (eV)
- k is the Boltzmann constant (8.617 x 10^(-5) eV/K)
- T is the temperature in Kelvin (K)
To find the temperature necessary, we need to rearrange the equation:
T = -Qv / (k * ln(Cv / C))
Let's substitute the given values:
Qv = 1.5 eV
C = 1 million atom sites (10^6)
Cv = 1 for every thousand atom sites (10^(-3))
T = -1.5 eV / (8.617 x 10^(-5) eV/K * ln(10^(-3) / 10^6))
Simplifying:
T = -1.5 eV / (8.617 x 10^(-5) eV/K * ln(10^(-9)))
T = -1.5 eV / (8.617 x 10^(-5) eV/K * (-20.723))
T = -1.5 eV / (-0.001784 eV/K)
T ≈ 840.96 K
To convert Kelvin to Celsius:
T (in °C) = T (in K) - 273.15
T ≈ 840.96 K - 273.15
T ≈ 567.81 °C
Therefore, the temperature necessary to achieve a vacancy fraction of one for every thousand atom sites is approximately 567.81 °C.