The vacancy fraction of a particular metal is found to double as the temperature of the metal is increased from 700 degrees C to 850 degrees C. Calculate the enthalpy of vacancy formation for this metal. Express your answer in units of eV.
1963.4
not right
Could someone give the formula and where the data is inserted?
Anonymous, could you please explain the answer. the answer you mentioned is wrong
could any one help me regarding correct answer of this question
0.435
To calculate the enthalpy of vacancy formation for the metal, we need to use the equation:
ln(V2/V1) = ΔHv/kT
Where:
- V2 is the vacancy fraction at the higher temperature (850 degrees C)
- V1 is the vacancy fraction at the lower temperature (700 degrees C)
- ΔHv is the enthalpy of vacancy formation
- k is the Boltzmann constant, approximately 8.617333262145 x 10^-5 eV/K
- T is the absolute temperature in Kelvin (700 degrees C = 973 K, 850 degrees C = 1123 K)
To calculate the vacancy fraction, we need to use the equation:
V = exp(-ΔHv/kT)
Let's solve for ΔHv step by step:
1. Calculate the vacancy fraction at both temperatures:
- V1 = exp(-ΔHv/kT1)
- V2 = exp(-ΔHv/kT2)
2. Divide the equation for V2 by the equation for V1 to find the ratio:
- V2/V1 = (exp(-ΔHv/kT2))/(exp(-ΔHv/kT1))
= exp((-ΔHv/kT2) + (ΔHv/kT1))
= exp((-ΔHv/k)(1/T2 - 1/T1))
3. Solve for ΔHv:
- ln(V2/V1) = (-ΔHv/k)(1/T2 - 1/T1)
- ΔHv = -k * (T2 - T1) * ln(V2/V1)
Now we can plug in the values and calculate ΔHv:
- T1 = 973 K
- T2 = 1123 K
- V2/V1 = 2 (given that the vacancy fraction doubles)
ΔHv = - (8.617333262145 x 10^-5 eV/K) * (1123 K - 973 K) * ln(2)
Calculating this expression will give you the enthalpy of vacancy formation for the metal in units of eV.