Answer:
Step-by-step explanation:
To calculate the number of vacancies per cubic meter per hour, we can use the following equation:
n = N exp(-Q/RT)
where:
- n is the number of vacancies per cubic meter per hour
- N is Avogadro's number (6.022 x 10^23 atoms/mol)
- Q is the activation energy for vacancy formation (in joules/mol)
- R is the gas constant (8.314 J/mol*K)
- T is the temperature in Kelvin
From the given information, we know that the equilibrium fraction of lattice sites that are vacant in silver at 700°C is 2x10^-4. This means that the number of vacancies per lattice site is also 2x10^-4. We can use this information to calculate the activation energy for vacancy formation:
2x10^-4 = exp(-Q/RT)
ln(2x10^-4) = -Q/RT
Q = -ln(2x10^-4) * R * T
At 700°C (973 K), this gives us:
Q = -ln(2x10^-4) * 8.314 J/mol*K * 973 K
Q = 2.06 eV
Now we can use the equation above to calculate the number of vacancies per cubic meter per hour:
n = N exp(-Q/RT)
n = 6.022 x 10^23 exp(-2.06 eV / (8.314 J/mol*K * 973 K))
n = 1.16 x 10^25 vacancies/m^3/hour
Therefore, the answer is O 1.16x 10^25.