The diffusion coefficient of silver (Ag) in copper (Cu) has the following values:
T (K) D (m2s-1)
923 5.42 x 10-16
1173 1.34 x 10-13
(a) Calculate the activation energy for diffusion of silver in copper. Express your answer in units of J/mol
To calculate the activation energy for diffusion of silver in copper, we can use the Arrhenius equation:
D = D0 * exp(-Q/RT)
Where:
D is the diffusion coefficient
D0 is the pre-exponential factor
Q is the activation energy
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
We can rearrange the equation to solve for Q:
Q = -RT * ln(D/D0)
Now, we will use the given values of diffusion coefficient at two different temperatures to find the activation energy.
At T1 = 923 K, D1 = 5.42 x 10^(-16) m^2/s
At T2 = 1173 K, D2 = 1.34 x 10^(-13) m^2/s
Let's solve for Q:
Q = - (8.314 J/(mol·K)) * (923 K) * ln((1.34 x 10^(-13) m^2/s) / (5.42 x 10^(-16) m^2/s))
Q = - (8.314 J/(mol·K)) * (923 K) * ln(2.46e2)
Q = 1.11 x 10^5 J/mol
Therefore, the activation energy for diffusion of silver in copper is 1.11 x 10^5 J/mol.