What is pre-exponential factor for diffusion, because i have a problem with this equation.
D=D0*exp[-Ea/R*T]
where D=2*10^-13
Ea=2.9*10^-19 joules/atom
T=1009 K
How to find the pre-exponential ?
What you have is just D = D0*x where x is all that exponential stuff.
So, D0 = D/x
Of course, R is not specified. If it's R you are looking for, then just work it out like this:
exp[-Ea/R*T] = D/D0
-Ea/R*T = ln(D/D0)
R = -Ea*T/ln(D/D0)
Yeah, R is a constant.The gas constant.
But i can't calculate this D0.
The pre-exponential factor for diffusion, denoted as D0 in this equation, represents the diffusion coefficient when the activation energy (Ea) and temperature (T) are taken into account. To find the pre-exponential factor, we can rearrange the equation and solve for D0. Here's how you can do it step by step:
1. Start with the diffusion equation:
D = D0 * exp(-Ea / (R * T))
2. Substitute the given values into the equation:
D = 2 * 10^(-13) m^2/s
Ea = 2.9 * 10^(-19) J/atom
T = 1009 K
3. Rearrange the equation:
Divide both sides of the equation by exp(-Ea / (R * T)):
D / exp(-Ea / (R * T)) = D0
4. Calculate the exponential term:
Calculate exp(-Ea / (R * T)) using the exponential function and the given values of Ea and T. The value of R (the gas constant) is approximately 8.314 J/(mol·K):
exp(-Ea / (R * T)) = exp(-2.9 * 10^(-19) J/atom / (8.314 J/(mol·K) * 1009 K))
5. Convert the atomic units to molar units:
Since the value of Ea is given per atom, and R is in molar units, you need to convert Ea to J/mol. The Avogadro's number (approximately 6.022 × 10^23 mol^(-1)) can be used for this conversion:
Ea = 2.9 * 10^(-19) J/atom * (6.022 × 10^23 atom/mol)
6. Calculate the pre-exponential factor (D0):
Plug in the calculated values from steps 4 and 5 into the rearranged equation:
D0 = D / exp(-Ea / (R * T))
By following these steps, you can determine the pre-exponential factor (D0) for the given diffusion equation using the given values for D, Ea, and T.