Isn't this the Arrhenius equation?
Post your work if you get stuck.
2NOCl(g) �¨ 2NO(g) + Cl2 (g)
has an activation energy of 100.0 kJ/mol and a rate constant at 350.0 K of 8.5 x 10-6 mol-1 L s-1. Determine the rate constant at 400 K.
Post your work if you get stuck.
k = Ae^(-Ea/RT)
Where:
k = rate constant at the desired temperature
A = frequency factor (pre-exponential factor)
Ea = activation energy
R = gas constant (8.314 J/mol∙K)
T = temperature in Kelvin
First, let's convert the activation energy from kJ/mol to J/mol:
Ea = 100.0 kJ/mol * 1000 J/1 kJ = 100,000 J/mol
Next, we'll convert the activation energy from J/mol to J/particle by dividing by Avogadro's number (6.022 x 10^23 particles/mol):
Ea = 100,000 J/mol / (6.022 x 10^23 particles/mol) = 1.661 x 10^-19 J/particle
Now, let's calculate the rate constant at 400 K using the Arrhenius equation:
k2 = A * e^(-Ea/RT2)
Where:
k2 = rate constant at 400 K
A = frequency factor (pre-exponential factor)
Ea = activation energy (in J/particle)
R = gas constant (8.314 J/mol∙K)
T2 = temperature at 400 K
Substituting the known values:
k2 = (8.5 x 10^-6 mol^-1 L s^-1) * e^(-1.661 x 10^-19 J/particle / (8.314 J/mol∙K * 400 K))
Now, let's calculate the rate constant at 400 K:
k2 = (8.5 x 10^-6 mol^-1 L s^-1) * e^(-1.661 x 10^-19 J/particle / (3325.6 J/mol∙K))
k2 ≈ (8.5 x 10^-6) * e^-4.989 x 10^-23
Using a calculator, we find:
k2 ≈ (8.5 x 10^-6) * 0.99999999995
k2 ≈ 8.5000000175 x 10^-6 mol^-1 L s^-1
Therefore, the rate constant at 400 K is approximately 8.5000000175 x 10^-6 mol^-1 L s^-1.
k = A * e^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor or the frequency factor
- e is the base of the natural logarithm (approximately 2.71828)
- Ea is the activation energy
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
Given:
- Activation energy (Ea) = 100.0 kJ/mol = 100000 J/mol (converted to J by multiplying by 1000)
- Rate constant (k) at 350 K = 8.5 x 10^(-6) mol^(-1) L s^(-1)
- Temperature (T) at 400 K
First, we convert the activation energy (Ea) to J/mol:
Ea = 100000 J/mol
Next, we rearrange the equation to solve for the pre-exponential factor (A):
A = k / e^(-Ea/RT)
Substituting the given values:
A = (8.5 x 10^(-6) mol^(-1) L s^(-1)) / e^(-100000 J/mol / (8.314 J/(mol·K) * 350 K))
Now, we can calculate the pre-exponential factor (A):
A ≈ 1.08 x 10^13 mol^(-1) L s^(-1)
Finally, we can plug in the new temperature (T = 400 K) into the Arrhenius equation to find the rate constant (k):
k = A * e^(-Ea/RT)
k = (1.08 x 10^13 mol^(-1) L s^(-1)) * e^(-100000 J/mol / (8.314 J/(mol·K) * 400 K))
Calculating the rate constant (k) at 400 K will give you the answer.