the frequency factor and activation energy for a chemical reaction ate A=4.8 x 10^-12cm^3 and Ea=11.1kJ/mol at 327 K respectively. Determine the rate constant for this reaction at 327K
ln(k2/k1) = A*Ea*(1/T1 - /T2)/RT
Substitute and solve for k2. Remember to convert kJ to J.
To determine the rate constant (k) for a chemical reaction, you can use the Arrhenius equation:
k = A * exp(-Ea / (R * T))
where:
k is the rate constant
A is the frequency factor
Ea is the activation energy
R is the gas constant (8.314 J/mol·K)
T is the temperature in Kelvin
In the given problem, the frequency factor (A) is 4.8 x 10^-12 cm^3 and the activation energy (Ea) is 11.1 kJ/mol. We are asked to find the rate constant (k) at a temperature of 327 K.
First, we need to convert the activation energy from kJ/mol to J/mol:
Ea = 11.1 kJ/mol * 1000 J/1 kJ = 11,100 J/mol
Plugging the values into the Arrhenius equation:
k = (4.8 x 10^-12 cm^3) * exp(-11,100 J/mol / (8.314 J/mol·K * 327 K))
To calculate the rate constant, we need to evaluate the exponential term using the appropriate units:
exp(-11,100 J/mol / (8.314 J/mol·K * 327 K))
Now, let's calculate it step by step:
Step 1: Calculate the denominator of the exponential term:
8.314 J/mol·K * 327 K = 2,716.878 J/mol
Step 2: Calculate the exponent:
-11,100 J/mol / 2,716.878 J/mol = -4.088
Step 3: Evaluate the exponential term:
exp(-4.088)
Using a scientific calculator, you can find that the exponential term is approximately 0.0161.
Finally, multiply the frequency factor (A) by the exponential term to find the rate constant (k):
k = (4.8 x 10^-12 cm^3) * 0.0161
Calculating this multiplication, the rate constant is approximately:
k ≈ 7.728 x 10^-14 cm^3
So, the rate constant for the given reaction at 327 K is approximately 7.728 x 10^-14 cm^3.