A reaction has a rate constant of 1.25×10−4 at 28 and 0.227 at 77. Determine activation barrier for reaction
What is the value of the rate constant at 18?
Use the Arrhenius equation and solve for Ea.
Use the Arrhenius equation a second time with the Ea determined in the first part along with either k1 or k2 and calculate k3 for 18 C.
To determine the activation barrier for the reaction, we can use the Arrhenius equation:
k = A * exp(-Ea/RT)
Where:
k is the rate constant
A is the pre-exponential factor
Ea is the activation energy
R is the gas constant
T is the temperature in Kelvin
Given that the rate constant is 1.25×10^(-4) at 28°C (which is 301 K) and 0.227 at 77°C (which is 350 K), we have two sets of values for k and T.
First, we need to convert the rate constants to the same unit. Let's convert the rate constant at 28°C to Kelvin:
k₁ = 1.25 * 10^(-4)
T₁ = 301 K
Next, let's convert the rate constant at 77°C to Kelvin:
k₂ = 0.227
T₂ = 350 K
Now we can rearrange the Arrhenius equation to solve for the activation energy (Ea):
ln(k₁/k₂) = (Ea/R) * (1/T₂ - 1/T₁)
Substituting the known values:
ln(1.25 * 10^(-4)/0.227) = (Ea/R) * (1/350 - 1/301)
Solving this equation will give us the value of (Ea/R). Then, we can multiply by the gas constant (R = 8.314 J/(mol·K)) to get the activation energy (Ea).