The rate constant for a first order reaction (based on the concentration of the single reactant) at 27∘C is observed to be 0.0404 s−1 and changes to 2.23 s−1 at 67∘C . Estimate the rate constant (in s−1 ) of the reaction at 47∘C
To estimate the rate constant of the reaction at 47°C, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a reaction with the temperature (T) using the following equation:
k2 / k1 = e^((Ea / R) * (1/T2 - 1/T1))
where:
k1 = rate constant at the initial temperature (27°C)
k2 = rate constant at the final temperature (67°C)
T1 = initial temperature in Kelvin (27 + 273 = 300 K)
T2 = final temperature in Kelvin (67 + 273 = 340 K)
Ea = activation energy of the reaction
R = gas constant (8.314 J/(mol·K))
We need to rearrange the equation to solve for k2, the rate constant at 47°C:
k2 = k1 * e^((Ea / R) * (1/T2 - 1/T1))
Now, let's plug in the given values:
k1 = 0.0404 s^(-1)
T1 = 300 K
T2 = 320 K (47 + 273 = 320 K)
R = 8.314 J/(mol·K)
Using the given activation energy is not provided in the question, it is not possible to calculate the exact rate constant at 47°C without this specific information. The activation energy would be needed to complete the calculation.