Question 14.5.2: The activation energy for the gas phase decomposition of t-b......

You are asked to calculate the rate constant for a reaction at a specific temperature.
You are given the activation energy for the reaction, the rate constant at a given temperature, and the temperature at which the rate constant is unknown.

First, create a table of the known and unknown variables.
T_{1} = 528 K                       T_{2} = 569 K
k_{1} = 3.80 × 10^{-4} s^{-1}     k_{2} = ?
E_{a} = 164 kJ/mol
Next, use the two-point version of the Arrhenius equation (Equation 14.8). The gas constant
can be expressed in units of kJ/K · mol.

ln\left(\frac{k_{2}}{3.80\times 10^{-4}\text{ s}^{-1}} \right) =\frac{-164\text{kJ/mol}}{8.3145\times 10^{-3}\text{kJ/K}\cdot \text{mol}} \left(\frac{1}{569\text{ K}}-\frac{1}{528 \text{ K}} \right)

ln\left(\frac{k_{2}}{3.80\times 10^{-4}\text{ s}^{-1}} \right) = 2.69

\frac{k_{2}}{3.80\times 10^{-4}\text{ s}^{-1}}=\text{e}^{2.69} = 14.8

k_{2} = 5.61 × 10^{-3}s^{-1}

Is your answer reasonable? At a higher temperature, the reaction is faster and the rate constant has increased.