Question 14.5.3: Use the Arrhenius equation to determine Ea. For the gas phas......

You are asked to determine the activation energy for a reaction.
You are given the rate constants for the reaction at two different temperatures.
First, create a table of the known and unknown variables.
T_{1} = 470 K                            T_{2} = 508 K
k_{1} = 1.05 × 10^{-3} s^{-1}          k_{2} = 1.11 × 10^{-2} s^{-1}
E_{a} = ?

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\frac{k_{2}}{k_{1}} = \frac{-E_{a}}{R} = \left(\frac{1}{T_{2}}-\frac{1}{T_{1}} \right)

ln\left(\frac{1.11  \times  10^{-2}\text{ s}^{-1}}{1.05  \times  10^{-3}\text{ s}^{-1}} \right) = \frac{-E_{a}}{8.3145  \times  10^{-3}  \text{ kJ/K}  \cdot  \text{mol}} \left(\frac{1}{508  \text{ K} } -\frac{1}{470  \text{ K}} \right)

2.358 = \frac{-E_{a}}{8.3145  \times  10^{-3}  \text{ kJ/K}  \cdot  \text{mol}} \left(-1.59\times 10^{-4}\text{ K}^{-1}\right)

E_{a} = 123 kJ/mol