A series of experiments is carried out with compounds F and G. Using the data obtained, the rate equation for the reaction between the two compounds is deduced to be
rate=k[F]2[G] \text{rate} = k[\text{F}]^2[\text{G}] rate=k[F]2[G]In one experiment at 45 ∘C45\ ^\circ\text{C}45 ∘C, the initial rate of reaction is 8.64×10−4 mol dm−3 s−18.64 \times 10^{-4}\ \text{mol}\ \text{dm}^{-3}\ \text{s}^{-1}8.64×10−4 mol dm−3 s−1 when the initial concentration of F is 0.24 mol dm−30.24\ \text{mol}\ \text{dm}^{-3}0.24 mol dm−3 and the initial concentration of G is 0.15 mol dm−30.15\ \text{mol}\ \text{dm}^{-3}0.15 mol dm−3.
Calculate a value for the rate constant kkk at this temperature and give its units.
An equation that relates the rate constant, kkk, to the activation energy, EaE_{\text{a}}Ea, and the temperature, TTT, is
lnk=−EaRT+lnA \ln k = \frac{-E_{\text{a}}}{RT} + \ln A lnk=RT−Ea+lnAUse this equation and your answer from part 1 to calculate a value, in kJ mol−1\text{kJ}\ \text{mol}^{-1}kJ mol−1, for the activation energy of this reaction at 45 ∘C45\ ^\circ\text{C}45 ∘C.
For this reaction lnA=28.2\ln A = 28.2lnA=28.2.
The gas constant R=8.31 J K−1 mol−1R = 8.31\ \text{J}\ \text{K}^{-1}\ \text{mol}^{-1}R=8.31 J K−1 mol−1.
(If you were unable to complete part 1, you should use the value of 0.250.250.25 for the rate constant. This is not the correct value.)
