For a chemical reaction, the temperature dependence of the rate constant, kkk, is given by the Arrhenius equation:
k=Ae−EaRTk = A e^{-\frac{E_a}{RT}}k=Ae−RTEa
For the thermal gas-phase decomposition of dinitrogen pentoxide:
- the activation energy, Ea=104 kJ mol−1E_a = 104 \text{ kJ mol}^{-1}Ea=104 kJ mol−1
- the Arrhenius constant, A=4.80×1013 s−1A = 4.80 \times 10^{13} \text{ s}^{-1}A=4.80×1013 s−1
At temperature T1T_1T1, the rate constant is measured to be k=1.41×10−2 s−1k = 1.41 \times 10^{-2} \text{ s}^{-1}k=1.41×10−2 s−1.
a.[3]
Calculate the temperature, T1T_1T1, in Kelvin. (The gas constant, R=8.31 J K−1 mol−1R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}R=8.31 J K−1 mol−1)
b.[3]
With reference to the distribution of molecular kinetic energies shown in the diagram, explain why the rate of this decomposition is significantly faster at temperature T2T_2T2 than at T1T_1T1.