Answer: Activation energy
[tex]E_{a}=110.243 kJ/mol[/tex]
Explanation:
Arrhenius expression activation energy is given by
[tex]k=Ae^{\frac{-E_{a}}{RT}[/tex]
where [tex]k[/tex] is the rate constant, [tex]A[/tex] is the pre-exponential factor
[tex]R[/tex]=The gas constant is 8.314 J / mol·K and [tex]T[/tex] is temperature
By substituting the values in the above equation we get two equations
[tex]k_{1}=Ae^{\frac{-E_{a}}{RT_{1}}}\\9\times 10^{-14}=Ae^{\frac{-E_{a}}{8.314\times 600}}...................(1)\\k_{2}=Ae^{\frac{-E_{a}}{RT_{2}}}\\6\times 10^{-11}=Ae^{\frac{-E_{a}}{8.314\times 850}}...................(2)[/tex]
by solving 1 and 2, we get
[tex]1.5\times 10^{-3}=\frac{e^{\frac{-E_{a}}{8.314\times 600}}}{e^{\frac{-E_{a}}{8.314\times 850}}}\\1.5\times 10^{-3}\tiimes {e^{\frac{-E_{a}}{8.314\times 850}}={e^{\frac{-E_{a}}{8.314\times 600}}\\ln(1.5\times 10^{-3})\tiimes+ln( {e^{\frac{-E_{a}}{8.314\times 850}})=ln({e^{\frac{-E_{a}}{8.314\times 600}})\\-6.50+ -E_{a}\div(8.314\times 850)={\frac{-E_{a}}{8.314\times 600}\\E_{a}=110.243 kJ/mol[/tex]
