The reaction,
cyclopropane propene (isomerization),
was observed to have rate constants k = 0.000213 s-1 at 477 °C and k = 0.0328 s-1 at 577 °C. What is the value of Ea expressed in kJ mol-1? Round your answer to 3 significant figures.
Plug your numbers into the Arrhenius equation and solve for Ea.
i don't get the right answer. Plus arent we missing A?
I use ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
Don't forget that Ea is in Joules, R = 8.314 and T must be in Kelvin.
Please for the love of god explain how i do the last bit of this equation on the calculator
To determine the value of Ea (activation energy) expressed in kJ mol-1, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a chemical reaction to the temperature (T) and the activation energy (Ea) of the reaction:
k = A * e^(-Ea/RT)
Where:
- k is the rate constant of the reaction.
- A is the pre-exponential factor, which represents the frequency of successful collisions between reactant molecules.
- Ea is the activation energy.
- R is the gas constant (8.314 J/mol∙K).
- T is the absolute temperature in Kelvin.
Given that the reaction rate constants are k = 0.000213 s-1 at 477 °C (750 K) and k = 0.0328 s-1 at 577 °C (850 K), we can set up two equations using the Arrhenius equation:
For the first temperature:
0.000213 s-1 = A * e^(-Ea/(8.314 J/mol∙K * 750 K))
For the second temperature:
0.0328 s-1 = A * e^(-Ea/(8.314 J/mol∙K * 850 K))
To determine the activation energy (Ea), we can take the ratio of the two equations:
(0.0328 s-1)/(0.000213 s-1) = e^(-Ea/(8.314 J/mol∙K * 850 K)) / e^(-Ea/(8.314 J/mol∙K * 750 K))
Simplifying:
(0.0328 s-1)/(0.000213 s-1) = e^(-Ea/(8.314 J/mol∙K)) * (e^(750 K/(8.314 J/mol∙K)) / e^(850 K/(8.314 J/mol∙K)))
Taking the natural logarithm (ln) of both sides to remove the exponential term:
ln((0.0328 s-1)/(0.000213 s-1)) = -Ea/(8.314 J/mol∙K) + (750 K - 850 K)/(8.314 J/mol∙K)
Simplifying further:
ln((0.0328 s-1)/(0.000213 s-1)) = -Ea/(8.314 J/mol∙K) - 120 K/(8.314 J/mol∙K)
Now, we can rearrange the equation to solve for Ea:
Ea = -8.314 J/mol∙K * (ln((0.0328 s-1)/(0.000213 s-1)) + 120 K)
Finally, we can convert the activation energy from J/mol to kJ/mol by dividing by 1000:
Ea = (-8.314 J/mol∙K * (ln((0.0328 s-1)/(0.000213 s-1)) + 120 K)) / 1000
Evaluating this equation using the given data will give you the value of Ea expressed in kJ mol-1, rounded to 3 significant figures.