In: Chemistry
The activation energy for the high temp conversion cyclo propane to propane is 270 killojoule per moles it what temperature would the rate constant for the rxn be 10 times that of 500 degree celcius.
According to Arrhenius equation,
ln(k2 / k1) = (Ea / R) * (1/T1 - 1/T2)
where
k1 = initial rate constant
T1 = initial temperature = 500 oC = (500 + 273) K = 773 K
k2 = final rate constant
T2 = final temperature
Ea = activation energy = 270 kJ/mol = 270 x 103 J/mol
R = constant = 8.314 J/mol-K
Given : k2 / k1 = 10
Substituting the values,
ln(10) = (270 x 103 J/mol / 8.314 J/mol-K) * (1/773 K - 1/T2)
1/773 K - 1/T2 = ln(10) / (270 x 103 J/mol / 8.314 J/mol-K)
1/773 K - 1/T2 = 7.09 x 10-5 K-1
1.294 x 10-3 K-1 - 1/T2 = 7.09 x 10-5 K-1
1/T2 = 1.294 x 10-3 K-1 - 7.09 x 10-5 K-1
1/T2 = 1.223 x 10-3 K-1
T2 = 1/(1.223 x 10-3 K-1)
T2 = 817.8 K
T2 = 544.8 oC
Temperature is 544.8 oC