Question

In: Chemistry

The activation energy for the high temp conversion cyclo propane to propane is 270 killojoule per...

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.

Solutions

Expert Solution

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


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