Question

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.

Answer 1

According to Arrhenius equation,

ln(k₂ / k₁) = (E_a / 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

E_a = 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