The rate constant of a reaction is 1.1 * 10-4 s-1 at 470 °c, and the activation energy is 264 kj/mol. what is the temperature of the reaction when the rate constant is equal to 4.36 * 10-3?

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Chemistry

30 June, 02:17

The rate constant of a reaction is 1.1 * 10-4 s-1 at 470 °c, and the activation energy is 264 kj/mol. what is the temperature of the reaction when the rate constant is equal to 4.36 * 10-3?

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Valeria Barry · Answer 1

Answer is: the temperature of the reaction is 546 °C.

k₁ = 1,1·10⁻⁴ 1/s.

T₁ = 470 °C = 743,15 K.

Ea = 264 kJ/mol = 264000 J/mol.

k₂ = 4,36·10⁻³ 1/s.

R = 8,314 J/K·mol.

T₂ = ?

Natural logarithm of Arrhenius' equation:

lnk₁ = lnA - Ea/RT₁.

lnk₂ = lnA - Ea/RT₂.

ln (k₂/k₁) = (Ea/R) · (1/T₁ - 1/T₂).

ln (4,36·10⁻³ 1/s / 1,1·10⁻⁴ 1/s) = (264000J/mol : 8,314 J/K·mol) · · (1/743,15K - 1/T₂).

3,68 = 31753,66 K · (0,00134 1/K - 1/T₂).

3,68 = 42,728 - 31753,66 · (1/T₂).

1/T₂ = 0,00122.

T₂ = 819 K = 546 °C.