Question

The first order rate constant for the decomposition of ethyl iodide by the reaction

\[\ce{C2H5I_{(g)} -> C2H4_{(g)} + HI_{(g)}}\]

at 600 K is 1.60 × 10⁻⁵ s^−l. Its energy of activation is 209 kJ/mol. Calculate the rate constant of the reaction at 700 K.

Answer 1

Given:

k₁ = 1.60 × 10⁻⁵ s⁻¹

T₁ = 600 K, T₂ = 700 K

E_a = 209 kJ/mol = 209000 J/mol

R = 8.314 J K⁻¹ mol⁻¹

`ln(k_2/k_1) = E_a/R ((T_2 - T_1)/(T_1T_2))`

⇒ `ln(k_2/(1.60 xx 10^-5)) = 209000/8.314 ((700 - 600)/(600 xx 700))`

⇒ `ln(k_2/(1.60 xx 10^-5)) = 209000/8.314 xx 100/420000`

⇒ `ln(k_2/(1.60 xx 10^-5)) = 209000/8.314 xx 2.381 xx 10^-4`

⇒ `ln(k_2/(1.60 xx 10^-5)) = 25134.9 xx 2.381 xx 10^−4`

k₂​ = 1.60 × 10⁻⁵ × 398.8

≈ 6.38 × 10⁻³ s⁻¹ at 700 K