Question

The activation energy for the gas phase isomerization of cis-cyanostyrene is 193 kJ. cis-C6H-CH=CHCN—>trans-C H3CH=CHCN The rate constant at 686 K is 7.75*10-4 /s. The rate constant will be /s at 727 K. Submit Answer Retry Entire Group 9 more group attempts remaining

Answer 1

The Arrhenius equation is:

k = A e^{( − E_a/RT)}

This equation gives the relationship between rate constant and temperature.

Rate constant (k₁) at 686 K = 7.75 x 10⁻⁴ s⁻¹

Activation energy (E_a) = 193 kJ = 193000 J

We can write for a reaction at two different temperature:

k₁ = A e^{( − E_a/RT₁)}

k₂ = A e^{( − E_a/RT₂)}

so, (k₁/k₂) = e^{( − E_a/RT₁) − ( − E_a/RT₂)} = e^{(Ea/R) (1/T₂ − 1/T₁)}

taking log_e in both side we get,

ln (k₁/k₂) = (Ea/R) (1/T₂ − 1/T₁)

so, ln (7.75 x 10⁻⁴ s⁻¹ / k₂) = (193000 J / 8.314 J mol^-1 K^-1) (1/727 − 1/686) = 23213.85 x (−8.22 x 10⁻⁵) = −1.908

or, (7.75 x 10⁻⁴ s⁻¹ / k₂) = e^−1.908 = 0.148

or, k₂ = (7.75 x 10⁻⁴) / 0.148 = 5.23 x 10⁻³ s⁻¹

So, the rate constant at 727 K will be 5.23 x 10⁻³ s⁻¹