Question

The first-order rearrangement of CH3NC is measured to have a rate constant of 3.61 × 10–15 s–1 at 298 K and a rate constant of 8.66 × 10–7 s–1 at 425 K. Determine the activation energy for this reaction.

Answer 1

The activation energy for this reaction, Ea = 159.98 kJ/mol

Step-by-step explanation:

Using the Arrhenius equation as:

`ln\frac {K_2}{K_1}=-\frac {E_a}{R}* (\frac {1}{T_2}-\frac {1}{T_1})`

Where, Ea is the activation energy.

R is the gas constant having value 8.314 J/K.mol

K₂ and K₁ are the rate constants

T₂ and T₁ are the temperature values in kelvin.

Given:

K₂ = 8.66×10⁻⁷ s⁻¹ , T₂ = 425 K

K₁ = 3.61×10⁻¹⁵ s⁻¹ , T₁ = 298 K

Applying in the equation as:

`ln\frac {8.66* 10^(-7)}{3.61* 10^(-15)}=-\frac {E_a}{8.314}* (\frac {1}{425}-\frac {1}{298})`

Solving for Ea as:

Ea = 159982.23 J /mol

1 J/mol = 10⁻³ kJ/mol

Ea = 159.98 kJ/mol