The reaction C4H8(g)⟶2C2H4(g) has an activation energy of 262 kJ/mol. At 600.0 K, the rate constant, 𝑘, is 6.1×10−8 s−1. What is the value of the rate constant at 830.0 K?

Question

The reaction

C4H8(g)⟶2C2H4(g)C4H8(g)⟶2C2H4(g)

has an activation energy of 262 kJ/mol.262 kJ/mol. At 600.0 K,600.0 K, the rate constant, 𝑘,�, is 6.1×10−8 s−1. What is the value of the rate constant at 830.0 K?

Answer 1

Arrhenius equation:

ln(k₂/k₁) = -Ea/R(1/T₂-1/T₁)

k₁ = 6.1x10^-8s^-1

k₂ = ?

Ea = 262 kJ/mol

R = 8.314 J/Kmol = 0.008314 kJ/Kmol (be sure to change units to agree with those of Ea)

T₁ = 600K

T₂ = 830K

Solving for k₂:

ln(k₂/6.1x10^-8) = -(262/0.008314)(1/830 - 1/600)

ln(k₂/6.1x10^-8) = -31,513 (0.00120 - 0.00167)

ln(k₂/6.1x10^-8) = 14.81

(k₂/6.1x10^-8) = 2706346

k₂ = 0.165 s^-1

(be sure to check all of the math)