General Chemistry

Question

The reaction

C4H8(g)⟶2C2H4(g)C4⁢H8⁡(g)⟶2⁢C2⁢H4⁡(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 800.0 K?

Answer 1

Arrhenius equation:

ln(k2/k1) = -Ea/R (1/T2 - 1/T1)

k1 = 6.1x10^-8s^-1

k2 = ?

T1 = 600K

T2 = 800K

Ea = 262 kJ/mol

R = 8.314 J/Kmol = 0.008314 kJ/Kmol (to keep units consistent with those of Ea)

Plug in values and solve for k2:

ln (k2/6.1x10^-8) = -262/0.008314 (1/800 - 1/600)

ln (k2/6.1x10^-8) = -31513 (0.00125 - 0.00167)

ln (k2/6.1x10^-8) = 13.24

k2/6.1x10^-8 = 5.624x10⁵

k2 = 9.22x10^-4s^-1

(be sure to check the math)