The reaction C4H8(g) → 2 C2H4(g)

Question

The reaction

C4H8(g) → 2 C2H4(g)

has an activation energy of 262 kJ/mol. At 600.0 K, the rate constant, k, is 6.1 x 10^-8 s^1. What is the value of the rate constant 750.0 K?

k = ____ s^-1

Answer 1

Arrhenius equation:

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

k1 = 6.1x10^-8 s^-1

k2 = ?

Ea = 262 kJ / mol

R = 8.314 J/Kmol = 0.008314 kJ / Kmol (changed units to agree with units of Ea)

T1 = 600K

T2 = 750K

ln (k2/6.1x10^-8) = -262/0.008314(1/750 - 1/600)

ln (k2/6.1x10^-8) = -31,513 (0.001333 - 0.001666)

ln (k2/6.1x10^-8) = -31,513 (-0.000333) = +10.49

ln k2 - ln 6.1x10^-8 = 10.49

ln k2 = 10.49 + ln 6.1x10^-8

ln k2 = 10.49 -16.61 = -6.12

k2 = 2.19x10^-3 s^-1

(be sure to check all of the math)