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 780.0 K?

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 = 780K

ln (k2/6.1x10^-8) = -262/0.008314(1/780 - 1/600)

ln (k2/6.1x10^-8) = -31,513 (0.001282 - 0.001666)

ln (k2/6.1x10^-8) = -31,513 (-0.000384) = +12.10

ln k2 - ln 6.1x10^-8 = 12.10

ln k2 = 12.10 + ln 6.1x10^-8

ln k2 = 12.10 -16.61 = -4.51

k2 = 0.0110 s^-1

(be sure to check all of the math)