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 805.0 K? k=s^-1

Answer 1

Use the Arrhenius equation:

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

k1 = 6.1x10^-8 s^-1

k2 = ?

T1 = 600K

T2 = 805K

Ea = 262 kJ/mol

R = 8.314 J/Kmol = 0.008314 kJ/Kmol (change units to match those of Ea)

Plug and chug:

ln(k2/6.1x10^-8) = -262/0.008314 (1/805 - 1/600)

ln(k2/6.1x10^-8) = -31513 (0.00124 - 0.00167)

ln(k2/6.1x10^-8) = -31513 x -0.00043 = 13.55

ln k2 - ln 6.1x10^-8 = 13.55

ln k2 - 16.61 = 13.55

ln k2 = 30.16

k2 = 1.25x10¹³s^-1

(be sure to check the math)