Question

the following reaction has an activation energy of 262 kJ/mol. C4H8(g)->2C2H4(g). At 600 K the rate...

the following reaction has an activation energy of 262 kJ/mol. C4H8(g)->2C2H4(g). At 600 K the rate constant is 6.1*10^-8s^-1. What is the value of the rate constant at 765.0 K?

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Answer #1

Step 1: According to Arrhenius Equation, We can relate rate constants with activation energy

log(k2/k1) = (Ea / 2.303 R) x (T2 - T1 / T1 xT2) ------------------- (1)
Step 2: Given Datas

T1 = 600 K   K1 = 6.1 x 10-8

T2 = 765 K   K2 = ??

R = 8.314 Jmol-1 K-I
Ea = 262 kJ/mol which will be convert to J/mol because R is in J/mol K-1 so...
Ea = 262000 J mol-I K-I

Step 3: Substituting the values in Eq(1)

log(k2/ 6.1 x 10-8 s-1) = (262000 J mol-I K-I / 2.303 x8.314 J mol-I K-I) x (765K - 600 K / 600K x 765K)

log(k2) - log(6.1 x 10-8 s-1) = (13683.5) x (0.0003594)

log(k2) - log(6.1 x 10-8 s-1) = (13683.5) x (3.594 x 10-4)

log(k2) =  log(6.1 x 10-8 s-1) + (13683.5) x (3.594 x 10-4)

log(k2) =  log(6.1 x 10-8 s-1) + (49178.5x 10-4)

log(k2) = -7.2147 +4.9179

log(k2)= -2.2977

k2 = 0.005038 s-1

k2 = 5.038 x 10-3 s-1

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