Consider an elementary first order reaction found to have an activation energy (EA) of 250 kJ/mole and a pre-exponential (A) of 1.7 x 1014 s–1.
(a) Determine the rate constant at T = 750°C.
(b) At what temperature will the reaction be three times as fast as at 750°C?
(c) What fraction of the reaction will be completed in a batch reactor at 300°C over a period of 10 minutes?
activation energy (EA) = 250 kJ/mole x 1000J/kJ
= 250*1000 J/mol
pre-exponential factor (A) = 1.7 x 10^14 s-1
Part a
T = 750 + 273 = 1023 K
From Arrhenius equation
Rate constant k = A x exp(-Ea/RT)
= 1.7 x 10^14 x exp(-250*1000/8.314*1023K)
= 1.7 x 10^14 x 1.72 x 10^-13
= 29.16 s-1
Part b
ln(k2/k1) = (Ea/R) (1/T1 - 1/T2)
ln 3 = (250*1000/8.314) (1/1023 - 1/T2)
1.0986 = 30069.76 (1/1023 - 1/T2)
(1/1023 - 1/T2) = 3.65 x 10^-5
1/T2 = (1/1023) - 3.65 x 10^-5
T2 = 1062.72 K
Part c
Time t = 10 min x 60s/min = 600 s
T = 300 + 273 = 573 K
Rate constant k = A x exp(-Ea/RT)
= 1.7 x 10^14 x exp(-250*1000/8.314*573K)
= 1.7 x 10^14 x 1.62 x 10^-23
= 2.75 x 10^-9 s-1
For the first order reaction
CA = CA0 exp(-kt)
CA = CA0 exp(-2.75*10^-9*600)
CA = CA0 x 0.999
CA/CA0 = 0.999
Consider an elementary first order reaction found to have an activation energy (EA) of 250 kJ/mole...
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