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If a first order reaction has a rate constant of 4.15 X 10-2 s-1 at a...

If a first order reaction has a rate constant of 4.15 X 10-2 s-1 at a temperature of 24.5oC, what would the value of k be if the reaction temperature was changed to 52oC given that the activation energy is 67.8 kJ/mol?

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Answer #1

Given, K1 = 4.15 x 10-2 s-1 , T1 = 24.50C = 297.5 K , T2 = 520C = 325 K, Ea = 67.8 KJ/mol = 67800 J/mol , K2 = ?

We have the relation as---

log K2/ K1 = Ea / 2.303 R [ 1/T1 - 1/T2]

=> log K2 / 4.15 x 10-2 s-1 = 67800 J/mol / 2.303 x 8.314 JK-1mol-1 [ 1/ 297.5 K - 1 / 325 K ]

=> log K2 / 4.15 x 10-2 s-1 = 67800 /19.147142 [ 325-297.5 / 297.5 x 325]

=> log K2 / 4.15 x 10-2 s-1 = 3540.998442x [ 27.5/96687.5]

=> log K2 / 4.15 x 10-2 s-1 = 97377.45716/96687.5

=> log K2 / 4.15 x 10-2 s-1 = 1.00713595

=> K2 / 4.15 x 10-2 s-1 = antilog ( 1.00713595]

=> K2 / 4.15 x 10-2 s-1= 10.16566866

=> K2 = 42.18752492 x 10-2 s-1

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