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the rate constant of a reaction is 4.0x10^-3 s^-1 at 25 degrees C, and the activation...

the rate constant of a reaction is 4.0x10^-3 s^-1 at 25 degrees C, and the activation energy is 33.6 kJ/mol. What is k at 75 degrees C? Enter in scientific notation

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Answer #1

Solution :-

Given

K1 = 4.0*10^-3 s-1 at 25 C + 273 = 298 K

K2 = ? at 75 C +273 = 348 K

Ea = 33.6 kJ per mol * 1000 J / 1 kJ = 33600 J per mol

Using the Arhenius equation we can find the rate constant at the given temperature

ln [K2/K1] = Ea/R [(1/T1)/(1/T2)]

ln [K2/4.0*10^-3 s-1] = 33600 J per mol / 8.314 J per mol K [(1/298)-(1/348)]

ln [K2/4.0*10^-3 s-1] = 1.9485

K2/4.0*10^-3 s-1 = antiln [1.9485]

K2/4.0*10^-3 s-1 = 7.02

K2 = 7.02* 4.0*10^-3 s-1

K2 = 2.8*10^-2 s-1

So the rate constant at 75 C is 2.8*10^-2 s-1

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