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at 25 degrees celsius, a rate constant has the value 5.21*10^-8 L /Mol*s. If the activation...

at 25 degrees celsius, a rate constant has the value 5.21*10^-8 L /Mol*s. If the activation energy is 75.2 kj/mol, calculate the rate constant when the temperature is 50 degrees celsius.

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Answer #1

For this, we will use the following expression:

K = Aexp(-Ea/RT)

We do know the rate constant K1, T1 and Ea which is constant along with the value of A. We have two ways of solving this, one is with the first data at T = 25 °C (298 K) solve for A first and then, calculate K2. the other way is to do a substitution equation and solve directly for K2. I'm gonna use the second method:

K1 = Aexp(-Ea/RT1)
K2 = Aexp(-Ea/RT2)

K1/K2 = exp(-Ea/RT1 + Ea/RT2)
K1/K2 = exp[Ea/R(1/T2-1/T1)]
K2 = K1/exp[Ea/R(1/T2-1/T1)]

Solving now for K2:
K2 = 5.21x10-8 / exp[75200/8.3144(1/323 - 1/298)]
K2 = 5.21x10-8 / exp(-2.3491)
K2 = 5.45x10-7 L/mol s

Hope this helps

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