Question

In: Chemistry

An uncatalyzed reaction has a rate of 4.4 x 10-7 s–1 at room temperature (25 °C)....

An uncatalyzed reaction has a rate of 4.4 x 10-7 s–1 at room temperature (25 °C). When an enzyme is added the rate is 3.3 x 104 s–1. If the height of the activation barrier for the uncatalyzed rate is 28 kcal/mol, what is the height of the activation barrier for the catalyzed rate? Report your answer in terms of kcal/mol to the nearest tenths. Also, assume the pre-exponential terms for the uncatalyzed and catalyzed reactions are the same.

Expert Solution

According to Arrhenius equation,

where is the rate constant, is pre-exponential term, is the activation energy (or energy barrier) and is the temperature.

Let, for the uncatalyzed reaction the equation be

and for the catalyzed reaction the equation be

where we assumed that in both the cases the pre-exponential terms are the same.

Now if we divide (ii) by (i),

Taking natural log,

Thus the height of the activation barrier for the catalyzed reaction is 13.2 kcal/mol.

queen_honey_blossom answered 2 years ago

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