5. The temperature dependence of the acid-catalyzed hydrolysis of penicillin is

Question

5. The temperature dependence of the acid-catalyzed hydrolysis of penicillin is Investigated, and the dependence of kr on temperature is given in the following table. What is the activation energy and Arrhenius pre-exponential factor for this branch of the hydrolysis reaction? Temperature TC) K1 (s) 22.2 27.2 7.0 x 10 9.8 x 10 1.6 x 10 2.0 x 10 33.7 38.0 6. Assuming that the pre-exponential factor remains constant, by how much would a catalyst have to decrease the activation energy of a reaction in order to increase its rate by 10-fold?

Explanation / Answer

Arhenius equation is K= Ko*e(-Ea/RT)

where K is rate constant, Ko = preexponential factor, Ea= activation energy and R= 8.314 J/mole.K, T is temperature in K ( T (K)= t(deg.c)+273

the Arheius equaton can also be written as

ln K= lnKo- Ea/RT

So a plot of lnK vs 1/T gives straight line whose slope is -Ea/R and intercept of lnKo.

from the equation of best fit, Ea/R= 6228, Ea= 6228*8.314 j/mole=51780 J/mole

lnKo= intercept = 13.83, K= 1014595

The Arhenius equation is K= 1014595*e(- 51780/RT),

let K1= rate constant in the absence of an enzyme, K2= rate constant in the presence of an enzyme

since pre-exponential factor remain the same. E2= Activation energy in the presence of an enzyme

wiring the Arheius equation in the presence and absence of an enzyme

K1= 1014595*e(-51780/RT), K2= 1014595*e(-E2/RT)

K2/K1= 10 ( given)= e(-E2/RT+ 51780/RT)

takin ln , 51780/RT- E2/RT= ln(10)

E2/RT = 51780/RT- ln(10) =51780/RT- 2.3

E2 =   51780- 2.3*RT

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