. Many drugs decompose in the body by a first order process. For the decompositi

Question

. Many drugs decompose in the body by a first order process. For the decomposition of an antibiotic in a person with a normal temperature (37oC) the half -life of the drug is 6 hours; for a person with a fever (40oC) the half-life of the drug is 5 hours.

i. Calculate the rate constants for the decomposition of the antibiotic at 37oC and at 40oC.

ii. If the person with the fever must take another pill when 2/3 of the first pill has decomposed, how many hours should she wait to take a second pill?

iii. What is the activation energy for the decomposition of the antibiotic, expressed in kilojoules/mol?

Explanation / Answer

i. for first order reaction

K at 37C = 0.693/t1/2   = 0.693/6 = 0.1155 hr-1.

K at 40C = 0.693/5 = 0.1386 hr-1.

ii.    K = 2.303/t log a/a-x

t = 2.303/0.1386 log 1/1-0.67

= 8.00 hr

iii. log(K2/K1) = Ea/2.303R[1/T1-1/T2]

log(0.1386/0.1155) = Ea/2.303*8.314[1/310-1/313]

Ea = 49.036 kj

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