Question

Fill in the Blanks

The following hydrolysis reaction of an active drug follows standard first order kinetics.

Reaction: Drug + H_2O \rightarrow Hydrolyzed Drug

The initial concentration is 0.010 M and the rate constant for the reaction is 1.5E-3, the concentration 6.0E2 minutes after the patient has taken the drug is ________ (do not include units in your answer)

Based on the information above, the half life of this drug would be _________ (do not include units in your answer)

Answer 1

First order reaction given.

Drug + H_2O \rightarrow Hydrolyzed Drug

rate law for a first order reaction ,

rate , r = K[drug]

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To derive first order integral rate equation

r = K[drug]

let reactant , A= drug

Integration on both sides,

Homogenisation ,

Giving limits for both A and t

Ao = initial concetration of drug

A = cocnetration of drug at time t s.

k = rate constant

But we have ,

   and therefore

  

lnx = 2.303

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Ao = initial concetration of drug

= 0.010 M

A = cocnetration of drug at time t s.

= ?

k = rate constant

= 1.5e-3

= 0.0015/m

time , t= 6.0e2

= 6.0 * 100 minutes

= 600 minutes

0.3908 = log0.010- logA

logA = -2-0.3908

= -2.3908

A = 10^-2.3908

= 0.00406 M

Answer

Concetration of drug after given time = 0.004

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Half life of drug

substitute,

= 462 minutes

Answer

half life of drug =

462