The anticancer drug cis-platin hydrolyzes in water with a rate constant of 1.5 × 10−3 min−1 at pH 7.0 and 25°C. Calculate the half-life for the hydrolysis reaction under these conditions. If a freshly prepared solution of cis-platin has a concentration of 0.053 M, what will be the concentration of cis-platin after 5 halflives? after 10 half-lives?
a) t1/2=0.693/k= 0.693/(1.5*10-3 min-1) =4.6*102 minutes
b) After 5 half-lives, the remaining concentration of cis-platin will be as follows:
0.053M/25 =0.053M/32 =0.0017M
After 10 half-lives, the remaining concentration of cis-platin will be as follows:
0.053M/210 =0.053M/1024= 5.2*10-5M
c) The % completion after 5 half-lives= {(0.053-0.0017)M/0.053M} *100%
=97%
The % completion after 10 half-lives= {(0.053-5.2*10-5)M/0.053M}*100%
=100%
Therefore, the first-order chemical reaction is 97% complete after 5 half-lives and 100% complete after 10 half-lives.
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