A substance 'A' decomposes by a first order reaction starting initially with `[A]= 2.00M` and after 200 min, [A] becomes `0.15M`. For this reaction, `t1//2` is

Options

A. 53.72 min
B. 50.49 min
C. 48.45 min
D. 46.45 min

Answer

A

Explanation

Given initial concentration (a)=2.00 M, Time taken (t)= 200 min and final concentration (a-x)=0.15 M. For a first order reaction rate constant,
`k=(2.303)/(t)log (a)/(a-x)=(2.303)/(200)log""(2.00)/(0.15)`
`=(2.303)/(200) xx (0.301+0.824)=1.29 xx 10^(-2) min^(-1)`
Further
`(t_(1 // 2))=(0.693)/(k)=(0.693)/(1.29 xx 10^(-2))=53.72 min.`