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For the zero-order reaction \mathrm{A\rightarrow B+C,} initial concentration of ′A′ is 0.1 M. If ′A′ is 0.08 M after 10 minutes, then the half-life and completion time for the reaction, are respectively

Option: 1

25 and 50 min


Option: 2

50 and 100 min


Option: 3

150 and 300 min


Option: 4

70 and 35 min


Answers (1)

best_answer

At the time of completion (tc), the reaction is completed which means [A]t=0

From integrated law for zero order reaction, 

[A]t=[A]0−Kt.....eqn(1)

Substitute value of \mathrm{[A]_t}  in equation (1),

\mathrm{ 0=[A]_0-K t_c \\ }

\mathrm{ t_c=\frac{[A]_0}{K} }

Also we know,

\mathrm{ K=\frac{[A]_0-[A]_t}{t} }

At 10 minutes, [A]=0.08

\mathrm{ \therefore ~=\frac{0.1-0.08}{10} \\ }

\mathrm{ K=2 \times 10^{-3} \mathrm{M} \mathrm{min}^{-1} }
Thus,
\mathrm{ t_c=\frac{[A]_0}{K} \\ }

\mathrm{ \Rightarrow t_c=\frac{0.1 \mathrm{M}}{2 \times 10^{-3} \mathrm{M} ~\mathrm{min}^{-1}} \\ }
\mathrm{ \Rightarrow t_c=50 \mathrm{~min}}

Also half life period,

\mathrm{ t_{\frac{1}{2}}=\frac{[A]_0}{2 K} \\ }

\mathrm{ \Rightarrow t_{\frac{1}{2}}=\frac{0.1 \mathrm{M}}{2 \times 2 \times 10^{-3} \mathrm{Mmin}^{-1}} \\ }

\mathrm{ \Rightarrow t_{\frac{1}{2}}=25 \mathrm{~min} }

Posted by

Kuldeep Maurya

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