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  • Consider the given reactions, the hall life of <img alt="\mathrm{(A) \rightarrow t_{1 / 2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28A%29%20%5Crightarrow%20t_%7B1%20/%20

Consider the given reactions, the hall life of \mathrm{(A) \rightarrow t_{1 / 2}} is \mathrm{1.386 \times 10^{2}} hour, each of the reaction follow first order kinctics. If the distribution of B in the product mixture is \mathrm{50 \%}. The partial half of \mathrm{A} for conversion into \mathrm{B} is.

Option: 1

231 \mathrm{hr}


Option: 2

131 \mathrm{hr}


Option: 3

115.5 \mathrm{hr}


Option: 4

31 \mathrm{hr}


Answers (1)

best_answer

\mathrm{\frac{2 k_{1}}{2 k_{1}+3 k_{2}}=0.5 \mathrm{~mol}}
\mathrm{k_{1}+k_{2}=\frac{0.693}{1.386 \times 10^{2}}=5 \times 10^{-3} \mathrm{hr}^{-1}}

\mathrm{Solving \, \, \frac{k_{1}}{k_{2}}=\frac{2}{3}\, \&\: k_{1}=2 \times 10^{-3} \mathrm{hr}^{\prime}, k_{2}=3 \times 10^{-3} \mathrm{hr}^{-1}}
\mathrm{t_{1 / 2(A \rightarrow B)}=\frac{0.693}{k_{2}}=\frac{0.693}{3 \times 10^{-3}}=231 \mathrm{~h}}

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