A) 0.383 min
B) 23.1 min
C) 8.73 min
D) 7.53 min
Correct Answer: B
Solution :
For the first order reaction \[\text{Rate}\left( \frac{dx}{dt} \right)=k[A]\] \[[A]\to \] concentration of reactant \[k\to \]rate constant Given that \[\frac{dx}{dt}=1.5\times {{10}^{-2}}mol\,{{L}^{-1}}\,{{\min }^{-1}}\] \[k=?\]and \[[A]=0.5\,M\] \[\therefore \] \[1.5\times {{10}^{-2}}=k\times 0.5\] \[\therefore \] \[k=\frac{1.5\times {{10}^{-2}}}{0.5}=3\times {{10}^{-2}}{{\min }^{-1}}\] For first order reaction, Half-life period, \[{{t}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{3\times {{10}^{-2}}}\] \[=23.1\text{ }min\]
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