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