Q52 / 160 · JIPMER 2012 · Chemistry

For a zero order reaction

  • Correct answer
    A
    $t_{1 / 2} \propto R_0$
  • B
    $t_{1 / 2} \propto 1 / R_0$
  • C
    $t_{1 / 2} \propto R_0^2$
  • D
    $t_{1 / 2} \propto 1 / R_0^2$

Solution

For a zero order reaction rate, $-\frac{d[R]}{d t}=k$ On integrating, we get $[R]=-k t+[C]$ When $t=0,[R]=\left[R_0\right]$ $\therefore \quad[C]=\left[R_0\right]$ $\therefore \quad[R]=-k t+\left[R_0\right]$ When, $t=t_{1 / 2},[R]=\frac{\left[R_0\right]}{2}$ $\therefore \quad \frac{\left[R_0\right]}{2}-\left[R_0\right]=-k t_{1 / 2}$ $\therefore \quad t_{1 / 2}=\frac{\left[R_0\right]}{2 k}$ $t_{1 / 2} \propto\left[R_0\right]$

Hence, the correct answer is option: 'A'.

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