For the reaction $3 \mathrm{BrO}^{-} ightarrow \mathrm{BrO}_{3}^{-}+2 \mathrm{Br}$ in alkaline aqueous…

For the reaction $3 \mathrm{BrO}^{-} ightarrow \mathrm{BrO}_{3}^{-}+2 \mathrm{Br}$ in alkaline aqueous solution, the value of the second order (in $\mathrm{BrO}^{-}$) rate constant at $80^{\circ} \mathrm{C}$ in the rate law $-\Delta\left[\mathrm{BrO}^{-}ight] / \Delta \mathrm{t}$ was found to be $0.056 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$. Rate constant when the rate law is written for $\frac{\Delta\left[\mathrm{BrO}_{3}^{-}ight]}{\Delta \mathrm{t}}$ is
  1. $0.056 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
  2. $\frac{0.056}{3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
  3. $0.056 \times \frac{2}{3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$
  4. $0.028 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$

Solution

\(-\frac{1}{3} \frac{d\left[\mathrm{BrO}^{-}ight]}{d t}=\frac{d\left[\mathrm{BrO}_3^{-}ight]}{d t}=+\frac{1}{3} \frac{d\left[\mathrm{Br}^{-}ight]}{d t}\) So, Rate \(=1 / 3 \times 0.056\) .

Asked in: JEE-TOPICTESTS-CHEMISTRY

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