# In the following reaction, how is the rate of appearance of the underlined product related to the rate of disapperance of the underlined reactant?${\mathrm{BrO}}_{3}^{-}\left(\mathrm{aq}\right)+5{\mathrm{Br}}^{-}\left(\mathrm{aq}\right)+6{\mathrm{H}}^{-}\left(\mathrm{aq}\right)\to 3{\mathrm{Br}}_{2}\left(\mathrm{t}\right)+3{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{t}\right)$

1. A

$\frac{\mathrm{d}\left[{\mathrm{Br}}_{2}\right]}{\mathrm{dt}}=-\frac{5}{3}\frac{d\left[B{r}^{-}\right]}{dt}$

2. B

$\frac{\mathrm{d}\left[{\mathrm{Br}}_{2}\right]}{\mathrm{dt}}=-\frac{d\left[B{r}^{-}\right]}{dt}$

3. C

$\frac{\mathrm{d}\left[{\mathrm{Br}}_{2}\right]}{\mathrm{dt}}=\frac{d\left[B{r}^{-}\right]}{dt}$

4. D

$\frac{\mathrm{d}\left[{\mathrm{Br}}_{2}\right]}{\mathrm{dt}}=-\frac{3}{5}\frac{d\left[B{r}^{-}\right]}{dt}$

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### Solution:

${\mathrm{BrO}}_{3}^{-}\left(\mathrm{aq}\right)+5{\mathrm{Br}}^{-}\left(\mathrm{aq}\right)+6{\mathrm{H}}^{-}\left(\mathrm{aq}\right)\to 3{\mathrm{Br}}_{2}\left(\mathrm{l}\right)+3{\mathrm{H}}_{2}\mathrm{O}\left(\mathrm{l}\right)$

$-\frac{1}{5}\frac{\mathrm{d}\left[{\mathrm{Br}}^{-}\right]}{\mathrm{dt}}=+\frac{1}{3}\frac{d\left[B{r}_{\mathit{2}}\right]}{dt}$

$⇒\frac{\mathrm{d}\left[{\mathrm{Br}}_{2}\right]}{\mathrm{dt}}=-\frac{3}{5}\frac{d\left[B{r}^{\mathit{-}}\right]}{dt}$

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