Question
Which of the following expressions is correct for the rate of reaction given below?
$$5Br_{\left( {aq} \right)}^ - + BrO_{3\left( {aq} \right)}^ - + 6H_{\left( {aq} \right)}^ + \to $$ $$3B{r_{2\left( {aq} \right)}} + 3{H_2}{O_{\left( l \right)}}$$
A.
$$\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} = 5\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}}$$
B.
$$\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} = \frac{6}{5}\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}}$$
C.
$$\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} = \frac{5}{6}\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}}$$
D.
$$\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} = 6\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}}$$
Answer :
$$\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} = \frac{5}{6}\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}}$$
Solution :
$${\text{For the reaction,}}$$
$$5Br_{\left( {aq} \right)}^ - + BrO_{3\left( {aq} \right)}^ - + 6H_{\left( {aq} \right)}^ + \to $$ $$3B{r_{2\left( {aq} \right)}} + 3{H_2}{O_{\left( l \right)}}$$
$$\eqalign{
& {\text{Rate}} = \frac{{ - 1}}{5}\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = - \frac{{\Delta \left[ {BrO_3^ - } \right]}}{{\Delta t}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{ - 1}}{6}\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}} \cr
& \therefore \,\,\frac{{\Delta \left[ {B{r^ - }} \right]}}{{\Delta t}} = \frac{5}{6}\frac{{\Delta \left[ {{H^ + }} \right]}}{{\Delta t}} \cr} $$