Question

In the reaction, \[BrO_{3}^{-}(aq)+5B{{r}^{-}}(aq)+6{{H}^{+}}(aq)\to 3B{{r}_{2}}(l)+3{{H}_{2}}O(l)\]. The rate of appearance of bromine\[(B{{r}_{2}})\] is related to the rate of disappearance of bromide \[(B{{r}^{-}})\] ions as following:
A. \[\dfrac{d[B{{r}_{2}}]}{dt}=\dfrac{2}{5}\dfrac{d[B{{r}^{-}}]}{dt}\]
B. \[\dfrac{d[B{{r}_{2}}]}{dt}=-\dfrac{3}{5}\dfrac{d[B{{r}^{-}}]}{dt}\]
C. \[\dfrac{d[B{{r}_{2}}]}{dt}=-\dfrac{5}{3}\dfrac{d[B{{r}^{-}}]}{dt}\]
D. \[\dfrac{d[B{{r}_{2}}]}{dt}=+\dfrac{5}{3}\dfrac{d[B{{r}^{-}}]}{dt}\]

Answer 1

Hint: To solve this question, you need to apply the concepts of chemical kinetics. The rate of disappearance is the rate by which the reactant diminished and product is produced. Rate of production of products is known as the rate of appearance.

Complete step by step answer:
The general formula for appearance or disappearance of a compound is calculated by the formula –
\[\pm \dfrac{\text{1}}{\text{stoichiometric coefficient}}\text{x}\dfrac{\text{reactant/product}}{\text{time}}\]
According to the question, we need to find the rate of appearance of bromine\[(B{{r}_{2}})\]related to the rate of disappearance of bromide\[(B{{r}^{-}})\]ions, in the reaction –
\[BrO_{3}^{-}(aq)+5B{{r}^{-}}(aq)+6{{H}^{+}}(aq)\to 3B{{r}_{2}}(l)+3{{H}_{2}}O(l)\]

As we can see, 5 moles of bromide ion react to produce 3 moles of bromine.

Rate of appearance of bromine\[(B{{r}_{2}})\]\[=+\dfrac{\text{1}}{\text{stoichiometric coefficient}}\text{x}\dfrac{\text{product}}{\text{time}}\]

Rate of appearance of bromine\[(B{{r}_{2}})\]\[=+\dfrac{\text{1}}{\text{3}}\text{x}\dfrac{\text{d }\!\![\!\!\text{ B}{{\text{r}}_{\text{2}}}\text{ }\!\!]\!\!\text{ }}{\text{dt}}\]

Rate of disappearance of bromide\[(B{{r}^{-}})\]ions = \[-\dfrac{\text{1}}{\text{stoichiometric coefficient}}\text{x}\dfrac{\text{reactant}}{\text{time}}\]

Rate of disappearance of bromide\[(B{{r}^{-}})\]ions\[=-\dfrac{\text{1}}{\text{5}}\text{x}\dfrac{\text{d }\!\![\!\!\text{ B}{{\text{r}}^{\text{-}}}\text{ }\!\!]\!\!\text{ }}{\text{dt}}\]

The rate of appearance and disappearance is always the same.

Therefore, \[-\dfrac{\text{1}}{\text{5}}\dfrac{\text{d }\!\![\!\!\text{ B}{{\text{r}}^{\text{-}}}\text{ }\!\!]\!\!\text{ }}{\text{dt}}=+\dfrac{\text{1}}{\text{3}}\dfrac{\text{d }\!\![\!\!\text{ B}{{\text{r}}_{\text{2}}}\text{ }\!\!]\!\!\text{ }}{\text{dt}}\]
\[\Rightarrow \dfrac{\text{d }\!\![\!\!\text{ B}{{\text{r}}_{\text{2}}}\text{ }\!\!]\!\!\text{ }}{\text{dt}}=-\dfrac{3}{\text{5}}\dfrac{\text{d }\!\![\!\!\text{ B}{{\text{r}}^{\text{-}}}\text{ }\!\!]\!\!\text{ }}{\text{dt}}\]
Therefore, the answer is – option (b).

Additional Information:
The word kinetic is derived from the Greek word ‘kinesis’ which means movement.

Note: As we can see, the rate of a reaction depends on concentration and time. Therefore, it is expressed in terms of concentration / time. If concentration is in mol/L, the unit of rate becomes \[mol{{L}^{-1}}{{s}^{-1}}\]. However, in case of gases, concentration is expressed in terms of its partial pressure. The rate becomes atm/s.