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Question: In acidic medium, the rate of reaction between \[[BrO_3^ - ]\]and \([B{r^ - }]\) ions is given by th...

In acidic medium, the rate of reaction between [BrO3−][BrO_3^ - ]and [Br−][B{r^ - }] ions is given by the expression −d[BrO3−]dt=k[BrO3−][Br−][H+]2 - \dfrac{{d[BrO_3^ - ]}}{{dt}} = k[BrO_3^ - ][B{r^ - }]{[{H^ + }]^2}
It means:
(i) Rate constant of the reaction depends upon the concentration of H+{H^ + }ions
(ii) Rate of reaction is independent of the concentration of acid added
(iii) The change in pHpH of the solution will affect the rate of reaction
(iv) Doubling the concentration of H+{H^ + } ions will increase the reaction rate by 44 times.
A.Only (ii)
B.Only (iii)
C.Only (i) and (ii)
D.Only (iii) and (iv)

Explanation

Solution

The rate constant does not depend upon the initial concentration of the reactants. The rate of a reaction depends upon the concentration of the reactants. pHpH is the measurement of hydrogen ion concentration so, if [H+{H^ + }] changes pH will also change.

Complete step by step answer:
The rate constant of a reaction is equal to the rate of reaction when the concentration of each of the reactants is unity. The rate constant of a reaction has a definite value at a particular temperature. Its value increases with increase in temperature. It does not depend upon the initial concentrations of reactants. Therefore the rate constant of the reaction between [BrO3−][BrO_3^ - ] and [Br−][B{r^ - }] does not depend upon the concentration of H+{H^ + } ions.
The rate of the reaction rate is the rate of change of concentration of a reactant or a product with respect to time. The reaction rate at a particular instant depends upon the concentration of reactants at that instant.
The rate equation of the reaction of reaction between [BrO3−][BrO_3^ - ] and [Br−][B{r^ - }] is given as:
Rate == −d[BrO3−]dt=k[BrO3−][Br−][H+]2 - \dfrac{{d[BrO_3^ - ]}}{{dt}} = k[BrO_3^ - ][B{r^ - }]{[{H^ + }]^2}
So, the rate of the reaction is dependent on the concentration of acid [H+{H^ + }] added.
We know that, pH=−log⁡[H+]pH = - \log [{H^ + }], it means that pHpH depends on the concentration of H+{H^ + } ions and the rate of the reaction depends on the concentration of H+{H^ + }ions. Therefore, the change in pHpH of the solution will affect the rate of reaction.
Rate== −d[BrO3−]dt=k[BrO3−][Br−][H+]2 - \dfrac{{d[BrO_3^ - ]}}{{dt}} = k[BrO_3^ - ][B{r^ - }]{[{H^ + }]^2}
On doubling the concentration of H+{H^ + } ions, we get
Rate== −d[BrO3−]dt=k[BrO3−][Br−][2H+]2=4k[BrO3−][Br−][H+]2 - \dfrac{{d[BrO_3^ - ]}}{{dt}} = k[BrO_3^ - ][B{r^ - }]{[2{H^ + }]^2} = 4k[BrO_3^ - ][B{r^ - }]{[{H^ + }]^2}
Therefore, doubling the concentration of H+{H^ + } ions will increase the reaction’s rate by 44 times.

Hence, option (D) is the correct answer.

Note:
Rate constant also known as specific reaction rate is a measure of the rate of a reaction, higher the value of rate constant greater is the rate of the reaction. It is a constant of proportionality and is equal to the rate of reaction when the molar concentration of each of the reactants is unity. A particular reaction has a definite value of rate constant at a particular temperature. The value of rate constant for a particular reaction increases with an increase in temperature. Its units depend upon the overall order of the reaction.