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Question: Which of the following expressions is correct for the rate of reaction given below? \[5B{r^{-}}_{(a...

Which of the following expressions is correct for the rate of reaction given below?

5Br−(aq)+BrO−3(aq)+6H+(aq)→3Br2(aq)+3H2O(l)5B{r^{-}}_{(aq) + Br{O^{-}}_{3(aq)}} + 6{H^{+}}_{(aq)} \rightarrow 3Br_{2(aq)} + 3H_{2}O_{(l)}

A

Δ[Br−]Δt=5Δ[H+]Δt\frac{\Delta\lbrack Br^{-}\rbrack}{\Delta t} = 5\frac{\Delta\lbrack H^{+}\rbrack}{\Delta t}

B

Δ[Br−]Δt=65Δ[H+]Δt\frac{\Delta\lbrack Br^{-}\rbrack}{\Delta t} = \frac{6}{5}\frac{\Delta\lbrack H^{+}\rbrack}{\Delta t}

C

Δ[Br−]Δt=56Δ[H+]Δt\frac{\Delta\lbrack Br^{-}\rbrack}{\Delta t} = \frac{5}{6}\frac{\Delta\lbrack H^{+}\rbrack}{\Delta t}

D

Δ[Br−]Δt=6Δ[H+]Δt\frac{\Delta\lbrack Br^{-}\rbrack}{\Delta t} = 6\frac{\Delta\lbrack H^{+}\rbrack}{\Delta t}

Answer

Δ[Br−]Δt=56Δ[H+]Δt\frac{\Delta\lbrack Br^{-}\rbrack}{\Delta t} = \frac{5}{6}\frac{\Delta\lbrack H^{+}\rbrack}{\Delta t}

Explanation

Solution

For the reaction,

5Br−(aq)+BrO−3(aq)+6H+(aq)→3Br2(aq)+3H2O(l)5B{r^{-}}_{(aq)} + Br{O^{-}}_{3(aq)} + 6{H^{+}}_{(aq)} \rightarrow 3Br_{2(aq)} + 3H_{2}O_{(l)}Rate = −1Δ5[Br−]Δt=−Δ[BrO3−]Δt=−1Δ[H+]6Δt\frac{- 1\Delta}{5}\frac{\lbrack Br^{-}\rbrack}{\Delta t} = - \frac{\Delta\lbrack BrO_{3}^{-}\rbrack}{\Delta t} = \frac{- 1\Delta\lbrack H^{+}\rbrack}{6\Delta t}

∴Δ[Br−]Δt=56Δ[H+]Δt\therefore\frac{\Delta\lbrack Br^{-}\rbrack}{\Delta t} = \frac{5}{6}\frac{\Delta\lbrack H^{+}\rbrack}{\Delta t}