Which of the following expression is correct for the rate of reaction given below?
\(5 Br^- (aq) + BrO_3^- (aq) + 6H^+ (aq) \longrightarrow 3Br_2 (aq) + 3H_2O (l)\)
Answer & explanation
Correct answer: option 3
The correct answer is option 3. \(\frac{\Delta [Br^-]}{\Delta t} = \frac{5}{6}\frac{\Delta [H^+]}{\Delta t}\)
To determine the correct expression for the rate of reaction, we need to analyze the balanced chemical equation:
\(5 Br^- (aq) + BrO_3^- (aq) + 6H^+ (aq) \longrightarrow 3Br_2 (aq) + 3H_2O (l)\)
Rate of disappearance \(= \frac{-1}{5}\frac{\Delta [Br^-]}{\Delta t} = -\frac{\Delta [BrO_3^-]}{\Delta t} = \frac{-1}{6}\frac{\Delta [H^+]}{\Delta t}\)
According to the stoichiometry of the reaction, 5 moles of bromide ions \((Br^-)\) react with 6 moles of hydrogen ions \((H^+)\). This means that the rate of change of bromide ions is directly proportional to the rate of change of hydrogen ions, but with a factor of 5/6.
Therefore, the correct expression for the rate of reaction is:
\(\frac{\Delta [Br^-]}{\Delta t} = \frac{5}{6}\frac{\Delta [H^+]}{\Delta t}\)