Question

At 298 K, the value of \( -\frac{d[Br^-]}{dt} \) for the reaction \[ 5Br^- (aq) + BrO_3^- (aq) + 6H^+ (aq) \rightarrow 3Br_2 (aq) + 3H_2O (l) \] is \( x \) mol \( L^{-1} \) min\(^{-1}\). What is the rate (in mol \( L^{-1} \) min\(^{-1}\)) of this reaction?

• A. \( 5x \)
• B. \( x \)
• C. \( \frac{x}{5} \)
• D. \( \frac{x}{3} \)

Hint:

- Always use the rate equation \( {Rate} = -\frac{1}{\nu} \frac{d[C]}{dt} \) for reactants. - The reaction rate is the same for all reactants and products when divided by their stoichiometric coefficients.

Answer 1

The Correct Option is C

Step 1: Understanding the Rate of Reaction - The rate of reaction is defined using the rate of disappearance of reactants or the rate of formation of products. - The general expression for rate is: \[ {Rate} = -\frac{1}{\nu} \frac{d[C]}{dt} \] where \( \nu \) is the stoichiometric coefficient of species \( C \). 
Step 2: Applying the Rate Expression - Given: \[ -\frac{d[Br^-]}{dt} = x \] Since the balanced equation gives a stoichiometric coefficient of 5 for \( Br^- \): \[ {Rate} = \frac{1}{5} \times \left(-\frac{d[Br^-]}{dt} \right) \] \[ = \frac{x}{5} \] Final Answer: The correct rate of the reaction is \( \frac{x}{5} \).