Question

For the following reaction choose the incorrect expression of rate of reaction. \[ 5\text{ Br}^{-}(aq.) + \text{BrO}_{3}^{-}(aq.) + 6\text{ H}^{+}(aq.) \rightarrow 3\text{ Br}_{2}(aq.) + 3\text{ H}_{2}\text{O}(l) \]

• A. \(\text{Rate} = -\frac{1}{5}\frac{\Delta[\text{Br}^{-}]}{\Delta t}\)
• B. \(\text{Rate} = -\frac{1}{6}\frac{\Delta[\text{H}^{+}]}{\Delta t}\)
• C. \(\text{Rate} = -\frac{1}{3}\frac{\Delta[\text{Br}_{2}]}{\Delta t}\)
• D. \(\text{Rate} = -\frac{\Delta[\text{BrO}_{3}^{-}]}{\Delta t}\)

Hint:

Always remember: reactants are consumed, so their rate terms carry a negative sign, while products are formed, so their rate terms carry a positive sign.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a generic chemical reaction \( aA + bB \rightarrow cC + dD \), the rate of reaction is expressed in terms of the change in concentration of reactants or products over time, divided by their respective stoichiometric coefficients. Reactant concentrations decrease over time (indicated by a negative sign), and product concentrations increase (positive sign).

Step 2: Detailed Explanation:
The general formula for the rate of the given reaction is: $$ \text{Rate} = -\frac{1}{5} \frac{\Delta[\text{Br}^-]}{\Delta t} = -\frac{\Delta[\text{BrO}_3^-]}{\Delta t} = -\frac{1}{6} \frac{\Delta[\text{H}^+]}{\Delta t} = +\frac{1}{3} \frac{\Delta[\text{Br}_2]}{\Delta t} = +\frac{1}{3} \frac{\Delta[\text{H}_2\text{O}]}{\Delta t} $$ Comparing this to the given options:
• Option (A) is correct as it represents the reactant \(\text{Br}^-\) with its stoichiometric coefficient of 5.
• Option (B) is correct as it represents the reactant \(\text{H}^+\) with its stoichiometric coefficient of 6.
• Option (C) is incorrect because \(\text{Br}_2\) is a product. The rate expression for a product should be \(\text{positive}\), not negative. The correct expression is \(+\frac{1}{3} \frac{\Delta[\text{Br}_2]}{\Delta t}\).
• Option (D) is correct as it represents the reactant \(\text{BrO}_3^-\) with a stoichiometric coefficient of 1.

Step 3: Final Answer:
The incorrect expression is (C).