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

Concept: For a balanced chemical reaction, the rate of reaction is expressed by dividing the rate of change in concentration of each reactant or product by its respective stoichiometric coefficient. For a general reaction \[ aA+bB \rightarrow cC+dD \] the rate is written as \[ \text{Rate} = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = -\frac{1}{b}\frac{\Delta[B]}{\Delta t} = \frac{1}{c}\frac{\Delta[C]}{\Delta t} = \frac{1}{d}\frac{\Delta[D]}{\Delta t} \] A negative sign is used for reactants because their concentrations decrease with time, whereas a positive sign is used for products because their concentrations increase with time.

Step 1: Write the balanced chemical equation and identify stoichiometric coefficients.
The given reaction is \[ 5\text{ Br}^{-} + \text{BrO}_{3}^{-} + 6\text{ H}^{+} \rightarrow 3\text{ Br}_{2} + 3\text{ H}_{2}\text{O} \] The stoichiometric coefficients are: \[ \text{Br}^{-}=5,\qquad \text{BrO}_{3}^{-}=1,\qquad \text{H}^{+}=6,\qquad \text{Br}_{2}=3 \]

Step 2: Write the correct rate expression.
Using the definition of rate, \[ \text{Rate} = -\frac{1}{5}\frac{\Delta[\text{Br}^{-}]}{\Delta t} = -\frac{\Delta[\text{BrO}_{3}^{-}]}{\Delta t} = -\frac{1}{6}\frac{\Delta[\text{H}^{+}]}{\Delta t} = \frac{1}{3}\frac{\Delta[\text{Br}_{2}]}{\Delta t} \] Notice carefully that the product term must carry a positive sign.

Step 3: Check each option.
Option (A): \[ -\frac{1}{5}\frac{\Delta[\text{Br}^{-}]}{\Delta t} \] Correct. Option (B): \[ -\frac{1}{6}\frac{\Delta[\text{H}^{+}]}{\Delta t} \] Correct. Option (C): \[ -\frac{1}{3}\frac{\Delta[\text{Br}_{2}]}{\Delta t} \] Incorrect because \(\text{Br}_2\) is a product and therefore its rate term should have a positive sign. Option (D): \[ -\frac{\Delta[\text{BrO}_{3}^{-}]}{\Delta t} \] Correct because the stoichiometric coefficient of \(\text{BrO}_{3}^{-}\) is 1.

Step 4: Identify the incorrect expression.
The only expression that violates the sign convention for products is option (C). Hence, the incorrect expression is \[ -\frac{1}{3}\frac{\Delta[\text{Br}_{2}]}{\Delta t} \]