Which of the following expressions is correct for the rate of reaction given below ? $5Br^{-}(aq)+BrO_{3}^{-}(aq)+6H^{+}(aq)\rightarrow 3Br_{2}(aq)+3H_{2}O(l)$

Q: Which of the following expressions is correct for the rate of reaction given below ? $5Br^{-}(aq)+BrO_{3}^{-}(aq)+6H^{+}(aq)\rightarrow 3Br_{2}(aq)+3H_{2}O(l)$

Which of the following expressions is correct for the rate of reaction given below ? $5Br^{-}(aq)+BrO_{3}^{-}(aq)+6H^{+}(aq)\rightarrow 3Br_{2}(aq)+3H_{2}O(l)$

Question

Accepted Answer

To determine the correct expression for the rate of reaction, we need to consider the stoichiometry of the given chemical equation:

$$ 5Br^{-}(aq) + BrO_{3}^{-}(aq) + 6H^{+}(aq) \rightarrow 3Br_{2}(aq) + 3H_{2}O(l) $$

The rate of reaction can be expressed in terms of the change in concentration of any of the reactants or products over time. The stoichiometric coefficients in the balanced equation are used to relate these rates.

### Explanation for Option 3:

**Option 3:**
$$ \frac{\Delta[Br^{-}]}{\Delta t} = \frac{5}{6} \frac{\Delta[H^{+}]}{\Delta t} $$

This option correctly relates the rate of change of concentration of $ Br^{-} $ to $ H^{+} $ using their stoichiometric coefficients. According to the balanced equation, 5 moles of $ Br^{-} $ react with 6 moles of $ H^{+} $. Therefore, the rate of consumption of $ Br^{-} $ is $\frac{5}{6}$ times the rate of consumption of $ H^{+} $. This is consistent with the stoichiometry of the reaction, making Option 3 the correct choice.

### Explanation for why other options are incorrect:

**Option 1:**
$$ \frac{\Delta[Br^{-}]}{\Delta t} = \frac{5\Delta[H^{+}]}{\Delta t} $$

This option incorrectly suggests that the rate of change of $ Br^{-} $ is 5 times that of $ H^{+} $. However, according to the stoichiometry, 5 moles of $ Br^{-} $ react with 6 moles of $ H^{+} $, so the rate should be $\frac{5}{6}$, not 5 times.

**Option 2:**
$$ \frac{\Delta[Br^{-}]}{\Delta t} = \frac{6}{5} \frac{\Delta[H^{+}]}{\Delta t} $$

This option incorrectly suggests that the rate of change of $ Br^{-} $ is $\frac{6}{5}$ times that of $ H^{+} $. This is the inverse of the correct relationship. The correct ratio, based on stoichiometry, is $\frac{5}{6}$.

**Option 4:**
$$ \frac{\Delta[Br^{-}]}{\Delta t} = \frac{6\Delta[H^{+}]}{\Delta t} $$

This option incorrectly suggests that the rate of change of $ Br^{-} $ is 6 times that of $ H^{+} $. Again, according to the stoichiometry, the correct relationship is $\frac{5}{6}$, not 6 times.

In conclusion, Option 3 is the correct expression for the rate of reaction, as it accurately reflects the stoichiometric relationship between $ Br^{-} $ and $ H^{+} $ in the balanced chemical equation.