Which of the following expression is correct for the rate of reaction given below ?
`5Br^(-)(aq) + BrO_(3)^(-)(aq) + 6H^(+) (aq) to 3Br_(2) (aq) + 3H_(2) O(l)` .

Options

A. `(Delta[Br^(-)])/(Delta t) = 5 (Delta[H^(+)])/(Delta)`
B. `(Delta[Br^(-)])/(Delta t) = (6)/(5) (Delta[H^(+)])/(Delta t)`
C. `(Delta[Br^(-)])/(Delta t) = (5)/(6) (Delta [H^(+)])/(Delta t)`
D. `(Delta[Br^(-)])/(Delta t) = 6 (Delta[H^(+)])/(Delta t)`

Explanation

To find the correct expression for the rate of the given reaction:

**Step 1: Write the balanced chemical equation.**
The reaction is:
\[ 5 \text{Br}^- (aq) + \text{BrO}_3^- (aq) + 6 \text{H}^+ (aq) \rightarrow 3 \text{Br}_2 (aq) + 3 \text{H}_2O (l) \]

**Step 2: Identify the reactants and their coefficients.**
From the balanced equation, we have:
- 5 moles of \(\text{Br}^-\)
- 1 mole of \(\text{BrO}_3^-\)
- 6 moles of \(\text{H}^+\)

**Step 3: Write the rate expressions for each reactant.**
The rate of reaction can be expressed in terms of the change in concentration of each reactant over time. The general form is:
\[ \text{Rate} = -\frac{1}{n} \frac{\Delta [A]}{\Delta t} \]
where \(n\) is the stoichiometric coefficient of the reactant \(A\).

For \(\text{Br}^-\):
\[ \text{Rate} = -\frac{1}{5} \frac{\Delta [\text{Br}^-]}{\Delta t} \]

For \(\text{H}^+\):
\[ \text{Rate} = -\frac{1}{6} \frac{\Delta [\text{H}^+]}{\Delta t} \]

**Step 4: Set the rate expressions equal to each other.**
Since all rate expressions represent the same reaction rate, we can equate them:
\[ -\frac{1}{5} \frac{\Delta [\text{Br}^-]}{\Delta t} = -\frac{1}{6} \frac{\Delta [\text{H}^+]}{\Delta t} \]

**Step 5: Simplify the equation.**
Removing the negative signs and rearranging gives:
\[ \frac{\Delta [\text{Br}^-]}{\Delta t} = \frac{5}{6} \frac{\Delta [\text{H}^+]}{\Delta t} \]

**Step 6: Final expression for the rate of reaction.**
Thus, the rate of reaction can be expressed as:
\[ \text{Rate} = -\frac{1}{5} \frac{\Delta [\text{Br}^-]}{\Delta t} = -\frac{1}{6} \frac{\Delta [\text{H}^+]}{\Delta t} \]

**Step 7: Identify the correct option.**
From the options provided, the correct expression for the rate of the reaction is:
\[ \Delta [\text{Br}^-] = \frac{5}{6} \Delta [\text{H}^+] \]

---