In acidic medium the rate of reaction between `[BrO_(3)^(-)]` and `[Br^(-)]` ions given by the expression
`- (d[BrO_(3)^(-)])/(dt) = k [BrO_(3)^(-)][Br^(-)][H^(+)]^(2)`
It means
(i) rate of constant of the reaction depends upon the concentration of `H^(+)` ions
(ii) rate of reaction is independent of the concentration of acid added
(iii) the change in pH of the solution will affect the rate of reaction
(iv) doubling the concentration of `H^(+)` ions will increase the reactions rate by 4 items.

Options

A. only (ii)
B. only (iii)
C. only (i) and (ii)
D. only (iii) and (iv)

Explanation

To solve the problem, we need to analyze the given rate expression and the implications of each statement regarding the reaction between `[BrO3^(-)]` and `[Br^(-)]` ions in an acidic medium.

### Step-by-Step Solution:

1. **Understanding the Rate Expression**:
The rate of reaction is given by the expression:
\[ -\frac{d[BrO_3^{-}]}{dt} = k [BrO_3^{-}][Br^{-}][H^{+}]^{2} \]
Here, \( k \) is the rate constant, and the rate depends on the concentrations of `[BrO3^-]`, `[Br^-]`, and `[H^+]`.

2. **Analyzing Statement (i)**:
- **Statement**: The rate constant of the reaction depends upon the concentration of \( H^{+} \) ions.
- **Analysis**: The rate constant \( k \) is a constant for a given reaction at a specific temperature and does not depend on the concentrations of the reactants. Therefore, this statement is **incorrect**.

3. **Analyzing Statement (ii)**:
- **Statement**: The rate of reaction is independent of the concentration of acid added.
- **Analysis**: The concentration of \( H^{+} \) ions directly affects the rate of reaction (as seen in the rate expression). Therefore, this statement is also **incorrect**.

4. **Analyzing Statement (iii)**:
- **Statement**: The change in pH of the solution will affect the rate of reaction.
- **Analysis**: Since pH is related to the concentration of \( H^{+} \) ions, any change in pH will affect the concentration of \( H^{+} \) and thus affect the rate of reaction. Therefore, this statement is **correct**.

5. **Analyzing Statement (iv)**:
- **Statement**: Doubling the concentration of \( H^{+} \) ions will increase the reaction rate by 4 times.
- **Analysis**: The rate is proportional to \( [H^{+}]^{2} \). If we double \( [H^{+}] \), the new rate becomes:
\[ \text{New Rate} = k [BrO_3^{-}][Br^{-}](2[H^{+}])^{2} = k [BrO_3^{-}][Br^{-}](4[H^{+}]^{2}) = 4 \times \text{Original Rate} \]
Thus, this statement is **correct**.

### Conclusion:
The correct options are (iii) and (iv).