In dilute aqueous `H_(2)SO_(4)` the complete diaquadioxalatoferrate (II) is oxidised by `MnO_(4)^(-)`. For the reaction, the ratio of the rate of change of `[H^(+)]` to the rate of change of `[MnO_(4)^(-)]` is

Answer

To solve the problem, we need to analyze the reaction between diaquadioxalatoferrate (II) and permanganate ion in the presence of dilute aqueous sulfuric acid. We will derive the balanced chemical equation and then determine the ratio of the rate of change of hydrogen ions \([H^+]\) to the rate of change of permanganate ions \([MnO_4^-]\).

### Step 1: Write the balanced chemical equation

1. **Identify the reactants and products**:
- Reactants: \(MnO_4^-\) (permanganate ion) and diaquadioxalatoferrate (II) complex, which can be represented as \(Fe(C_2O_4)_2(H_2O)_2^{2-}\).
- Products: \(Mn^{2+}\), \(Fe^{3+}\), \(CO_2\), and \(H_2O\).

2. **Write the half-reactions**:
- The reduction half-reaction for permanganate:
\[ MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O \]
- The oxidation half-reaction for the diaquadioxalatoferrate (II):
\[ Fe(C_2O_4)_2(H_2O)_2^{2-} \rightarrow Fe^{3+} + 4CO_2 + 2H_2O + 5e^- \]

3. **Combine the half-reactions**:
- The overall balanced reaction is:
\[ MnO_4^- + Fe(C_2O_4)_2(H_2O)_2^{2-} + 8H^+ \rightarrow Mn^{2+} + Fe^{3+} + 4CO_2 + 2H_2O \]

### Step 2: Determine the rates of change

1. **Use the stoichiometry of the balanced equation**:
- From the balanced equation, we can see:
- For every 1 mole of \(MnO_4^-\) consumed, 8 moles of \(H^+\) are consumed.
- Therefore, the relationship between the rates of change can be expressed as:
\[ -\frac{d[MnO_4^-]}{dt} = \frac{1}{1} \quad \text{and} \quad -\frac{d[H^+]}{dt} = \frac{8}{1} \]

### Step 3: Calculate the ratio of rates

1. **Set up the ratio**:
- The ratio of the rate of change of \([H^+]\) to the rate of change of \([MnO_4^-]\) is:
\[ \frac{-\frac{d[H^+]}{dt}}{-\frac{d[MnO_4^-]}{dt}} = \frac{8}{1} = 8 \]

### Final Answer
The ratio of the rate of change of \([H^+]\) to the rate of change of \([MnO_4^-]\) is **8**.

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