For the redox reation
`MnO_(4)^(-)+C_(2)O_(4)^(2-)+H^(+)rarrMn^(2+)CO_(2)+H_(2)O`
The correct stoichiometric coefficients of `Mno_(4)^(-),C_(2)O_(4)^(2-)` and `H^(+)` respectively:

Options

A. 2, 5, 16
B. 16, 5, 2
C. 5, 16, 2
D. 2, 16, 5

Answer

To determine the correct stoichiometric coefficients for the redox reaction:

\[ \text{MnO}_4^{-} + \text{C}_2\text{O}_4^{2-} + \text{H}^{+} \rightarrow \text{Mn}^{2+} + \text{CO}_2 + \text{H}_2\text{O} \]

we will follow these steps:

### Step 1: Identify Oxidation States
- **Manganese (Mn)** in \(\text{MnO}_4^{-}\) has an oxidation state of +7.
- **Carbon (C)** in \(\text{C}_2\text{O}_4^{2-}\) has an oxidation state of +3 (since \(2x + 4(-2) = -2\)).
- **Manganese (Mn)** in \(\text{Mn}^{2+}\) has an oxidation state of +2.
- **Carbon (C)** in \(\text{CO}_2\) has an oxidation state of +4.

### Step 2: Determine Changes in Oxidation States
- For Mn: +7 to +2 (reduction, gain of 5 electrons).
- For C: +3 to +4 (oxidation, loss of 1 electron per carbon atom; since there are 2 carbon atoms in \(\text{C}_2\text{O}_4^{2-}\), a total of 2 electrons are lost).

### Step 3: Balance the Electrons
- The reduction of 2 Mn requires 10 electrons (2 Mn × 5 electrons).
- The oxidation of 5 C requires 5 × 2 = 10 electrons.
- Therefore, the electrons lost and gained are balanced.

### Step 4: Write Half-Reactions
1. **Reduction Half-Reaction**:
\[ 2 \text{MnO}_4^{-} + 16 \text{H}^{+} + 10 \text{e}^{-} \rightarrow 2 \text{Mn}^{2+} + 8 \text{H}_2\text{O} \]

2. **Oxidation Half-Reaction**:
\[ 5 \text{C}_2\text{O}_4^{2-} \rightarrow 10 \text{CO}_2 + 10 \text{e}^{-} \]

### Step 5: Combine Half-Reactions
Combine the two half-reactions to obtain the overall balanced equation:
\[ 2 \text{MnO}_4^{-} + 5 \text{C}_2\text{O}_4^{2-} + 16 \text{H}^{+} \rightarrow 2 \text{Mn}^{2+} + 10 \text{CO}_2 + 8 \text{H}_2\text{O} \]

### Step 6: Identify Stoichiometric Coefficients
From the balanced equation, we can identify the stoichiometric coefficients:
- Coefficient of \(\text{MnO}_4^{-}\) = 2
- Coefficient of \(\text{C}_2\text{O}_4^{2-}\) = 5
- Coefficient of \(\text{H}^{+}\) = 16

### Final Answer
Thus, the correct stoichiometric coefficients of \(\text{MnO}_4^{-}\), \(\text{C}_2\text{O}_4^{2-}\), and \(\text{H}^{+}\) are **2, 5, and 16**, respectively.

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