For the redox reaction
`MnO_(4)^(ө)+C_(2)O_(4)^(2-)+H^(o+)rarrMn^(2+)+CO_(2)+H_(2)O`
the correct coefficients of the reactions for the balanced reaction are

Options

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

Explanation

To balance 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
- For \(\text{MnO}_4^{-}\), the oxidation state of Mn is +7.
- For \(\text{C}_2\text{O}_4^{2-}\), the oxidation state of carbon is +3.
- In \(\text{Mn}^{2+}\), the oxidation state of Mn is +2.
- In \(\text{CO}_2\), the oxidation state of carbon is +4.

### Step 2: Determine the Half-Reactions
- **Reduction Half-Reaction**:
\[ \text{MnO}_4^{-} + 8\text{H}^{+} + 5\text{e}^{-} \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O} \]
- **Oxidation Half-Reaction**:
\[ \text{C}_2\text{O}_4^{2-} \rightarrow 2\text{CO}_2 + 2\text{e}^{-} \]

### Step 3: Balance the Half-Reactions
- The reduction half-reaction is already balanced in terms of atoms and charge.
- The oxidation half-reaction needs to be multiplied by 5 to balance the number of electrons:
\[ 5\text{C}_2\text{O}_4^{2-} \rightarrow 10\text{CO}_2 + 10\text{e}^{-} \]

### Step 4: Combine the Half-Reactions
Now we can combine the balanced half-reactions:
- Multiply the oxidation half-reaction by 5:
\[ 5\text{C}_2\text{O}_4^{2-} \rightarrow 10\text{CO}_2 + 10\text{e}^{-} \]
- The reduction half-reaction remains the same:
\[ 2\text{MnO}_4^{-} + 8\text{H}^{+} + 10\text{e}^{-} \rightarrow 2\text{Mn}^{2+} + 4\text{H}_2\text{O} \]

### Step 5: Add the Half-Reactions
Adding both half-reactions gives:
\[ 2\text{MnO}_4^{-} + 5\text{C}_2\text{O}_4^{2-} + 16\text{H}^{+} \rightarrow 2\text{Mn}^{2+} + 10\text{CO}_2 + 8\text{H}_2\text{O} \]

### Final Balanced Equation
The balanced equation is:
\[ 2\text{MnO}_4^{-} + 5\text{C}_2\text{O}_4^{2-} + 16\text{H}^{+} \rightarrow 2\text{Mn}^{2+} + 10\text{CO}_2 + 8\text{H}_2\text{O} \]

### Coefficients
The correct coefficients for the balanced reaction are:
- \(2\) for \(\text{MnO}_4^{-}\)
- \(5\) for \(\text{C}_2\text{O}_4^{2-}\)
- \(16\) for \(\text{H}^{+}\)

### Answer
Thus, the answer is \(2, 5, 16\).

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