For the redox reaction:
`Cr_(2)O_(7)^(2-)+H^(o+)+NirarrCr^(3+)+Ni^(2)+H_(2)O`
The correct coefficient of the reactants for the balanced reaction are:

Options

A. `Cr_(2)O_(7)^(2-)=1, Ni=3, H^(o+)=14`
B. `Cr_(2)O_(7)^(2-)=3, Ni=3, H^(o+)=12`
C. `Cr_(2)O_(7)^(2-)=2, Ni=3, H^(o+)=14`
D. `Cr_(2)O_(7)^(2-)=1, Ni=1, H^(o+)=16`

Explanation

To balance the redox reaction given, we will follow the ion-electron method, which involves separating the oxidation and reduction half-reactions. Here’s a step-by-step solution:

### Step 1: Identify the oxidation and reduction half-reactions
In the reaction:
\[ \text{Cr}_2\text{O}_7^{2-} + \text{H}^+ + \text{Ni} \rightarrow \text{Cr}^{3+} + \text{Ni}^{2+} + \text{H}_2\text{O} \]

- **Oxidation half-reaction**: Nickel (Ni) is oxidized to Nickel ion (Ni²⁺).
- **Reduction half-reaction**: Dichromate ion (Cr₂O₇²⁻) is reduced to Chromium ion (Cr³⁺).

### Step 2: Write the oxidation half-reaction
Nickel is oxidized as follows:
\[ \text{Ni} \rightarrow \text{Ni}^{2+} + 2e^- \]
This indicates that each nickel atom loses 2 electrons.

### Step 3: Write the reduction half-reaction
The reduction of dichromate can be written as:
\[ \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \]
Here, we balance the chromium atoms, oxygen atoms (using water), and hydrogen ions.

### Step 4: Balance the electrons
To balance the electrons lost in oxidation with those gained in reduction, we need to multiply the oxidation half-reaction by 3 (since 3 Ni will produce 6 electrons):
\[ 3\text{Ni} \rightarrow 3\text{Ni}^{2+} + 6e^- \]

### Step 5: Combine the half-reactions
Now we can combine the balanced half-reactions:
\[ 3\text{Ni} + \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 3\text{Ni}^{2+} + 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \]

### Step 6: Identify the coefficients of the reactants
From the balanced equation, we can identify the coefficients of the reactants:
- Coefficient of Ni = 3
- Coefficient of Cr₂O₇²⁻ = 1
- Coefficient of H⁺ = 14

### Final Answer
The correct coefficients of the reactants for the balanced reaction are:
- Ni: 3
- Cr₂O₇²⁻: 1
- H⁺: 14