For the redox reaction
`Zn+NO_(3)^(-)rarr Zn^(2+)+NH_(4)^(-)` is basic medium, coefficients of `Zn, NO_(3)^(-) and OH^(-)` in the balanced equation respectively are :

Options

A. 4, 1, 7
B. 7, 4, 1
C. 4, 1, 10
D. 1, 4, 10

Answer

To balance the redox reaction \( \text{Zn} + \text{NO}_3^- \rightarrow \text{Zn}^{2+} + \text{NH}_4^+ \) in a basic medium, we will follow these steps:

### Step 1: Identify Oxidation States
- For zinc (\( \text{Zn} \)), the oxidation state is 0 (elemental form).
- For nitrogen in nitrate (\( \text{NO}_3^- \)), the oxidation state is +5.
- For nitrogen in ammonium (\( \text{NH}_4^+ \)), the oxidation state is -3.
- For zinc ion (\( \text{Zn}^{2+} \)), the oxidation state is +2.

### Step 2: Determine Changes in Oxidation States
- Zinc is oxidized from 0 to +2 (change of +2).
- Nitrogen is reduced from +5 in nitrate to -3 in ammonium (change of -8).

### Step 3: Balance the Changes in Oxidation States
To balance the total change in oxidation states, we need to equalize the electrons lost and gained. The total change for zinc is +2, and for nitrogen, it is -8. To balance these, we can multiply the zinc oxidation by 4 (since \( 4 \times 2 = 8 \)):
\[ 4 \text{Zn} + \text{NO}_3^- \rightarrow 4 \text{Zn}^{2+} + \text{NH}_4^+ \]

### Step 4: Balance the Charges
Now, we need to balance the charges on both sides.
- Left side: \( 4 \times 0 + (-1) = -1 \)
- Right side: \( 4 \times (+2) + (+1) = +9 \)

To balance the charges, we will add \( 10 \text{OH}^- \) to the left side:
\[ 4 \text{Zn} + \text{NO}_3^- + 10 \text{OH}^- \rightarrow 4 \text{Zn}^{2+} + \text{NH}_4^+ + 10 \text{H}_2O \]

### Step 5: Balance Oxygen and Hydrogen
Now we need to balance the oxygen and hydrogen atoms.
- On the left side, we have \( 10 \text{OH}^- \) which contributes 10 oxygen atoms.
- On the right side, we have \( 7 \text{H}_2O \) which contributes 7 oxygen atoms.

To balance the oxygen, we need to add \( 7 \text{H}_2O \) to the left side:
\[ 4 \text{Zn} + \text{NO}_3^- + 10 \text{OH}^- \rightarrow 4 \text{Zn}^{2+} + \text{NH}_4^+ + 7 \text{H}_2O \]

### Final Balanced Equation
The final balanced equation is:
\[ 4 \text{Zn} + \text{NO}_3^- + 10 \text{OH}^- \rightarrow 4 \text{Zn}^{2+} + \text{NH}_4^+ + 7 \text{H}_2O \]

### Coefficients
- Coefficient of \( \text{Zn} \) = 4
- Coefficient of \( \text{NO}_3^- \) = 1
- Coefficient of \( \text{OH}^- \) = 10

### Final Answer
The coefficients of \( \text{Zn}, \text{NO}_3^-, \text{OH}^- \) in the balanced equation are: **4, 1, 10**.