The ratio of coefficient of `HNO_(3), Fe(NO_(3))_(2)` and `NH_(4)NO_(3)` in the following redox reaction `Fe + HNO_(3) rarr Fe (NO_(3))_(2) + NH_(4)NO_(3) + H_(2)O`
are respectively

Options

A. `10:1:4`
B. `10:4:1`
C. `4:10:1`
D. `4:1:10`

Answer

To solve the problem, we need to balance the given redox reaction and then determine the coefficients of the reactants and products involved. The reaction is:

\[ \text{Fe} + \text{HNO}_3 \rightarrow \text{Fe(NO}_3\text{)}_2 + \text{NH}_4\text{NO}_3 + \text{H}_2\text{O} \]

### Step 1: Write the unbalanced equation
The unbalanced equation is already given. We have:
\[ \text{Fe} + \text{HNO}_3 \rightarrow \text{Fe(NO}_3\text{)}_2 + \text{NH}_4\text{NO}_3 + \text{H}_2\text{O} \]

### Step 2: Identify the number of atoms on both sides
- **Reactants:**
- Fe: 1
- H: 1
- N: 1
- O: 3

- **Products:**
- Fe: 1 (from Fe(NO3)2)
- N: 2 (from Fe(NO3)2) + 1 (from NH4NO3) = 3
- H: 4 (from NH4NO3) + 2 (from H2O) = 6
- O: 6 (from Fe(NO3)2) + 3 (from NH4NO3) + 1 (from H2O) = 10

### Step 3: Balance the equation
To balance the equation, we need to ensure that the number of each type of atom is the same on both sides.

1. **Balance Fe:**
- 1 Fe on both sides is already balanced.

2. **Balance N:**
- We have 3 N on the product side (2 from Fe(NO3)2 and 1 from NH4NO3) and 1 N on the reactant side.
- To balance, we need to add a coefficient of 10 in front of HNO3:
\[ \text{Fe} + 10 \text{HNO}_3 \rightarrow \text{Fe(NO}_3\text{)}_2 + \text{NH}_4\text{NO}_3 + \text{H}_2\text{O} \]

3. **Balance H:**
- Now we have 10 H from HNO3 and we need to balance it with NH4NO3 and H2O.
- We can add coefficients to balance the H and O atoms as follows:
\[ 4 \text{Fe} + 10 \text{HNO}_3 \rightarrow 4 \text{Fe(NO}_3\text{)}_2 + 1 \text{NH}_4\text{NO}_3 + 3 \text{H}_2\text{O} \]

### Step 4: Write the balanced equation
The balanced equation is:
\[ 4 \text{Fe} + 10 \text{HNO}_3 \rightarrow 4 \text{Fe(NO}_3\text{)}_2 + 1 \text{NH}_4\text{NO}_3 + 3 \text{H}_2\text{O} \]

### Step 5: Determine the coefficients
From the balanced equation, we can see the coefficients:
- Coefficient of HNO3 = 10
- Coefficient of Fe(NO3)2 = 4
- Coefficient of NH4NO3 = 1

### Step 6: Write the ratio
The ratio of the coefficients is:
\[ \text{HNO}_3 : \text{Fe(NO}_3\text{)}_2 : \text{NH}_4\text{NO}_3 = 10 : 4 : 1 \]

### Final Answer
The ratio of the coefficients of HNO3, Fe(NO3)2, and NH4NO3 in the reaction is:
\[ 10 : 4 : 1 \]