`aZn+bNO^(-)+cH+todNH_4^++eH_2O+fZn^(+2)` a, b, c, d, e and f are :

Options

A. `{:(a,b,c,d,e,f),(2,4,6,8,4,2):}`
B. `{:(a,b,c,d,e,f),(1,4,10,3,1,4):}`
C. `{:(a,b,c,d,e,f),(4,2,12,2,2,4):}`
D. `{:(a,b,c,d,e,f),(10,4,1,3,4,2):}`

Answer

To solve the given reaction and find the stoichiometric coefficients \( a, b, c, d, e, \) and \( f \), we will follow these steps:

### Step 1: Write the unbalanced equation
The unbalanced reaction is given as:
\[ \text{Zn} + \text{NO}^- + \text{H}^+ \rightarrow \text{NH}_4^+ + \text{Zn}^{2+} + \text{H}_2\text{O} \]

### Step 2: Determine oxidation states
- **Zinc (Zn)**: In the reactants, Zn is in the oxidation state of 0, and in the products, it is in the oxidation state of +2.
- **Nitrogen (N)**: In NO\(^-\), nitrogen has an oxidation state of +1, and in NH\(_4^+\), it has an oxidation state of -3.

### Step 3: Calculate changes in oxidation states
- For Zn: Change = \( +2 - 0 = +2 \)
- For N: Change = \( +1 - (-3) = 4 \)

### Step 4: Determine the stoichiometric coefficients based on changes
The valency factor for Zn is 2 and for N is 4. Therefore, we can write the coefficients:
- For Zn: 4 (because it needs to balance with the change in N)
- For NO\(^-\): 2 (to balance the nitrogen)
- For H\(^+\): To balance the total charge and hydrogen atoms.

### Step 5: Balance the equation
Now we can write the balanced equation:
\[ 4\text{Zn} + 2\text{NO}^- + 12\text{H}^+ \rightarrow 2\text{NH}_4^+ + 4\text{Zn}^{2+} + 2\text{H}_2\text{O} \]

### Step 6: Identify coefficients
From the balanced equation, we can identify:
- \( a = 4 \) (for Zn)
- \( b = 2 \) (for NO\(^-\))
- \( c = 12 \) (for H\(^+\))
- \( d = 2 \) (for NH\(_4^+\))
- \( e = 2 \) (for H\(_2\)O)
- \( f = 4 \) (for Zn\(^{2+}\))

### Final Answer
Thus, the values of \( a, b, c, d, e, \) and \( f \) are:
- \( a = 4 \)
- \( b = 2 \)
- \( c = 12 \)
- \( d = 2 \)
- \( e = 2 \)
- \( f = 4 \)

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