Consider the reaction
`aFeS_(2) + bO_(2) to cFe_(3)O_(3) + dSO_(2)`
Which is correct for the above reaction

Options

A. n-factor for `FeS_(2)` is 11
B. The ratio of moles of a:b is 4:11
C. The ratio of moles of a:b is 11:4
D. The ratio of moles of c:d is 1:4

Answer

To solve the reaction \( aFeS_2 + bO_2 \rightarrow cFe_3O_3 + dSO_2 \), we need to balance the equation and determine the correct relationships between the coefficients.

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ FeS_2 + O_2 \rightarrow Fe_2O_3 + SO_2 \]

### Step 2: Balance the iron (Fe) atoms
In \( Fe_2O_3 \), there are 2 iron atoms. Therefore, to balance the iron, we need 4 moles of \( FeS_2 \) (since each \( FeS_2 \) has 1 iron atom):
\[ 4FeS_2 + O_2 \rightarrow 2Fe_2O_3 + SO_2 \]

### Step 3: Balance the sulfur (S) atoms
In \( 4FeS_2 \), there are 8 sulfur atoms (since each \( FeS_2 \) has 2 sulfur atoms). To balance the sulfur, we need 8 moles of \( SO_2 \):
\[ 4FeS_2 + O_2 \rightarrow 2Fe_2O_3 + 8SO_2 \]

### Step 4: Balance the oxygen (O) atoms
Now, we need to balance the oxygen atoms. On the right side, we have:
- From \( 2Fe_2O_3 \): \( 2 \times 3 = 6 \) oxygen atoms
- From \( 8SO_2 \): \( 8 \times 2 = 16 \) oxygen atoms
- Total on the right side: \( 6 + 16 = 22 \) oxygen atoms

On the left side, each \( O_2 \) molecule provides 2 oxygen atoms. To balance 22 oxygen atoms, we need:
\[ b = \frac{22}{2} = 11 \]
Thus, we have:
\[ 4FeS_2 + 11O_2 \rightarrow 2Fe_2O_3 + 8SO_2 \]

### Step 5: Write the final balanced equation
The balanced equation is:
\[ 4FeS_2 + 11O_2 \rightarrow 2Fe_2O_3 + 8SO_2 \]

### Step 6: Determine the coefficients
From the balanced equation, we can identify:
- \( a = 4 \) (for \( FeS_2 \))
- \( b = 11 \) (for \( O_2 \))
- \( c = 2 \) (for \( Fe_2O_3 \))
- \( d = 8 \) (for \( SO_2 \))

### Step 7: Analyze the options
1. The n-factor of \( FeS_2 \) is 11 (correct).
2. The ratio of moles \( A:B \) is \( 4:11 \) (correct).
3. The ratio of moles \( C:D \) is \( 1:4 \) (incorrect, as \( C:D \) is \( 2:8 \) which simplifies to \( 1:4 \)).
4. The reaction is a redox reaction, as both oxidation and reduction occur.

### Conclusion
The correct relationships for the reaction are:
- The n-factor of \( FeS_2 \) is 11.
- The ratio of moles \( A:B \) is \( 4:11 \).
- The ratio of moles \( C:D \) is \( 1:4 \) (which is correct).