In the following reaction `xFe_3O_4+8Al(s)rarryFe(s)+4Al_2O_3(s)` what are the value of x and y?

Options

A. x=2,y=6
B. x=3,y8
C. x=4,y=12
D. x=3,y=9

Answer

To determine the values of x and y in the reaction \( xFe_3O_4 + 8Al(s) \rightarrow yFe(s) + 4Al_2O_3(s) \), we need to balance the chemical equation. Here are the steps to find the values of x and y:

### Step 1: Write down the unbalanced equation
The unbalanced equation is:
\[ xFe_3O_4 + 8Al \rightarrow yFe + 4Al_2O_3 \]

### Step 2: Identify the number of atoms for each element
- On the left side (reactants):
- Iron (Fe) from \( Fe_3O_4 \): \( 3x \)
- Oxygen (O) from \( Fe_3O_4 \): \( 4x \)
- Aluminium (Al): \( 8 \)

- On the right side (products):
- Iron (Fe): \( y \)
- Aluminium (Al) from \( Al_2O_3 \): \( 2 \times 4 = 8 \) (since there are 4 \( Al_2O_3 \))
- Oxygen (O) from \( Al_2O_3 \): \( 3 \times 4 = 12 \)

### Step 3: Balance the Aluminium
From the equation, we see that Aluminium is already balanced:
\[ 8Al \text{ (reactants)} = 8Al \text{ (products)} \]

### Step 4: Balance the Oxygen
We have:
- Left side: \( 4x \) (from \( Fe_3O_4 \))
- Right side: \( 12 \) (from \( Al_2O_3 \))

Setting them equal gives:
\[ 4x = 12 \]
\[ x = 3 \]

### Step 5: Balance the Iron
Now we need to balance Iron:
- Left side: \( 3x = 3(3) = 9 \)
- Right side: \( y \)

Setting them equal gives:
\[ y = 9 \]

### Conclusion
Thus, the values of \( x \) and \( y \) are:
- \( x = 3 \)
- \( y = 9 \)

### Final Balanced Equation
The balanced equation is:
\[ 3Fe_3O_4 + 8Al \rightarrow 9Fe + 4Al_2O_3 \]