The given reaction represents formation of iron from its oxide.
`Fe_2O_3 + xC to 2Fe + xCO`
Here, x is

Explanation

To find the value of \( x \) in the reaction \( \text{Fe}_2\text{O}_3 + xC \rightarrow 2Fe + xCO \), we need to balance the chemical equation. Here are the steps to do that:

### Step 1: Write down the unbalanced equation
The given reaction is:
\[ \text{Fe}_2\text{O}_3 + xC \rightarrow 2Fe + xCO \]

### Step 2: Count the number of atoms for each element
- On the left side (reactants):
- Iron (Fe): 2 (from \(\text{Fe}_2\text{O}_3\))
- Oxygen (O): 3 (from \(\text{Fe}_2\text{O}_3\))
- Carbon (C): \( x \)

- On the right side (products):
- Iron (Fe): 2 (from \( 2Fe \))
- Oxygen (O): \( x \) (from \( xCO \))
- Carbon (C): \( x \) (from \( xCO \))

### Step 3: Balance the iron atoms
The iron atoms are already balanced with 2 on both sides.

### Step 4: Balance the oxygen atoms
On the left side, we have 3 oxygen atoms from \(\text{Fe}_2\text{O}_3\). On the right side, we have \( x \) oxygen atoms from \( xCO \). To balance the oxygen, we set:
\[ x = 3 \]

### Step 5: Substitute \( x \) back into the equation
Now, substituting \( x = 3 \) into the equation gives us:
\[ \text{Fe}_2\text{O}_3 + 3C \rightarrow 2Fe + 3CO \]

### Step 6: Check the balance
Now, let's check if the equation is balanced:
- Left side:
- Fe: 2
- O: 3
- C: 3

- Right side:
- Fe: 2
- O: 3 (from \( 3CO \))
- C: 3

Both sides have the same number of atoms for each element, confirming that the equation is balanced.

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{3} \]