In the balanced reaction
`aFe_(2)O_(3) + bH_(2) to cFe + dH_(2)O`
a, b, c and d, respectivel, are

Options

A. 1123
B. 1111
C. 1323
D. 1223

Explanation

To balance the reaction \( aFe_{2}O_{3} + bH_{2} \rightarrow cFe + dH_{2}O \), we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's break this down step by step:

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ Fe_{2}O_{3} + H_{2} \rightarrow Fe + H_{2}O \]

### Step 2: Count the number of atoms of each element
- On the left side (reactants):
- Iron (Fe): 2 (from \( Fe_{2}O_{3} \))
- Oxygen (O): 3 (from \( Fe_{2}O_{3} \))
- Hydrogen (H): 2 (from \( H_{2} \))

- On the right side (products):
- Iron (Fe): 1 (from \( Fe \))
- Oxygen (O): 1 (from \( H_{2}O \))
- Hydrogen (H): 2 (from \( H_{2}O \))

### Step 3: Balance the iron (Fe) atoms
To balance the iron atoms, we need 2 iron atoms on the product side. Therefore, we will put a coefficient of 2 in front of \( Fe \):
\[ Fe_{2}O_{3} + H_{2} \rightarrow 2Fe + H_{2}O \]

### Step 4: Count the atoms again
Now, let's recount:
- On the left side:
- Fe: 2
- O: 3
- H: 2

- On the right side:
- Fe: 2
- O: 1 (from \( H_{2}O \))
- H: 2 (from \( H_{2}O \))

### Step 5: Balance the oxygen (O) atoms
We have 3 oxygen atoms on the left and only 1 on the right. To balance the oxygen, we need to put a coefficient of 3 in front of \( H_{2}O \):
\[ Fe_{2}O_{3} + H_{2} \rightarrow 2Fe + 3H_{2}O \]

### Step 6: Count the hydrogen (H) atoms
Now we recount:
- On the left side:
- Fe: 2
- O: 3
- H: 2

- On the right side:
- Fe: 2
- O: 3 (from \( 3H_{2}O \))
- H: 6 (from \( 3H_{2}O \))

### Step 7: Balance the hydrogen (H) atoms
We have 6 hydrogen atoms on the right side but only 2 on the left. To balance the hydrogen, we need to put a coefficient of 3 in front of \( H_{2} \):
\[ Fe_{2}O_{3} + 3H_{2} \rightarrow 2Fe + 3H_{2}O \]

### Final Step: Write the balanced equation
The balanced equation is:
\[ 1Fe_{2}O_{3} + 3H_{2} \rightarrow 2Fe + 3H_{2}O \]

### Coefficients:
- \( a = 1 \)
- \( b = 3 \)
- \( c = 2 \)
- \( d = 3 \)

### Summary of Coefficients:
- \( a = 1 \)
- \( b = 3 \)
- \( c = 2 \)
- \( d = 3 \)