Let's balance the chemical equation step-by-step.
Consider the unbalanced chemical equation:
[tex]\[ \text{CaSO}_4 \rightarrow x \cdot \text{O}_2 + y \cdot \text{CaS} \][/tex]
We'll need to balance each type of atom on both sides of the equation.
### Step 1: Balance Oxygen (O) atoms.
On the left-hand side of the equation:
- There are 4 oxygen atoms in [tex]\( \text{CaSO}_4 \)[/tex].
On the right-hand side of the equation:
- Each [tex]\( \text{O}_2 \)[/tex] molecule has 2 oxygen atoms, so with [tex]\( x \cdot \text{O}_2 \)[/tex], we have [tex]\( 2x \)[/tex] oxygen atoms.
To balance the oxygen atoms:
[tex]\[ 4 = 2x \][/tex]
[tex]\[ x = 2 \][/tex]
### Step 2: Balance Calcium (Ca) atoms.
On the left-hand side of the equation:
- There is 1 calcium atom in [tex]\( \text{CaSO}_4 \)[/tex].
On the right-hand side of the equation:
- Each [tex]\( \text{CaS} \)[/tex] molecule has 1 calcium atom. So, with [tex]\( y \cdot \text{CaS} \)[/tex], we have [tex]\( y \)[/tex] calcium atoms.
To balance the calcium atoms:
[tex]\[ 1 = y \][/tex]
[tex]\[ y = 1 \][/tex]
### Step 3: Balance Sulfur (S) atoms.
On the left-hand side of the equation:
- There is 1 sulfur atom in [tex]\( \text{CaSO}_4 \)[/tex].
On the right-hand side of the equation:
- Each [tex]\( \text{CaS} \)[/tex] molecule has 1 sulfur atom. So, with [tex]\( y \cdot \text{CaS} \)[/tex], we have [tex]\( y \)[/tex] sulfur atoms.
To balance the sulfur atoms:
[tex]\[ 1 = y \][/tex]
[tex]\[ y = 1 \][/tex]
### Final Balanced Equation
Incorporating the coefficients [tex]\( x = 2 \)[/tex] and [tex]\( y = 1 \)[/tex] into the original equation, we get:
[tex]\[ \text{CaSO}_4 \rightarrow 2 \text{O}_2 + 1 \text{CaS} \][/tex]
Therefore, the balanced chemical equation is:
[tex]\[ \boxed{CaSO_4 \rightarrow 2 O_2 + 1 CaS} \][/tex]
So, the coefficients that balance the chemical equation are:
- For [tex]\( O_2 \)[/tex]: 2
- For [tex]\( CaS \)[/tex]: 1
