To find the balanced equation for the given chemical reaction [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex], we need to ensure that the number of atoms for each element on the reactants side is equal to the number of atoms on the products side. Here is the step-by-step process for each option:
1. Option 1: [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex]
- Vanadium (V): Reactants: 2 atoms, Products: 2 atoms (Balanced)
- Oxygen (O): Reactants: 5 atoms, Products: 1 atom (Not balanced)
- Calcium (Ca): Reactants: 1 atom, Products: 1 atom (Balanced)
- Sulfur (S): Reactants: 1 atom, Products: 5 atoms (Not balanced)
This option is not balanced.
2. Option 2: [tex]\( 5 V_2O_5 + 5 CaS \rightarrow 10 CaO + 5 V_2S_5 \)[/tex]
- Vanadium (V): Reactants: 10 atoms (5 [tex]\(\times\)[/tex] 2), Products: 10 atoms (5 [tex]\(\times\)[/tex] 2) (Balanced)
- Oxygen (O): Reactants: 25 atoms (5 [tex]\(\times\)[/tex] 5), Products: 10 atoms (10 [tex]\(\times\)[/tex] 1) (Not balanced)
- Calcium (Ca): Reactants: 5 atoms, Products: 10 atoms (Not balanced)
- Sulfur (S): Reactants: 5 atoms, Products: 25 atoms (5 [tex]\(\times\)[/tex] 5) (Not balanced)
This option is not balanced.
3. Option 3: [tex]\( 3 V_2O_5 + 3 CaS \rightarrow 3 CaO + 3 V_2S_5 \)[/tex]
- Vanadium (V): Reactants: 6 atoms (3 [tex]\(\times\)[/tex] 2), Products: 6 atoms (3 [tex]\(\times\)[/tex] 2) (Balanced)
- Oxygen (O): Reactants: 15 atoms (3 [tex]\(\times\)[/tex] 5), Products: 3 atoms (3 [tex]\(\times\)[/tex] 1) (Not balanced)
- Calcium (Ca): Reactants: 3 atoms, Products: 3 atoms (Balanced)
- Sulfur (S): Reactants: 3 atoms, Products: 15 atoms (3 [tex]\(\times\)[/tex] 5) (Not balanced)
This option is not balanced.
4. Option 4: [tex]\( V_2O_5 + 5 CaS \rightarrow 5 CaO + V_2S_5 \)[/tex]
- Vanadium (V): Reactants: 2 atoms, Products: 2 atoms (Balanced)
- Oxygen (O): Reactants: 5 atoms, Products: 5 atoms (Balanced)
- Calcium (Ca): Reactants: 5 atoms, Products: 5 atoms (Balanced)
- Sulfur (S): Reactants: 5 atoms, Products: 5 atoms (Balanced)
This option is balanced.
Therefore, the balanced equation for the reaction [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex] is:
[tex]\[ V_2O_5 + 5 CaS \rightarrow 5 CaO + V_2S_5 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{V_2O_5 + 5 CaS \rightarrow 5 CaO + V_2S_5} \][/tex]
