Answer :
To determine the balanced equation for the reaction \( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \), follow these steps:
1. Identify the number of atoms for each element on both sides of the equation.
For the initial (unbalanced) equation:
[tex]\[ V_2O_5 + CaS \rightarrow CaO + V_2S_5 \][/tex]
On the left side (reactants):
- \( V_2O_5 \)
- Vanadium (V): 2 atoms
- Oxygen (O): 5 atoms
- \( CaS \)
- Calcium (Ca): 1 atom
- Sulfur (S): 1 atom
On the right side (products):
- \( CaO \)
- Calcium (Ca): 1 atom
- Oxygen (O): 1 atom
- \( V_2S_5 \)
- Vanadium (V): 2 atoms
- Sulfur (S): 5 atoms
2. Compare the number of atoms for each element on both sides:
Vanadium (V):
- Reactants: 2
- Products: 2
Oxygen (O):
- Reactants: 5
- Products: 1
Calcium (Ca):
- Reactants: 1
- Products: 1
Sulfur (S):
- Reactants: 1
- Products: 5
3. Balance the atoms step-by-step:
Since the number of vanadium atoms is already balanced, we can move on to balance sulfur and oxygen.
Balancing Sulfur (S):
To balance sulfur, we need 5 sulfur atoms on the left side to match the 5 sulfur atoms on the right:
[tex]\[ V_2O_5 + 5 CaS \rightarrow CaO + V_2S_5 \][/tex]
Balancing Calcium (Ca):
Now, placing a factor of 5 in front of \( CaO \) to balance calcium:
[tex]\[ V_2O_5 + 5 CaS \rightarrow 5 CaO + V_2S_5 \][/tex]
Balancing Oxygen (O):
There are now 5 oxygen atoms on both sides (all from \( V_2O_5 \) and \( 5 CaO \)).
4. Verify that the equation is balanced:
On the left side (reactants):
- Vanadium (V): 2 atoms from \( V_2O_5 \)
- Oxygen (O): 5 atoms from \( V_2O_5 \)
- Calcium (Ca): 5 atoms from \( 5 CaS \)
- Sulfur (S): 5 atoms from \( 5 CaS \)
On the right side (products):
- Vanadium (V): 2 atoms from \( V_2S_5 \)
- Oxygen (O): 5 atoms from \( 5 CaO \)
- Calcium (Ca): 5 atoms from \( 5 CaO \)
- Sulfur (S): 5 atoms from \( V_2S_5 \)
Since the equation is now balanced, the balanced equation is:
[tex]\[ 5 CaS + V_2O_5 \rightarrow 5 CaO + V_2S_5 \][/tex]
Therefore, the index of the correct balanced equation from the given list is \( 3 \), which corresponds to the balanced equation:
[tex]\[ 5 CaS + V_2O_5 \rightarrow 5 CaO + V_2S_5 \][/tex]
1. Identify the number of atoms for each element on both sides of the equation.
For the initial (unbalanced) equation:
[tex]\[ V_2O_5 + CaS \rightarrow CaO + V_2S_5 \][/tex]
On the left side (reactants):
- \( V_2O_5 \)
- Vanadium (V): 2 atoms
- Oxygen (O): 5 atoms
- \( CaS \)
- Calcium (Ca): 1 atom
- Sulfur (S): 1 atom
On the right side (products):
- \( CaO \)
- Calcium (Ca): 1 atom
- Oxygen (O): 1 atom
- \( V_2S_5 \)
- Vanadium (V): 2 atoms
- Sulfur (S): 5 atoms
2. Compare the number of atoms for each element on both sides:
Vanadium (V):
- Reactants: 2
- Products: 2
Oxygen (O):
- Reactants: 5
- Products: 1
Calcium (Ca):
- Reactants: 1
- Products: 1
Sulfur (S):
- Reactants: 1
- Products: 5
3. Balance the atoms step-by-step:
Since the number of vanadium atoms is already balanced, we can move on to balance sulfur and oxygen.
Balancing Sulfur (S):
To balance sulfur, we need 5 sulfur atoms on the left side to match the 5 sulfur atoms on the right:
[tex]\[ V_2O_5 + 5 CaS \rightarrow CaO + V_2S_5 \][/tex]
Balancing Calcium (Ca):
Now, placing a factor of 5 in front of \( CaO \) to balance calcium:
[tex]\[ V_2O_5 + 5 CaS \rightarrow 5 CaO + V_2S_5 \][/tex]
Balancing Oxygen (O):
There are now 5 oxygen atoms on both sides (all from \( V_2O_5 \) and \( 5 CaO \)).
4. Verify that the equation is balanced:
On the left side (reactants):
- Vanadium (V): 2 atoms from \( V_2O_5 \)
- Oxygen (O): 5 atoms from \( V_2O_5 \)
- Calcium (Ca): 5 atoms from \( 5 CaS \)
- Sulfur (S): 5 atoms from \( 5 CaS \)
On the right side (products):
- Vanadium (V): 2 atoms from \( V_2S_5 \)
- Oxygen (O): 5 atoms from \( 5 CaO \)
- Calcium (Ca): 5 atoms from \( 5 CaO \)
- Sulfur (S): 5 atoms from \( V_2S_5 \)
Since the equation is now balanced, the balanced equation is:
[tex]\[ 5 CaS + V_2O_5 \rightarrow 5 CaO + V_2S_5 \][/tex]
Therefore, the index of the correct balanced equation from the given list is \( 3 \), which corresponds to the balanced equation:
[tex]\[ 5 CaS + V_2O_5 \rightarrow 5 CaO + V_2S_5 \][/tex]
