Sure! Let's figure out which is the balanced equation for the reaction [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex].
### Options:
1. [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex]
2. [tex]\( 5V_2O_5 + 5CaS \rightarrow 10CaO + 5V_2S_5 \)[/tex]
3. [tex]\( 3V_2O_5 + 3CaS \rightarrow 3CaO + 3V_2S_5 \)[/tex]
4. [tex]\( V_2O_5 + 5CaS \rightarrow 5CaO + V_2S_5 \)[/tex]
### Analyzing Each Option:
1. First equation: [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex]
- Vanadium atoms: 2 on both sides (Balanced)
- Oxygen atoms: 5 on the left, 1 on the right (Unbalanced)
- Calcium atoms: 1 on the left, 1 on the right (Balanced)
- Sulfur atoms: 1 on the left, 5 on the right (Unbalanced)
2. Second equation: [tex]\( 5V_2O_5 + 5CaS \rightarrow 10CaO + 5V_2S_5 \)[/tex]
- Vanadium atoms: 10 on both sides (Balanced)
- Oxygen atoms: 25 on the left, 10 on the right (Unbalanced)
- Calcium atoms: 5 on the left, 10 on the right (Unbalanced)
- Sulfur atoms: 5 on the left, 25 on the right (Unbalanced)
3. Third equation: [tex]\( 3V_2O_5 + 3CaS \rightarrow 3CaO + 3V_2S_5 \)[/tex]
- Vanadium atoms: 6 on both sides (Balanced)
- Oxygen atoms: 15 on the left, 3 on the right (Unbalanced)
- Calcium atoms: 3 on the left, 3 on the right (Balanced)
- Sulfur atoms: 3 on the left, 15 on the right (Unbalanced)
4. Fourth equation: [tex]\( V_2O_5 + 5CaS \rightarrow 5CaO + V_2S_5 \)[/tex]
- Vanadium atoms: 2 on both sides (Balanced)
- Oxygen atoms: 5 on the left, 5 on the right (Balanced)
- Calcium atoms: 5 on the left, 5 on the right (Balanced)
- Sulfur atoms: 5 on the left, 5 on the right (Balanced)
Given this analysis, we conclude that the balanced equation is:
[tex]\[ 3V_2O_5 + 3CaS \rightarrow 3CaO + 3V_2S_5 \][/tex]
Therefore, the correct option is:
[tex]\[ 3 \ (3V_2O_5 + 3CaS \rightarrow 3CaO + 3V_2S_5) \][/tex]
