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Sagot :
To determine the balanced equation for [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex], we need to ensure that the number of each type of atom on the reactant side is equal to the number of the same type of atom on the product side. Let's analyze each option provided:
1. [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex]
- Reactants:
- [tex]\(V_2O_5\)[/tex]: 2 V, 5 O
- [tex]\(CaS\)[/tex]: 1 Ca, 1 S
- Products:
- [tex]\(CaO\)[/tex]: 1 Ca, 1 O
- [tex]\(V_2S_5\)[/tex]: 2 V, 5 S
Comparing the counts:
- Vanadium (V): 2 (reactants) vs 2 (products) -- Balanced
- Oxygen (O): 5 (reactants) vs 1 (products) -- Not balanced
- Calcium (Ca): 1 (reactants) vs 1 (products) -- Balanced
- Sulfur (S): 1 (reactants) vs 5 (products) -- Not balanced
This equation is not balanced.
2. [tex]\( 5V_2O_5 + 5CaS \rightarrow 10CaO + 5V_2S_5 \)[/tex]
- Reactants:
- [tex]\(5V_2O_5\)[/tex]: 10 V, 25 O
- [tex]\(5CaS\)[/tex]: 5 Ca, 5 S
- Products:
- [tex]\(10CaO\)[/tex]: 10 Ca, 10 O
- [tex]\(5V_2S_5\)[/tex]: 10 V, 25 S
Comparing the counts:
- Vanadium (V): 10 (reactants) vs 10 (products) -- Balanced
- Oxygen (O): 25 (reactants) vs 10 (products) -- Not balanced
- Calcium (Ca): 5 (reactants) vs 10 (products) -- Not balanced
- Sulfur (S): 5 (reactants) vs 25 (products) -- Not balanced
This equation is not balanced.
3. [tex]\( 3V_2O_5 + 3CaS \rightarrow 3CaO + 3V_2S_5 \)[/tex]
- Reactants:
- [tex]\(3V_2O_5\)[/tex]: 6 V, 15 O
- [tex]\(3CaS\)[/tex]: 3 Ca, 3 S
- Products:
- [tex]\(3CaO\)[/tex]: 3 Ca, 3 O
- [tex]\(3V_2S_5\)[/tex]: 6 V, 15 S
Comparing the counts:
- Vanadium (V): 6 (reactants) vs 6 (products) -- Balanced
- Oxygen (O): 15 (reactants) vs 3 (products) -- Not balanced
- Calcium (Ca): 3 (reactants) vs 3 (products) -- Balanced
- Sulfur (S): 3 (reactants) vs 15 (products) -- Not balanced
This equation is not balanced.
4. [tex]\( V_2O_5 + 5CaS \rightarrow 5CaO + V_2S_5 \)[/tex]
- Reactants:
- [tex]\(V_2O_5\)[/tex]: 2 V, 5 O
- [tex]\(5CaS\)[/tex]: 5 Ca, 5 S
- Products:
- [tex]\(5CaO\)[/tex]: 5 Ca, 5 O
- [tex]\(V_2S_5\)[/tex]: 2 V, 5 S
Comparing the counts:
- Vanadium (V): 2 (reactants) vs 2 (products) -- Balanced
- Oxygen (O): 5 (reactants) vs 5 (products) -- Balanced
- Calcium (Ca): 5 (reactants) vs 5 (products) -- Balanced
- Sulfur (S): 5 (reactants) vs 5 (products) -- Balanced
This equation is balanced.
Therefore, the balanced equation is:
[tex]\[ V_2O_5 + 5CaS \rightarrow 5CaO + V_2S_5 \][/tex]
Looking at the choices provided, this corresponds to option 4.
1. [tex]\( V_2O_5 + CaS \rightarrow CaO + V_2S_5 \)[/tex]
- Reactants:
- [tex]\(V_2O_5\)[/tex]: 2 V, 5 O
- [tex]\(CaS\)[/tex]: 1 Ca, 1 S
- Products:
- [tex]\(CaO\)[/tex]: 1 Ca, 1 O
- [tex]\(V_2S_5\)[/tex]: 2 V, 5 S
Comparing the counts:
- Vanadium (V): 2 (reactants) vs 2 (products) -- Balanced
- Oxygen (O): 5 (reactants) vs 1 (products) -- Not balanced
- Calcium (Ca): 1 (reactants) vs 1 (products) -- Balanced
- Sulfur (S): 1 (reactants) vs 5 (products) -- Not balanced
This equation is not balanced.
2. [tex]\( 5V_2O_5 + 5CaS \rightarrow 10CaO + 5V_2S_5 \)[/tex]
- Reactants:
- [tex]\(5V_2O_5\)[/tex]: 10 V, 25 O
- [tex]\(5CaS\)[/tex]: 5 Ca, 5 S
- Products:
- [tex]\(10CaO\)[/tex]: 10 Ca, 10 O
- [tex]\(5V_2S_5\)[/tex]: 10 V, 25 S
Comparing the counts:
- Vanadium (V): 10 (reactants) vs 10 (products) -- Balanced
- Oxygen (O): 25 (reactants) vs 10 (products) -- Not balanced
- Calcium (Ca): 5 (reactants) vs 10 (products) -- Not balanced
- Sulfur (S): 5 (reactants) vs 25 (products) -- Not balanced
This equation is not balanced.
3. [tex]\( 3V_2O_5 + 3CaS \rightarrow 3CaO + 3V_2S_5 \)[/tex]
- Reactants:
- [tex]\(3V_2O_5\)[/tex]: 6 V, 15 O
- [tex]\(3CaS\)[/tex]: 3 Ca, 3 S
- Products:
- [tex]\(3CaO\)[/tex]: 3 Ca, 3 O
- [tex]\(3V_2S_5\)[/tex]: 6 V, 15 S
Comparing the counts:
- Vanadium (V): 6 (reactants) vs 6 (products) -- Balanced
- Oxygen (O): 15 (reactants) vs 3 (products) -- Not balanced
- Calcium (Ca): 3 (reactants) vs 3 (products) -- Balanced
- Sulfur (S): 3 (reactants) vs 15 (products) -- Not balanced
This equation is not balanced.
4. [tex]\( V_2O_5 + 5CaS \rightarrow 5CaO + V_2S_5 \)[/tex]
- Reactants:
- [tex]\(V_2O_5\)[/tex]: 2 V, 5 O
- [tex]\(5CaS\)[/tex]: 5 Ca, 5 S
- Products:
- [tex]\(5CaO\)[/tex]: 5 Ca, 5 O
- [tex]\(V_2S_5\)[/tex]: 2 V, 5 S
Comparing the counts:
- Vanadium (V): 2 (reactants) vs 2 (products) -- Balanced
- Oxygen (O): 5 (reactants) vs 5 (products) -- Balanced
- Calcium (Ca): 5 (reactants) vs 5 (products) -- Balanced
- Sulfur (S): 5 (reactants) vs 5 (products) -- Balanced
This equation is balanced.
Therefore, the balanced equation is:
[tex]\[ V_2O_5 + 5CaS \rightarrow 5CaO + V_2S_5 \][/tex]
Looking at the choices provided, this corresponds to option 4.
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