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Sagot :
To solve the problem of balancing the given unbalanced chemical equation [tex]\( \text{CO}_2 + \text{C} \rightarrow \text{CO} \)[/tex]:
We need to ensure that the number of each type of atom on the reactants side is equal to the number on the products side. Let's analyze each option given:
Option A: [tex]\( \text{CO}_2 + \text{C} \rightarrow 2 \text{CO} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(1 \text{ C from CO}_2 + 1 \text{ C from C} = 2 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from CO}_2\)[/tex]
- Products:
- Carbon (C): [tex]\(2 \text{ C atoms from 2 CO}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from 2 CO}\)[/tex]
Both sides have 2 carbon atoms and 2 oxygen atoms. Thus, this equation is balanced.
Option B: [tex]\(2 \text{CO}_2 + \text{C} \rightarrow \text{CO} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(2 \text{ C atoms from 2 CO}_2 + 1 \text{ C from C} = 3 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ CO}_2 \cdot 2 = 4 \text{ O atoms}\)[/tex]
- Products:
- Carbon (C): [tex]\(1 \text{ C atom from CO}\)[/tex]
- Oxygen (O): [tex]\(1 \text{ O atom from CO}\)[/tex]
The number of carbon and oxygen atoms are not balanced. Thus, this equation is not balanced.
Option C: [tex]\( \text{CO}_2 + \text{C} \rightarrow \text{C}_2\text{O} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(1 \text{ C from CO}_2 + 1 \text{ C from C} = 2 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from CO}_2\)[/tex]
- Products:
- Carbon (C): [tex]\(2 \text{ C atoms from C}_2\text{O}\)[/tex]
- Oxygen (O): [tex]\(1 \text{ O atom from C}_2\text{O}\)[/tex]
The number of oxygen atoms are not balanced. Thus, this equation is not balanced.
Option D: [tex]\( \text{CO}_2 + \text{C}_2 \rightarrow \text{CO} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(1 \text{ C from CO}_2 + 2 \text{ C atoms from C}_2 = 3 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from CO}_2\)[/tex]
- Products:
- Carbon (C): [tex]\(1 \text{ C atom from CO}\)[/tex]
- Oxygen (O): [tex]\(1 \text{ O atom from CO}\)[/tex]
The number of carbon and oxygen atoms are not balanced. Thus, this equation is not balanced.
After examining all options, we conclude that:
The correct balanced form of the equation is:
Option A: [tex]\( \text{CO}_2 + \text{C} \rightarrow 2 \text{CO} \)[/tex]
We need to ensure that the number of each type of atom on the reactants side is equal to the number on the products side. Let's analyze each option given:
Option A: [tex]\( \text{CO}_2 + \text{C} \rightarrow 2 \text{CO} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(1 \text{ C from CO}_2 + 1 \text{ C from C} = 2 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from CO}_2\)[/tex]
- Products:
- Carbon (C): [tex]\(2 \text{ C atoms from 2 CO}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from 2 CO}\)[/tex]
Both sides have 2 carbon atoms and 2 oxygen atoms. Thus, this equation is balanced.
Option B: [tex]\(2 \text{CO}_2 + \text{C} \rightarrow \text{CO} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(2 \text{ C atoms from 2 CO}_2 + 1 \text{ C from C} = 3 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ CO}_2 \cdot 2 = 4 \text{ O atoms}\)[/tex]
- Products:
- Carbon (C): [tex]\(1 \text{ C atom from CO}\)[/tex]
- Oxygen (O): [tex]\(1 \text{ O atom from CO}\)[/tex]
The number of carbon and oxygen atoms are not balanced. Thus, this equation is not balanced.
Option C: [tex]\( \text{CO}_2 + \text{C} \rightarrow \text{C}_2\text{O} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(1 \text{ C from CO}_2 + 1 \text{ C from C} = 2 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from CO}_2\)[/tex]
- Products:
- Carbon (C): [tex]\(2 \text{ C atoms from C}_2\text{O}\)[/tex]
- Oxygen (O): [tex]\(1 \text{ O atom from C}_2\text{O}\)[/tex]
The number of oxygen atoms are not balanced. Thus, this equation is not balanced.
Option D: [tex]\( \text{CO}_2 + \text{C}_2 \rightarrow \text{CO} \)[/tex]
- Reactants:
- Carbon (C): [tex]\(1 \text{ C from CO}_2 + 2 \text{ C atoms from C}_2 = 3 \text{ C atoms}\)[/tex]
- Oxygen (O): [tex]\(2 \text{ O atoms from CO}_2\)[/tex]
- Products:
- Carbon (C): [tex]\(1 \text{ C atom from CO}\)[/tex]
- Oxygen (O): [tex]\(1 \text{ O atom from CO}\)[/tex]
The number of carbon and oxygen atoms are not balanced. Thus, this equation is not balanced.
After examining all options, we conclude that:
The correct balanced form of the equation is:
Option A: [tex]\( \text{CO}_2 + \text{C} \rightarrow 2 \text{CO} \)[/tex]
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