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To determine which chemical equation is correctly balanced, we need to check whether the number of atoms of each element on the reactant side is equal to the number of atoms of that element on the product side.
Let's go through each equation one by one:
1. Equation 1: [tex]\(2 \text{Ca (s)} + \text{Cl}_2 \text{(g)} \rightarrow \text{CaCl}_2 \text{(s)}\)[/tex]
- Reactants:
- Calcium (Ca): [tex]\(2\)[/tex] atoms
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(\text{Cl}_2\)[/tex])
- Products:
- Calcium (Ca): [tex]\(1\)[/tex] atom (from [tex]\(\text{CaCl}_2\)[/tex])
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(\text{CaCl}_2\)[/tex])
This equation is not balanced because the number of calcium atoms on the reactant side is [tex]\(2\)[/tex], but there is only [tex]\(1\)[/tex] calcium atom on the product side.
2. Equation 2: [tex]\(4 \text{Mg (s)} + \text{O}_2 \text{(g)} \rightarrow 2 \text{MgO (s)}\)[/tex]
- Reactants:
- Magnesium (Mg): [tex]\(4\)[/tex] atoms
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\(\text{O}_2\)[/tex])
- Products:
- Magnesium (Mg): [tex]\(2 \times 1 = 2\)[/tex] atoms (from [tex]\(2 \text{MgO}\)[/tex])
- Oxygen (O): [tex]\(2 \)[/tex] atoms (from [tex]\(2 \text{MgO}\)[/tex])
This equation is not balanced because the number of magnesium atoms on the reactant side is [tex]\(4\)[/tex], but there are only [tex]\(2\)[/tex] magnesium atoms on the product side.
3. Equation 3: [tex]\(\text{Li (s)} + \text{Cl}_2 \text{(g)} \rightarrow 2 \text{LiCl (s)}\)[/tex]
- Reactants:
- Lithium (Li): [tex]\(1\)[/tex] atom
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(\text{Cl}_2\)[/tex])
- Products:
- Lithium (Li): [tex]\(2\)[/tex] atoms (from [tex]\(2 \text{LiCl}\)[/tex])
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(2 \text{LiCl}\)[/tex])
This equation is not balanced because the number of lithium atoms on the reactant side is [tex]\(1\)[/tex], but there are [tex]\(2\)[/tex] lithium atoms on the product side.
4. Equation 4: [tex]\(\text{C (s)} + \text{O}_2 \text{(g)} \rightarrow \text{CO}_2 \text{(g)}\)[/tex]
- Reactants:
- Carbon (C): [tex]\(1\)[/tex] atom
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\(\text{O}_2\)[/tex])
- Products:
- Carbon (C): [tex]\(1\)[/tex] atom (from [tex]\(\text{CO}_2\)[/tex])
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\(\text{CO}_2\)[/tex])
This equation is balanced because the number of each type of atom is the same on both the reactant and product side. There are [tex]\(1\)[/tex] carbon atom and [tex]\(2\)[/tex] oxygen atoms on both sides.
Therefore, the correctly balanced chemical equation is:
[tex]\[ \text{C (s)} + \text{O}_2 \text{(g)} \rightarrow \text{CO}_2 \text{(g)} \][/tex]
Which corresponds to Equation 4.
Let's go through each equation one by one:
1. Equation 1: [tex]\(2 \text{Ca (s)} + \text{Cl}_2 \text{(g)} \rightarrow \text{CaCl}_2 \text{(s)}\)[/tex]
- Reactants:
- Calcium (Ca): [tex]\(2\)[/tex] atoms
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(\text{Cl}_2\)[/tex])
- Products:
- Calcium (Ca): [tex]\(1\)[/tex] atom (from [tex]\(\text{CaCl}_2\)[/tex])
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(\text{CaCl}_2\)[/tex])
This equation is not balanced because the number of calcium atoms on the reactant side is [tex]\(2\)[/tex], but there is only [tex]\(1\)[/tex] calcium atom on the product side.
2. Equation 2: [tex]\(4 \text{Mg (s)} + \text{O}_2 \text{(g)} \rightarrow 2 \text{MgO (s)}\)[/tex]
- Reactants:
- Magnesium (Mg): [tex]\(4\)[/tex] atoms
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\(\text{O}_2\)[/tex])
- Products:
- Magnesium (Mg): [tex]\(2 \times 1 = 2\)[/tex] atoms (from [tex]\(2 \text{MgO}\)[/tex])
- Oxygen (O): [tex]\(2 \)[/tex] atoms (from [tex]\(2 \text{MgO}\)[/tex])
This equation is not balanced because the number of magnesium atoms on the reactant side is [tex]\(4\)[/tex], but there are only [tex]\(2\)[/tex] magnesium atoms on the product side.
3. Equation 3: [tex]\(\text{Li (s)} + \text{Cl}_2 \text{(g)} \rightarrow 2 \text{LiCl (s)}\)[/tex]
- Reactants:
- Lithium (Li): [tex]\(1\)[/tex] atom
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(\text{Cl}_2\)[/tex])
- Products:
- Lithium (Li): [tex]\(2\)[/tex] atoms (from [tex]\(2 \text{LiCl}\)[/tex])
- Chlorine (Cl): [tex]\(2\)[/tex] atoms (from [tex]\(2 \text{LiCl}\)[/tex])
This equation is not balanced because the number of lithium atoms on the reactant side is [tex]\(1\)[/tex], but there are [tex]\(2\)[/tex] lithium atoms on the product side.
4. Equation 4: [tex]\(\text{C (s)} + \text{O}_2 \text{(g)} \rightarrow \text{CO}_2 \text{(g)}\)[/tex]
- Reactants:
- Carbon (C): [tex]\(1\)[/tex] atom
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\(\text{O}_2\)[/tex])
- Products:
- Carbon (C): [tex]\(1\)[/tex] atom (from [tex]\(\text{CO}_2\)[/tex])
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\(\text{CO}_2\)[/tex])
This equation is balanced because the number of each type of atom is the same on both the reactant and product side. There are [tex]\(1\)[/tex] carbon atom and [tex]\(2\)[/tex] oxygen atoms on both sides.
Therefore, the correctly balanced chemical equation is:
[tex]\[ \text{C (s)} + \text{O}_2 \text{(g)} \rightarrow \text{CO}_2 \text{(g)} \][/tex]
Which corresponds to Equation 4.
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