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Let's go through each of these equations step-by-step to understand how they are balanced.
### 2. Balance [tex]\($4 Al +3 \quad O_2 \rightarrow 2 Al_2 O_3\)[/tex]
Step-by-Step Balancing:
- Reactants: 4 Al, 3 O₂ (each O₂ molecule has 2 oxygen atoms, so [tex]\(3 \times 2 = 6\)[/tex])
- Products: 2 Al₂O₃ (each Al₂O₃ molecule has 2 aluminum atoms and 3 oxygen atoms, so [tex]\(2 \times 2 = 4\)[/tex] Al and [tex]\(2 \times 3 = 6\)[/tex] O)
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ 4 Al + 3 O_2 \rightarrow 2 Al_2 O_3 \][/tex]
### 3. Balance [tex]\($1 K_3 PO_4 + 3 HCl \rightarrow 3 KCl + 1 H_3 PO_4\)[/tex]
Step-by-Step Balancing:
- Reactants: 1 K₃PO₄, 3 HCl (K₃PO₄ has 3 potassium (K), 1 phosphate (PO₄), and 3 chlorine (Cl)), HCl has 1 hydrogen (H) and 1 chlorine (Cl)
- Breakdown: 3 K, 1 PO₄, 3 H, 3 Cl
- Products: 3 KCl, 1 H₃PO₄ (KCl has 1 K and 1 Cl, H₃PO₄ has 3 H and 1 PO₄)
- Breakdown: 3 K, 1 PO₄, 3 H, 3 Cl
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ K_3 PO_4 + 3 HCl \rightarrow 3 KCl + H_3 PO_4 \][/tex]
### 4. Balance [tex]\($1 C_3 H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O\)[/tex]
Step-by-Step Balancing:
- Reactants: 1 C₃H₈, 5 O₂ (C₃H₈ has 3 carbon (C) and 8 hydrogen (H), O₂ has 2 oxygen atoms)
- Breakdown: 3 C, 8 H, [tex]\(5 \times 2 = 10\)[/tex] O
- Products: 3 CO₂, 4 H₂O (CO₂ has 1 C and 2 O, H₂O has 2 H and 1 O)
- Breakdown: [tex]\(3 \times 1 = 3\)[/tex] C, [tex]\(4 \times 2 = 8\)[/tex] H, [tex]\(3 \times 2 = 6\)[/tex] O + [tex]\(4 \times 1 = 4\)[/tex] O = 10 O
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ C_3 H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O \][/tex]
### 5. Balance [tex]\($2 BaCl_2 + 2 KIO_3 \rightarrow Ba(IO_3)_2 + 4 KCl\)[/tex]
Step-by-Step Balancing:
- Reactants: 2 BaCl₂, 2 KIO₃ (BaCl₂ has 1 Ba and 2 Cl, KIO₃ has 1 K, 1 I, and 3 O)
- Breakdown: 2 Ba, [tex]\(2 \times 2 = 4\)[/tex] Cl, 2 K, 2 I, [tex]\(2 \times 3 = 6\)[/tex] O
- Products: 1 Ba(IO₃)₂, 4 KCl (Ba(IO₃)₂ has 1 Ba, 2 I, 6 O, KCl has 1 K and 1 Cl)
- Breakdown: 1 Ba, [tex]\(4 \times 1 = 4\)[/tex] K, [tex]\(4 \times 1 = 4\)[/tex] Cl, 2 I, 6 O
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ 2 BaCl_2 + 2 KIO_3 \rightarrow Ba(IO_3)_2 + 4 KCl \][/tex]
### 6. Balance [tex]\($2 C_8 H_{18} + 2 O_2 \rightarrow 16 CO_2 + 18 H_2O\)[/tex]
Step-by-Step Balancing:
- Reactants: 2 C₈H₁₈, 25 O₂ (C₈H₁₈ has 8 C and 18 H, O₂ has 2 O atoms)
- Breakdown: [tex]\(2 \times 8 = 16\)[/tex] C, [tex]\(2 \times 18 = 36\)[/tex] H, [tex]\(25 \times 2 = 50\)[/tex] O
- Products: 16 CO₂, 18 H₂O (CO₂ has 1 C and 2 O, H₂O has 2 H and 1 O)
- Breakdown: [tex]\(16 \times 1 = 16\)[/tex] C, [tex]\(18 \times 2 = 36\)[/tex] H, [tex]\(16 \times 2 = 32\)[/tex] O + [tex]\(18 \times 1 = 18\)[/tex] O = 50 O
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ 2 C_8 H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O \][/tex]
### 2. Balance [tex]\($4 Al +3 \quad O_2 \rightarrow 2 Al_2 O_3\)[/tex]
Step-by-Step Balancing:
- Reactants: 4 Al, 3 O₂ (each O₂ molecule has 2 oxygen atoms, so [tex]\(3 \times 2 = 6\)[/tex])
- Products: 2 Al₂O₃ (each Al₂O₃ molecule has 2 aluminum atoms and 3 oxygen atoms, so [tex]\(2 \times 2 = 4\)[/tex] Al and [tex]\(2 \times 3 = 6\)[/tex] O)
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ 4 Al + 3 O_2 \rightarrow 2 Al_2 O_3 \][/tex]
### 3. Balance [tex]\($1 K_3 PO_4 + 3 HCl \rightarrow 3 KCl + 1 H_3 PO_4\)[/tex]
Step-by-Step Balancing:
- Reactants: 1 K₃PO₄, 3 HCl (K₃PO₄ has 3 potassium (K), 1 phosphate (PO₄), and 3 chlorine (Cl)), HCl has 1 hydrogen (H) and 1 chlorine (Cl)
- Breakdown: 3 K, 1 PO₄, 3 H, 3 Cl
- Products: 3 KCl, 1 H₃PO₄ (KCl has 1 K and 1 Cl, H₃PO₄ has 3 H and 1 PO₄)
- Breakdown: 3 K, 1 PO₄, 3 H, 3 Cl
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ K_3 PO_4 + 3 HCl \rightarrow 3 KCl + H_3 PO_4 \][/tex]
### 4. Balance [tex]\($1 C_3 H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O\)[/tex]
Step-by-Step Balancing:
- Reactants: 1 C₃H₈, 5 O₂ (C₃H₈ has 3 carbon (C) and 8 hydrogen (H), O₂ has 2 oxygen atoms)
- Breakdown: 3 C, 8 H, [tex]\(5 \times 2 = 10\)[/tex] O
- Products: 3 CO₂, 4 H₂O (CO₂ has 1 C and 2 O, H₂O has 2 H and 1 O)
- Breakdown: [tex]\(3 \times 1 = 3\)[/tex] C, [tex]\(4 \times 2 = 8\)[/tex] H, [tex]\(3 \times 2 = 6\)[/tex] O + [tex]\(4 \times 1 = 4\)[/tex] O = 10 O
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ C_3 H_8 + 5 O_2 \rightarrow 3 CO_2 + 4 H_2O \][/tex]
### 5. Balance [tex]\($2 BaCl_2 + 2 KIO_3 \rightarrow Ba(IO_3)_2 + 4 KCl\)[/tex]
Step-by-Step Balancing:
- Reactants: 2 BaCl₂, 2 KIO₃ (BaCl₂ has 1 Ba and 2 Cl, KIO₃ has 1 K, 1 I, and 3 O)
- Breakdown: 2 Ba, [tex]\(2 \times 2 = 4\)[/tex] Cl, 2 K, 2 I, [tex]\(2 \times 3 = 6\)[/tex] O
- Products: 1 Ba(IO₃)₂, 4 KCl (Ba(IO₃)₂ has 1 Ba, 2 I, 6 O, KCl has 1 K and 1 Cl)
- Breakdown: 1 Ba, [tex]\(4 \times 1 = 4\)[/tex] K, [tex]\(4 \times 1 = 4\)[/tex] Cl, 2 I, 6 O
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ 2 BaCl_2 + 2 KIO_3 \rightarrow Ba(IO_3)_2 + 4 KCl \][/tex]
### 6. Balance [tex]\($2 C_8 H_{18} + 2 O_2 \rightarrow 16 CO_2 + 18 H_2O\)[/tex]
Step-by-Step Balancing:
- Reactants: 2 C₈H₁₈, 25 O₂ (C₈H₁₈ has 8 C and 18 H, O₂ has 2 O atoms)
- Breakdown: [tex]\(2 \times 8 = 16\)[/tex] C, [tex]\(2 \times 18 = 36\)[/tex] H, [tex]\(25 \times 2 = 50\)[/tex] O
- Products: 16 CO₂, 18 H₂O (CO₂ has 1 C and 2 O, H₂O has 2 H and 1 O)
- Breakdown: [tex]\(16 \times 1 = 16\)[/tex] C, [tex]\(18 \times 2 = 36\)[/tex] H, [tex]\(16 \times 2 = 32\)[/tex] O + [tex]\(18 \times 1 = 18\)[/tex] O = 50 O
- Result: The number of atoms for each element on both sides is equal, so the equation is balanced.
Balanced Equation:
[tex]\[ 2 C_8 H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O \][/tex]
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