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Sagot :
Let's balance each of these chemical equations step-by-step.
### Equation 1: [tex]\( CH_4 + O_2 \rightarrow CO_2 + H_2O \)[/tex]
1. Identify the atoms present on each side:
- Reactants: 1 C, 4 H, 2 O
- Products: 1 C, 2 H, 3 O
2. Balance Carbon (C):
- There is 1 carbon atom on each side already, so carbon is balanced.
3. Balance Hydrogen (H):
- There are 4 hydrogen atoms on the reactant side (from [tex]\(CH_4\)[/tex]) and 2 hydrogen atoms on the product side (from [tex]\(H_2O\)[/tex]).
- To balance hydrogen, place a coefficient of 2 in front of [tex]\(H_2O\)[/tex]:
[tex]\[ CH_4 + O_2 \rightarrow CO_2 + 2H_2O \][/tex]
- Now, the hydrogen atoms are balanced (4 H atoms on each side).
4. Balance Oxygen (O):
- There are now 2 oxygen atoms from [tex]\(CO_2\)[/tex] and [tex]\(2\times1=2\)[/tex] oxygen atoms from [tex]\(2H_2O\)[/tex], resulting in a total of 4 oxygen atoms on the product side.
- On the reactant side, we currently only have [tex]\(O_2\)[/tex], which gives 2 oxygen atoms.
- To balance the oxygen atoms, place a coefficient of 2 in front of [tex]\(O_2\)[/tex]:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
- Now, the oxygen atoms are balanced (4 O atoms on each side).
The balanced equation is:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
### Equation 2: [tex]\( CaCl_2 + \square AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + \square AgCl \)[/tex]
1. Identify the atoms present on each side:
- Reactants: 1 Ca, 2 Cl, 1 Ag, 1 N, 3 O
- Products: 1 Ca, 2 NO_3, 2 Ag, 2 Cl
2. Balance Calcium (Ca):
- There's 1 Ca atom on each side, so calcium is balanced.
3. Balance Chlorine (Cl):
- There's 2 Cl atoms on the reactant side (from [tex]\(CaCl_2\)[/tex]) and 1 Cl atom on the product side (from [tex]\(AgCl\)[/tex]).
- To balance chlorine, place a coefficient of 2 in front of [tex]\(AgCl\)[/tex]:
[tex]\[ CaCl_2 + AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
- Now, the chlorine atoms are balanced (2 Cl atoms on each side).
4. Balance Silver (Ag):
- Now, there are 2 Ag atoms needed on the reactant side.
- Place a coefficient of 2 in front of [tex]\(AgNO_3\)[/tex]:
[tex]\[ CaCl_2 + 2AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
- Now, the silver atoms are balanced (2 Ag atoms on each side).
5. Verify Nitrogen (N) and Oxygen (O):
- Nitrogen: 2 NO_3 groups on the product side corresponds to 2 N atoms (and 6 O atoms).
- Reactants now have [tex]\( 2\times1=2\)[/tex] N atoms and [tex]\(2\times3=6\)[/tex] O atoms from [tex]\(2AgNO_3\)[/tex], which is balanced with the product side.
The balanced equation is:
[tex]\[ CaCl_2 + 2AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
### Equation 3: [tex]\( C_2H_6O + O_2 \rightarrow CO_2 + H_2O \)[/tex]
1. Identify the atoms present on each side:
- Reactants: 2 C, 6 H, x O
- Products: y C, z H, w O
2. Balance Carbon (C):
- There are 2 carbon atoms in [tex]\(C_2H_6O\)[/tex].
- Place a coefficient of 2 in front of [tex]\(CO_2\)[/tex]:
[tex]\[ C_2H_6O + O_2 \rightarrow 2CO_2 + H_2O \][/tex]
- Now, the carbon atoms are balanced (2 C atoms on each side).
3. Balance Hydrogen (H):
- There are 6 hydrogen atoms in [tex]\(C_2H_6O\)[/tex] and 2 hydrogen atoms in [tex]\(H_2O\)[/tex].
- Place a coefficient of 3 in front of [tex]\(H_2O\)[/tex]:
[tex]\[ C_2H_6O + O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
- Now, the hydrogen atoms are balanced (6 H atoms on each side).
4. Balance Oxygen (O):
- There are [tex]\(2\times2=4\)[/tex] oxygen atoms from [tex]\(CO_2\)[/tex] and [tex]\(3 \times 1 = 3\)[/tex] oxygen atoms from [tex]\(H_2O\)[/tex], resulting in a total of 7 oxygen atoms on the product side.
- On the reactant side, we have 1 oxygen in [tex]\(C_2H_6O\)[/tex] and the rest must come from [tex]\(O_2\)[/tex].
- To get 7 oxygen atoms in total, [tex]\(1 + 2 \times \left( x \right) = 7 \Rightarrow x = 3\)[/tex]:
[tex]\[ C_2H_6O + 3O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
The balanced equation is:
[tex]\[ C_2H_6O + 3O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
So, the final balanced equations are:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
[tex]\[ CaCl_2 + 2AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
[tex]\[ C_2H_6O + 3O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
### Equation 1: [tex]\( CH_4 + O_2 \rightarrow CO_2 + H_2O \)[/tex]
1. Identify the atoms present on each side:
- Reactants: 1 C, 4 H, 2 O
- Products: 1 C, 2 H, 3 O
2. Balance Carbon (C):
- There is 1 carbon atom on each side already, so carbon is balanced.
3. Balance Hydrogen (H):
- There are 4 hydrogen atoms on the reactant side (from [tex]\(CH_4\)[/tex]) and 2 hydrogen atoms on the product side (from [tex]\(H_2O\)[/tex]).
- To balance hydrogen, place a coefficient of 2 in front of [tex]\(H_2O\)[/tex]:
[tex]\[ CH_4 + O_2 \rightarrow CO_2 + 2H_2O \][/tex]
- Now, the hydrogen atoms are balanced (4 H atoms on each side).
4. Balance Oxygen (O):
- There are now 2 oxygen atoms from [tex]\(CO_2\)[/tex] and [tex]\(2\times1=2\)[/tex] oxygen atoms from [tex]\(2H_2O\)[/tex], resulting in a total of 4 oxygen atoms on the product side.
- On the reactant side, we currently only have [tex]\(O_2\)[/tex], which gives 2 oxygen atoms.
- To balance the oxygen atoms, place a coefficient of 2 in front of [tex]\(O_2\)[/tex]:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
- Now, the oxygen atoms are balanced (4 O atoms on each side).
The balanced equation is:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
### Equation 2: [tex]\( CaCl_2 + \square AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + \square AgCl \)[/tex]
1. Identify the atoms present on each side:
- Reactants: 1 Ca, 2 Cl, 1 Ag, 1 N, 3 O
- Products: 1 Ca, 2 NO_3, 2 Ag, 2 Cl
2. Balance Calcium (Ca):
- There's 1 Ca atom on each side, so calcium is balanced.
3. Balance Chlorine (Cl):
- There's 2 Cl atoms on the reactant side (from [tex]\(CaCl_2\)[/tex]) and 1 Cl atom on the product side (from [tex]\(AgCl\)[/tex]).
- To balance chlorine, place a coefficient of 2 in front of [tex]\(AgCl\)[/tex]:
[tex]\[ CaCl_2 + AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
- Now, the chlorine atoms are balanced (2 Cl atoms on each side).
4. Balance Silver (Ag):
- Now, there are 2 Ag atoms needed on the reactant side.
- Place a coefficient of 2 in front of [tex]\(AgNO_3\)[/tex]:
[tex]\[ CaCl_2 + 2AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
- Now, the silver atoms are balanced (2 Ag atoms on each side).
5. Verify Nitrogen (N) and Oxygen (O):
- Nitrogen: 2 NO_3 groups on the product side corresponds to 2 N atoms (and 6 O atoms).
- Reactants now have [tex]\( 2\times1=2\)[/tex] N atoms and [tex]\(2\times3=6\)[/tex] O atoms from [tex]\(2AgNO_3\)[/tex], which is balanced with the product side.
The balanced equation is:
[tex]\[ CaCl_2 + 2AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
### Equation 3: [tex]\( C_2H_6O + O_2 \rightarrow CO_2 + H_2O \)[/tex]
1. Identify the atoms present on each side:
- Reactants: 2 C, 6 H, x O
- Products: y C, z H, w O
2. Balance Carbon (C):
- There are 2 carbon atoms in [tex]\(C_2H_6O\)[/tex].
- Place a coefficient of 2 in front of [tex]\(CO_2\)[/tex]:
[tex]\[ C_2H_6O + O_2 \rightarrow 2CO_2 + H_2O \][/tex]
- Now, the carbon atoms are balanced (2 C atoms on each side).
3. Balance Hydrogen (H):
- There are 6 hydrogen atoms in [tex]\(C_2H_6O\)[/tex] and 2 hydrogen atoms in [tex]\(H_2O\)[/tex].
- Place a coefficient of 3 in front of [tex]\(H_2O\)[/tex]:
[tex]\[ C_2H_6O + O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
- Now, the hydrogen atoms are balanced (6 H atoms on each side).
4. Balance Oxygen (O):
- There are [tex]\(2\times2=4\)[/tex] oxygen atoms from [tex]\(CO_2\)[/tex] and [tex]\(3 \times 1 = 3\)[/tex] oxygen atoms from [tex]\(H_2O\)[/tex], resulting in a total of 7 oxygen atoms on the product side.
- On the reactant side, we have 1 oxygen in [tex]\(C_2H_6O\)[/tex] and the rest must come from [tex]\(O_2\)[/tex].
- To get 7 oxygen atoms in total, [tex]\(1 + 2 \times \left( x \right) = 7 \Rightarrow x = 3\)[/tex]:
[tex]\[ C_2H_6O + 3O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
The balanced equation is:
[tex]\[ C_2H_6O + 3O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
So, the final balanced equations are:
[tex]\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \][/tex]
[tex]\[ CaCl_2 + 2AgNO_3 \rightarrow Ca\left(NO_3\right)_2 + 2AgCl \][/tex]
[tex]\[ C_2H_6O + 3O_2 \rightarrow 2CO_2 + 3H_2O \][/tex]
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