Sure, let's go through the process of balancing these chemical equations step by step.
### 1. [tex]\( CH_4 + \square O_2 \rightarrow CO_2 + \square H_2O \)[/tex]
To balance this equation:
- Start with carbon (C): There is 1 carbon atom on each side (1 CH4 to 1 CO2), so carbon is already balanced.
- Next, balance hydrogen (H): There are 4 hydrogen atoms from CH4. To have 4 hydrogen atoms in water (H2O), we need 2 H2O molecules (since each H2O has 2 hydrogen atoms).
Thus,
[tex]\[ CH_4 + \square O_2 \rightarrow CO_2 + 2 H_2O \][/tex]
- Lastly, balance oxygen (O):
On the right side, we have 1 CO2 (which has 2 oxygen atoms) and 2 H2O (each H2O has 1 oxygen atom, so 2 H2O gives 2 oxygen atoms). In total, that's 4 oxygen atoms on the right.
On the left side, we need 4 oxygen atoms, which means we need 2 O2 molecules (since each O2 molecule contains 2 oxygen atoms).
Therefore, the balanced equation is:
[tex]\[ CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O \][/tex]
### 2. [tex]\( CaCl_2 + \square AgNO_3 \rightarrow Ca(NO_3)_2 + \square AgCl \)[/tex]
To balance this equation:
- Start with calcium (Ca): There is 1 Ca on each side, so calcium is already balanced.
- Next, balance nitrate (NO3): There are 2 nitrate groups (NO3) on the right side in Ca(NO3)2, meaning we need 2 AgNO3 to provide 2 NO3 groups.
Thus,
[tex]\[ CaCl_2 + 2 AgNO_3 \rightarrow Ca(NO_3)_2 + \square AgCl \][/tex]
- Lastly, balance silver (Ag) and chloride (Cl):
We have 2 Ag from 2 AgNO3 on the left, so we need the same number of AgCl on the right.
Additionally, there are 2 Cl from CaCl2 on the left, matching with 2 Cl in 2 AgCl on the right.
Therefore, the balanced equation is:
[tex]\[ CaCl_2 + 2 AgNO_3 \rightarrow Ca(NO_3)_2 + 2 AgCl \][/tex]
### 3. [tex]\( C_2H_6O + \square O_2 \rightarrow \square CO_2 + \square H_2O \)[/tex]
To balance this equation:
- Start with carbon (C): There are 2 carbon atoms in C2H6O, so we need 2 CO2 to balance the carbon atoms.
Thus,
[tex]\[ C_2H_6O + \square O_2 \rightarrow 2 CO_2 + \square H_2O \][/tex]
- Next, balance hydrogen (H): There are 6 hydrogen atoms in C2H6O, which means we need 3 H2O (since each H2O has 2 hydrogen atoms) to provide 6 hydrogen atoms.
[tex]\[ C_2H_6O + \square O_2 \rightarrow 2 CO_2 + 3 H_2O \][/tex]
- Lastly, balance oxygen (O):
On the right side, we have 2 CO2 (which provides 4 oxygen atoms), and 3 H2O (which provides 3 more oxygen atoms), making a total of 7 oxygen atoms on the right.
On the left side, we need 3 O2 to provide 6 oxygen atoms. Adding the 1 oxygen atom already in C2H6O, we get the required 7 oxygen atoms.
Therefore, the balanced equation is:
[tex]\[ C_2H_6O + 3 O_2 \rightarrow 2 CO_2 + 3 H_2O \][/tex]
To summarize, the balanced equations are:
1. [tex]\( CH_4 + 2 O_2 \rightarrow CO_2 + 2 H_2O \)[/tex]
2. [tex]\( CaCl_2 + 2 AgNO_3 \rightarrow Ca(NO_3)_2 + 2 AgCl \)[/tex]
3. [tex]\( C_2H_6O + 3 O_2 \rightarrow 2 CO_2 + 3 H_2O \)[/tex]
