Answer :
Sure, let's go through the process of balancing each of the provided chemical equations step-by-step.
### (a) [tex]\( \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \][/tex]
2. List the number of atoms of each element on both sides:
- Left side: 1 H, 1 N, 3 O, 1 Ca, 2 OH (equivalent to 2 H and 2 O)
- Right side: 2 N, 6 O (from 2 NO₃⁻), 1 Ca, 1 H₂O (equivalent to 2 H and 1 O)
3. Balance the most complex molecule first (Ca(NO₃)₂):
[tex]\[ \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \][/tex]
4. Add coefficients to balance each atom. Start with nitric acid (HNO₃):
[tex]\[ 2 \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \][/tex]
5. Verify the balance:
- Left: 2 H, 2 N, 6 O, 1 Ca, 2 OH (equivalent to 2 H and 2 O)
- Right: 2 N, 6 O (2×3=6), 1 Ca, 2 H, 2 O
Thus, the balanced equation is:
[tex]\[ \boxed{2 \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + 2 \text{H}_2\text{O}} \][/tex]
### (b) [tex]\( \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} \][/tex]
2. List the atoms:
- Left: 1 Na, 1 OH (equivalent to 1 Na, 1 O, 1 H), 2 H, 1 S, and 4 O (from H₂SO₄)
- Right: 2 Na, 1 S, 4 O (from Na₂SO₄), 2 H and 1 O (from H₂O)
3. Balance sodium (Na) first by placing coefficient 2 before NaOH:
[tex]\[ 2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} \][/tex]
4. Recalculate the atoms:
- Left: 2 Na, 2 OH (equivalent to 2 Na, 2 O, 2 H), 2 H, 1 S, and 4 O (from H₂SO₄)
- Right: 2 Na, 1 S, 4 O (from Na₂SO₄), 2 H and 1 O (from H₂O)
5. Balance hydrogen (H) and oxygen (O) by adding a coefficient 2 before H₂O:
[tex]\[ 2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \][/tex]
6. Verify the balance:
- Left: 2 Na, 2 OH (equivalent to 2 Na, 2 O, 2 H), 2 H, 1 S, and 4 O
- Right: 2 Na, 1 S, 4 O, 2 H, and 2 O
Thus, the balanced equation is:
[tex]\[ \boxed{2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O}} \][/tex]
### (c) [tex]\( \text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3 \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3 \][/tex]
2. List the atoms:
- Left: 1 Na, 1 Cl, 1 Ag, 1 N, 3 O
- Right: 1 Ag, 1 Cl, 1 Na, 1 N, 3 O
3. Check if it's already balanced:
- Left: 1 Na, 1 Cl, 1 Ag, 1 N, 3 O
- Right: 1 Na, 1 Cl, 1 Ag, 1 N, 3 O
All elements have the same numbers on both sides, so the equation is already balanced:
[tex]\[ \boxed{\text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3} \][/tex]
### (d) [tex]\( \text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + \text{HCl} \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + \text{HCl} \][/tex]
2. List the atoms:
- Left: 1 Ba, 2 Cl, 2 H, 1 S, and 4 O
- Right: 1 Ba, 1 S, 4 O, 1 H, and 1 Cl
3. Balance chlorine (Cl) by placing coefficient 2 before HCl:
[tex]\[ \text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + 2 \text{HCl} \][/tex]
4. Recalculate the atoms:
- Left: 1 Ba, 2 Cl, 2 H, 1 S, and 4 O
- Right: 1 Ba, 1 S, 4 O, 2 H, and 2 Cl
Thus, the balanced equation is:
[tex]\[ \boxed{\text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + 2 \text{HCl}} \][/tex]
Each of the provided chemical equations has been balanced.
### (a) [tex]\( \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \][/tex]
2. List the number of atoms of each element on both sides:
- Left side: 1 H, 1 N, 3 O, 1 Ca, 2 OH (equivalent to 2 H and 2 O)
- Right side: 2 N, 6 O (from 2 NO₃⁻), 1 Ca, 1 H₂O (equivalent to 2 H and 1 O)
3. Balance the most complex molecule first (Ca(NO₃)₂):
[tex]\[ \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \][/tex]
4. Add coefficients to balance each atom. Start with nitric acid (HNO₃):
[tex]\[ 2 \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + \text{H}_2\text{O} \][/tex]
5. Verify the balance:
- Left: 2 H, 2 N, 6 O, 1 Ca, 2 OH (equivalent to 2 H and 2 O)
- Right: 2 N, 6 O (2×3=6), 1 Ca, 2 H, 2 O
Thus, the balanced equation is:
[tex]\[ \boxed{2 \text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3\text{)}_2 + 2 \text{H}_2\text{O}} \][/tex]
### (b) [tex]\( \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} \][/tex]
2. List the atoms:
- Left: 1 Na, 1 OH (equivalent to 1 Na, 1 O, 1 H), 2 H, 1 S, and 4 O (from H₂SO₄)
- Right: 2 Na, 1 S, 4 O (from Na₂SO₄), 2 H and 1 O (from H₂O)
3. Balance sodium (Na) first by placing coefficient 2 before NaOH:
[tex]\[ 2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2\text{O} \][/tex]
4. Recalculate the atoms:
- Left: 2 Na, 2 OH (equivalent to 2 Na, 2 O, 2 H), 2 H, 1 S, and 4 O (from H₂SO₄)
- Right: 2 Na, 1 S, 4 O (from Na₂SO₄), 2 H and 1 O (from H₂O)
5. Balance hydrogen (H) and oxygen (O) by adding a coefficient 2 before H₂O:
[tex]\[ 2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \][/tex]
6. Verify the balance:
- Left: 2 Na, 2 OH (equivalent to 2 Na, 2 O, 2 H), 2 H, 1 S, and 4 O
- Right: 2 Na, 1 S, 4 O, 2 H, and 2 O
Thus, the balanced equation is:
[tex]\[ \boxed{2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O}} \][/tex]
### (c) [tex]\( \text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3 \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3 \][/tex]
2. List the atoms:
- Left: 1 Na, 1 Cl, 1 Ag, 1 N, 3 O
- Right: 1 Ag, 1 Cl, 1 Na, 1 N, 3 O
3. Check if it's already balanced:
- Left: 1 Na, 1 Cl, 1 Ag, 1 N, 3 O
- Right: 1 Na, 1 Cl, 1 Ag, 1 N, 3 O
All elements have the same numbers on both sides, so the equation is already balanced:
[tex]\[ \boxed{\text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3} \][/tex]
### (d) [tex]\( \text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + \text{HCl} \)[/tex]
1. Write down the unbalanced equation:
[tex]\[ \text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + \text{HCl} \][/tex]
2. List the atoms:
- Left: 1 Ba, 2 Cl, 2 H, 1 S, and 4 O
- Right: 1 Ba, 1 S, 4 O, 1 H, and 1 Cl
3. Balance chlorine (Cl) by placing coefficient 2 before HCl:
[tex]\[ \text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + 2 \text{HCl} \][/tex]
4. Recalculate the atoms:
- Left: 1 Ba, 2 Cl, 2 H, 1 S, and 4 O
- Right: 1 Ba, 1 S, 4 O, 2 H, and 2 Cl
Thus, the balanced equation is:
[tex]\[ \boxed{\text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + 2 \text{HCl}} \][/tex]
Each of the provided chemical equations has been balanced.
