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Balance each of the following chemical equations:

a. [tex]\[ Mg(s) + AgNO_3(aq) \longrightarrow Mg(NO_3)_2(aq) + Ag(s) \][/tex]

b. [tex]\[ Al(s) + CuSO_4(aq) \longrightarrow Al_2(SO_4)_3(aq) + Cu(s) \][/tex]

c. [tex]\[ Pb(NO_3)_2(aq) + NaCl(aq) \longrightarrow PbCl_2(s) + NaNO_3(aq) \][/tex]

d. [tex]\[ HCl(aq) + Al(s) \longrightarrow H_2(g) + AlCl_3(aq) \][/tex]



Answer :

GinnyAnswer
To balance each of these chemical equations, we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms of each element on the product side. Here is the detailed, step-by-step solution for each equation:

### a. [tex]\( \text{Mg} (s) + \text{AgNO}_3 (aq) \rightarrow \text{Mg}(\text{NO}_3)_2 (aq) + \text{Ag} (s) \)[/tex]

1. _Identify each element in the equation:_ Mg, Ag, N, and O.
2. _Count atoms on both sides:_
- Reactants: 1 Mg, 1 Ag, 1 N, 3 O
- Products: 1 Mg, 2 Ag, 2 N, 6 O
3. _Balance nitric acid (NO[tex]\(_3\)[/tex]) groups: Place coefficient 2 before AgNO[tex]\(_3\)[/tex]:_
- Reactants: 1 Mg, 2 Ag, 2 N, 6 O
- Products: 1 Mg, 2 Ag, 2 N, 6 O
4. Now we can see the equation is balanced.

Balanced equation:
[tex]\[ \text{Mg} (s) + 2\text{AgNO}_3 (aq) \rightarrow \text{Mg}(\text{NO}_3)_2 (aq) + 2\text{Ag} (s) \][/tex]

### b. [tex]\( \text{Al} (s) + \text{CuSO}_4 (aq) \rightarrow \text{Al}_2(\text{SO}_4)_3 (aq) + \text{Cu} (s) \)[/tex]

1. _Identify each element:_ Al, Cu, S, and O.
2. _Count atoms on both sides:_
- Reactants: 1 Al, 1 Cu, 1 S, 4 O
- Products: 2 Al, 3 Cu, 3 S, 12 O
3. _Balance Al atoms: Place coefficient 2 before Al:_
- Reactants: 2 Al, 1 Cu, 1 S, 4 O
- Products: 2 Al, 3 Cu, 3 S, 12 O
4. _Balance CuSO[tex]\(_4\)[/tex] groups: Place coefficient 3 before CuSO[tex]\(_4\)[/tex]:_
- Reactants: 2 Al, 3 Cu, 3 S, 12 O
- Products: 2 Al, 3 Cu, 3 S, 12 O
5. Now we can see the equation is balanced.

Balanced equation:
[tex]\[ 2\text{Al} (s) + 3\text{CuSO}_4 (aq) \rightarrow \text{Al}_2(\text{SO}_4)_3 (aq) + 3\text{Cu} (s) \][/tex]

### c. [tex]\( \text{Pb(NO}_3)_2 (aq) + \text{NaCl} (aq) \rightarrow \text{PbCl}_2 (s) + \text{NaNO}_3 (aq) \)[/tex]

1. _Identify each element:_ Pb, N, O, Na, and Cl.
2. _Count atoms on both sides:_
- Reactants: 1 Pb, 2 N, 6 O, 1 Na, 1 Cl
- Products: 1 Pb, 1 N, 3 O, 1 Na, 2 Cl
3. _Balance Cl: Place coefficient 2 before NaCl:_
- Reactants: 1 Pb, 2 N, 6 O, 2 Na, 2 Cl
- Products: 1 Pb, 2 N, 6 O, 1 Na, 2 Cl
4. _Balance NaNO[tex]\(_3\)[/tex]: Place coefficient 2 before NaNO[tex]\(_3\)[/tex]:_
- Reactants: 1 Pb, 2 N, 6 O, 2 Na, 2 Cl
- Products: 1 Pb, 2 N, 6 O, 2 Na, 2 Cl
5. Now we can see the equation is balanced.

Balanced equation:
[tex]\[ \text{Pb(NO}_3)_2 (aq) + 2\text{NaCl} (aq) \rightarrow \text{PbCl}_2 (s) + 2\text{NaNO}_3 (aq) \][/tex]

### d. [tex]\( \text{HCl} (aq) + \text{Al} (s) \rightarrow \text{H}_2 (g) + \text{AlCl}_3 (aq) \)[/tex]

1. _Identify each element:_ H, Cl, and Al.
2. _Count atoms on both sides:_
- Reactants: 1 H, 1 Cl, 1 Al
- Products: 2 H, 3 Cl, 1 Al
3. _Balance Cl: Place coefficient 3 before HCl:_
- Reactants: 3 H, 3 Cl, 1 Al
- Products: 2 H, 3 Cl, 1 Al
4. _Balance H: Place coefficient 3 before H[tex]\(_2\)[/tex]:_
- Reactants: 6 H, 3 Cl, 2 Al
- Products: 3 H[tex]\(_2\)[/tex], 6 Cl, 2 Al
5. _Balance Al and H_2_: Place coefficients respectively 2 before Al and 3 before H2:
- Reactants: 6 H, 6 Cl, 2 Al
- Products: 3 H[tex]\(_2\)[/tex], 6 Cl, 2 Al
6. Now we can see the equation is balanced.

Balanced equation:
[tex]\[ 6\text{HCl} (aq) + 2\text{Al} (s) \rightarrow 3\text{H}_2 (g) + 2\text{AlCl}_3 (aq) \][/tex]

In conclusion, the balanced chemical equations are:

a. [tex]\( \text{Mg} (s) + 2\text{AgNO}_3 (aq) \rightarrow \text{Mg}(\text{NO}_3)_2 (aq) + 2\text{Ag} (s) \)[/tex]

b. [tex]\( 2\text{Al} (s) + 3\text{CuSO}_4 (aq) \rightarrow \text{Al}_2(\text{SO}_4)_3 (aq) + 3\text{Cu} (s) \)[/tex]

c. [tex]\( \text{Pb(NO}_3)_2 (aq) + 2\text{NaCl} (aq) \rightarrow \text{PbCl}_2 (s) + 2\text{NaNO}_3 (aq) \)[/tex]

d. [tex]\( 6\text{HCl} (aq) + 2\text{Al} (s) \rightarrow 3\text{H}_2 (g) + 2\text{AlCl}_3 (aq) \)[/tex]

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