Certainly! To balance the given chemical equation and identify the phases, let's go through it step-by-step.
The unbalanced chemical equation is:
[tex]\[ \text{Na}_2\text{S} \,(\text{aq}) + \text{Pb(NO}_3)_2 \,(\text{aq}) \rightarrow \text{NaNO}_3 \,(\text{aq}) + \text{PbS} \,(\text{s}) \][/tex]
1. Identify the phases:
- Na₂S (sodium sulfide) in aqueous phase: (aq)
- Pb(NO₃)₂ (lead(II) nitrate) in aqueous phase: (aq)
- NaNO₃ (sodium nitrate) in aqueous phase: (aq)
- PbS (lead(II) sulfide) in solid phase: (s)
2. Balance the sodium (Na) atoms:
- On the reactant side, we have 2 sodium atoms in Na₂S.
- On the product side, we currently have 1 sodium atom in NaNO₃.
- To balance this, we need 2 molecules of NaNO₃ on the product side.
So, the equation with sodium balanced looks like:
[tex]\[ \text{Na}_2\text{S} \,(\text{aq}) + \text{Pb(NO}_3)_2 \,(\text{aq}) \rightarrow 2 \, \text{NaNO}_3 \,(\text{aq}) + \text{PbS} \,(\text{s}) \][/tex]
3. Now, let's check the balance for the other atoms:
- Sulfur (S):
- Reactant side: 1 atom in Na₂S.
- Product side: 1 atom in PbS.
- Sulfur is balanced.
- Lead (Pb):
- Reactant side: 1 atom in Pb(NO₃)₂.
- Product side: 1 atom in PbS.
- Lead is balanced.
- Nitrogen (N):
- Reactant side: 2 atoms in Pb(NO₃)₂.
- Product side: 2 atoms in 2 NaNO₃ (since each NaNO₃ has 1 nitrogen atom and there are 2 molecules).
- Nitrogen is balanced.
- Oxygen (O):
- Reactant side: 6 atoms in Pb(NO₃)₂ (2 molecules of NO₃, each having 3 oxygen atoms).
- Product side: 6 atoms in 2 NaNO₃ (2 molecules of NaNO₃, each having 3 oxygen atoms).
- Oxygen is balanced.
Since all the atoms are balanced, the final balanced chemical equation is:
[tex]\[ \boxed{\text{Na}_2\text{S} \,(\text{aq}) + \text{Pb(NO}_3)_2 \,(\text{aq}) \rightarrow 2 \, \text{NaNO}_3 \,(\text{aq}) + \text{PbS} \,(\text{s})} \][/tex]
