Complete and balance the following reactions :
(i) `P_4O_10 + PCl_5 rarr"___"`
(ii) `NH_3 + NaOCl rarr "____" + NaCl + H_2 O`
(iii) `Ca(PO_4)_3 + 4H_3PO_4 rarr"____"`
(iv) `AgCl + NH_4OH rarr "_____" + "____"`
(v) `Pb(NO_3)_2 overset (Delta)rarr PbO + "___" + "____"`
(vi) `Mg + HNO_3 rarr "____" + "____"`.

Explanation

Let's complete and balance the given reactions step by step.

### (i) \( P_4O_{10} + PCl_5 \rightarrow \)

1. **Identify the reactants**: We have phosphorus pentoxide (\( P_4O_{10} \)) and phosphorus pentachloride (\( PCl_5 \)).
2. **Determine the products**: The reaction between these two compounds typically forms phosphoryl chloride (\( POCl_3 \)).
3. **Write the unbalanced equation**:
\[ P_4O_{10} + PCl_5 \rightarrow POCl_3 \]
4. **Balance the equation**:
- There are 4 phosphorus atoms in \( P_4O_{10} \) and 1 in \( POCl_3 \), so we need 4 \( POCl_3 \).
- Balance oxygen and chlorine accordingly.
\[ P_4O_{10} + 6PCl_5 \rightarrow 4POCl_3 + 2PCl_3 \]

### (ii) \( NH_3 + NaOCl \rightarrow \)

1. **Identify the reactants**: Ammonia (\( NH_3 \)) and sodium hypochlorite (\( NaOCl \)).
2. **Determine the products**: The reaction produces hydrazine (\( N_2H_4 \)), sodium chloride (\( NaCl \)), and water (\( H_2O \)).
3. **Write the unbalanced equation**:
\[ NH_3 + NaOCl \rightarrow N_2H_4 + NaCl + H_2O \]
4. **Balance the equation**:
- We need 2 moles of \( NH_3 \) to form 1 mole of \( N_2H_4 \).
\[ 2NH_3 + NaOCl \rightarrow N_2H_4 + NaCl + H_2O \]

### (iii) \( Ca(PO_4)_3 + 4H_3PO_4 \rightarrow \)

1. **Identify the reactants**: Tricalcium phosphate (\( Ca_3(PO_4)_2 \)) and phosphoric acid (\( H_3PO_4 \)).
2. **Determine the products**: The reaction forms calcium dihydrogen phosphate (\( Ca(H_2PO_4)_2 \)).
3. **Write the unbalanced equation**:
\[ Ca_3(PO_4)_2 + 4H_3PO_4 \rightarrow Ca(H_2PO_4)_2 \]
4. **Balance the equation**:
\[ Ca_3(PO_4)_2 + 4H_3PO_4 \rightarrow 3Ca(H_2PO_4)_2 \]

### (iv) \( AgCl + NH_4OH \rightarrow \)

1. **Identify the reactants**: Silver chloride (\( AgCl \)) and ammonium hydroxide (\( NH_4OH \)).
2. **Determine the products**: The reaction produces a soluble complex \( Ag(NH_3)_2Cl \) and water (\( H_2O \)).
3. **Write the unbalanced equation**:
\[ AgCl + NH_4OH \rightarrow Ag(NH_3)_2Cl + H_2O \]
4. **Balance the equation**:
\[ AgCl + 2NH_4OH \rightarrow Ag(NH_3)_2Cl + 2H_2O \]

### (v) \( Pb(NO_3)_2 \overset{\Delta}{\rightarrow} \)

1. **Identify the reactant**: Lead nitrate (\( Pb(NO_3)_2 \)).
2. **Determine the products**: The decomposition produces lead oxide (\( PbO \)), nitrogen dioxide (\( NO_2 \)), and oxygen gas (\( O_2 \)).
3. **Write the unbalanced equation**:
\[ Pb(NO_3)_2 \rightarrow PbO + NO_2 + O_2 \]
4. **Balance the equation**:
\[ 2Pb(NO_3)_2 \rightarrow 2PbO + 4NO_2 + O_2 \]

### (vi) \( Mg + HNO_3 \rightarrow \)

1. **Identify the reactants**: Magnesium (\( Mg \)) and nitric acid (\( HNO_3 \)).
2. **Determine the products**: The reaction produces magnesium nitrate (\( Mg(NO_3)_2 \)) and hydrogen gas (\( H_2 \)).
3. **Write the unbalanced equation**:
\[ Mg + HNO_3 \rightarrow Mg(NO_3)_2 + H_2 \]
4. **Balance the equation**:
\[ Mg + 2HNO_3 \rightarrow Mg(NO_3)_2 + H_2 \]

### Final Balanced Reactions:
1. \( P_4O_{10} + 6PCl_5 \rightarrow 4POCl_3 + 2PCl_3 \)
2. \( 2NH_3 + NaOCl \rightarrow N_2H_4 + NaCl + H_2O \)
3. \( Ca_3(PO_4)_2 + 4H_3PO_4 \rightarrow 3Ca(H_2PO_4)_2 \)
4. \( AgCl + 2NH_4OH \rightarrow Ag(NH_3)_2Cl + 2H_2O \)
5. \( 2Pb(NO_3)_2 \rightarrow 2PbO + 4NO_2 + O_2 \)
6. \( Mg + 2HNO_3 \rightarrow Mg(NO_3)_2 + H_2 \)