Lead nitrate on heating decomposes to give lead oxide, nitrogen dioxide, and oxygen.

1. Balanced chemical equation: A balanced chemical equation has the same number of each type of atom on both sides of the arrow in a chemical equation.
2. Reactant: Lead nitrate ($\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$)
3. Products: Lead oxide ($\mathrm{PbO}$), nitrogen dioxide (${\mathrm{NO}}_2$), and oxygen (${\mathrm{O}}_2$).
4. The chemical equation representing the reaction is: $$\begin{gathered} \mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2\left(\mathrm{s}\right)\stackrel{∆}{\to }\mathrm{PbO}\left(\mathrm{s}\right)+{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right) \\ \mathrm{Lead}\mathrm{nitrate}\mathrm{Lead}\mathrm{oxide}\mathrm{Nitrogen}\mathrm{dioxide}\mathrm{Oxygen} \end{gathered}$$
5. But the above equation is not balanced as both sides do not have the same number of atoms of each type.

Atom	Reactant side	Product side
Lead ($\mathrm{Pb}$)	1	1
Nitrogen ($\mathrm{N}$)	2	1
Oxygen ($\mathrm{O}$)	6	5

6. Now, to balance the number of nitrogen atoms, multiply ${\mathrm{NO}}_2$ by 2.

$$\begin{gathered} \mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2\left(\mathrm{s}\right)\stackrel{∆}{\to }\mathrm{PbO}\left(\mathrm{s}\right)+2{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right) \\ \mathrm{Lead}\mathrm{nitrate}\mathrm{Lead}\mathrm{oxide}\mathrm{Nitrogen}\mathrm{dioxide}\mathrm{Oxygen} \end{gathered}$$

Atom	Reactant side	Product side
Lead ($\mathrm{Pb}$)	1	1
Nitrogen ($\mathrm{N}$)	2	2
Oxygen ($\mathrm{O}$)	6	7

7. Next, to balance the oxygen atom, multiply ${\mathrm{O}}_2$ by $\frac{1}{2}$.

$$\begin{gathered} \mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2\left(\mathrm{s}\right)\stackrel{∆}{\to }\mathrm{PbO}\left(\mathrm{s}\right)+2{\mathrm{NO}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right) \\ \mathrm{Lead}\mathrm{nitrate}\mathrm{Lead}\mathrm{oxide}\mathrm{Nitrogen}\mathrm{dioxide}\mathrm{Oxygen} \end{gathered}$$

Atom	Reactant side	Product side
Lead ($\mathrm{Pb}$)	1	1
Nitrogen ($\mathrm{N}$)	2	2
Oxygen ($\mathrm{O}$)	6	6

8. Finally, the balanced equation is:

$$\begin{gathered} \mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2\left(\mathrm{s}\right)\stackrel{∆}{\to }\mathrm{PbO}\left(\mathrm{s}\right)+2{\mathrm{NO}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right) \\ \mathrm{Lead}\mathrm{nitrate}\mathrm{Lead}\mathrm{oxide}\mathrm{Nitrogen}\mathrm{dioxide}\mathrm{Oxygen} \end{gathered}$$