Step 1: Formation of sol \(P\).
On boiling \(\mathrm{FeCl_3}\) solution with water,
\[
\mathrm{FeCl_3+3H_2O
\rightarrow
Fe(OH)_3+3HCl}
\]
The hydrated ferric oxide particles preferentially adsorb \(\mathrm{Fe^{3+}}\) ions and become positively charged.
Hence,
\[
P=\mathrm{Fe_2O_3\cdot xH_2O/Fe^{3+}}
\]
Step 2: Formation of sol \(Q\).
When \(\mathrm{FeCl_3}\) is added to excess NaOH,
\[
\mathrm{FeCl_3+3NaOH
\rightarrow
Fe(OH)_3+3NaCl}
\]
The precipitated ferric hydroxide adsorbs excess \(\mathrm{OH^-}\) ions and forms a negatively charged sol.
Hence,
\[
Q=\mathrm{Fe_2O_3\cdot xH_2O/OH^-}
\]
Step 3: Final conclusion.
Therefore,
\[
\boxed{P=\mathrm{Fe_2O_3\cdot xH_2O/Fe^{3+}},\;
Q=\mathrm{Fe_2O_3\cdot xH_2O/OH^-}}
\]
Hence, the correct option is \(\boxed{(C)}\).