Step 1: Recall the Lewis acid nature of boric acid $H_3BO_3$.
Boric acid is a weak Lewis acid. The boron atom has an incomplete octet and an empty p-orbital, enabling it to accept electron pairs. It does NOT donate $H^+$ directly.
Step 2: Write the correct reaction of boric acid with water.
Boric acid accepts $OH^-$ from water: \[ H_3BO_3 + 2H_2O \longrightarrow [B(OH)_4]^- + H_3O^+ \] One $H_3BO_3$ and two water molecules ($2H_2O$) are the reactants.
Step 3: Match with the given reaction format.
Given: $P + Q \to [B(OH)_4]^- + H_3O^+$. Comparing: $P = H_3BO_3$ and $Q = 2H_2O$.
Step 4: Verify by atom balance.
Left: $H_3BO_3$ (1B, 3O, 3H) + $2H_2O$ (2O, 4H) = 1B, 5O, 7H. Right: $[B(OH)_4]^-$ (1B, 4O, 4H) + $H_3O^+$ (1O, 4H). Total right: 1B, 5O, 8H. Charges and atoms balance.
Step 5: Rule out other options.
Option (a) uses $3H_2O$ (wrong stoichiometry). Option (c) uses $HBO_2$ (different compound). Option (d) uses $2H_3BO_3$. None match.
Step 6: State the final answer.
\[ \boxed{P = H_3BO_3;\ Q = 2H_2O} \]