Step 1: Identify the nature of boric acid.
Boric acid is
\[
H_3BO_3
\]
It behaves as a Lewis acid because boron has an incomplete octet and can accept an electron pair from water.
Step 2: Write the reaction of boric acid with water.
Boric acid does not donate a proton directly. Instead, it accepts hydroxide ion from water.
The reaction is
\[
H_3BO_3+2H_2O\longrightarrow [B(OH)_4]^-+H_3O^+
\]
Step 3: Compare with the given reaction.
Given reaction is
\[
P+Q\longrightarrow [B(OH)_4]^-+H_3O^+
\]
Comparing both reactions, we get
\[
P=H_3BO_3
\]
and
\[
Q=2H_2O
\]
Step 4: Final conclusion.
Therefore,
\[
\boxed{P=H_3BO_3;\;Q=2H_2O}
\]