We were estimating dissolved $\ce{CO2}$ in water by American Public Health Association (APHA) method. It was a titrimetric method using phenolphthalein indicator.
Titrant used was $\ce{NaOH}$ and analyte was sample water. Reactions involved:
$$\ce{CO2 (g) ⇌ CO2 (aq)}$$ $$\ce{CO2 aq + H2O ⇌ H2CO3 ⇌ H+ + HCO3^2-} \label{rxn:1}\tag{1}$$
(Only $10\%$ of dissolved $\ce{CO2}$ get converted into $\ce{H2CO3}$.)
On addition of $\ce{NaOH}$:
\begin{align} \ce{2NaOH + CO2 &-> Na2CO3 + H2O} \label{rxn:2}\tag{2} \\ \ce{Na2CO3 + H2O + CO2 &-> 2NaHCO3} \label{rxn:3}\tag{3}\\ \ce{NaHCO3 &-> Na+ + HCO3-} \label{rxn:4}\tag{4} \\ \ce{\underset{from \eqref{rxn:1} and \eqref{rxn:4}}{HCO3-} + H2O &-> H2CO3 + OH-} \\ \ce{OH- + H+ &-> H2O} \\ \ce{HIn &⇌ H+ + In-} \end{align}
(The equilibrium shift to the right and when $[\ce{HIn}]:[\ce{In^-}]=1:10$ pink colour appears.)
But when we calculate the concentration of $\ce{CO2}$ we consider only reaction $\eqref{rxn:2}$, which means we are calculating only a portion of the molecular $\ce{CO2}$ while the $\ce{CO2}$ that was present in the solution and reacted in step 3 and the $\ce{CO2}$ (the $10\%$) that was directly converted into $\ce{H2CO3}$ (Rxn. $\eqref{rxn:1}$) are not taken into account.
So it means we are calculating only a part of the free $\ce{CO2}$ ($45\%$) and not all.
From this can we conclude that APHA's method is not very accurate at estimating the free $\ce{CO2}$ in water?
P. S. I read the procedure and also the calculations in a practical book.