The carbonaceous theoretical oxygen demand of the waste is \(25 \, \text{mg/L}\).
The carbonaceous theoretical oxygen demand (CTOD) is an estimate of the amount of oxygen needed to oxidize the organic carbon present in a waste.
The formula for calculating CTOD is:
\[ CTOD = \frac{{\text{Concentration of Carbon (mg/L)}} \times \text{Stoichiometric Coefficient}}{\text{Molecular Weight of Carbon (mg/mmol)}} \]
For phenol (C6H6O), the stoichiometric coefficient for carbon is 6, and the molecular weight of carbon is \(12 \, \text{g/mol}\).
\[ CTOD = \frac{{50 \, \text{mg/L} \times 6}}{{12 \, \text{mg/mmol}}} \]
\[ CTOD = \frac{{300}}{{12}} \]
\[ CTOD = 25 \, \text{mg/L} \]
Therefore, the carbonaceous theoretical oxygen demand of the waste is \(25 \, \text{mg/L}\).