We can calculate the required mass of \( \text{Br}_2 \) by first determining the molar mass of phenol and the stoichiometry of the reaction.
- Molar mass of phenol = 94 g/mol.
- Molar mass of \( \text{Br}_2 \) = 159.808 g/mol.
For every mole of phenol, 3 moles of \( \text{Br}_2 \) are needed to form 2,4,6-tribromophenol. Therefore, the number of moles of \( \text{Br}_2 \) required is:
\[
\frac{2}{94} \times 3 \times 159.808 = \text{grams of } \text{Br}_2.
\]
Thus, the required mass of \( \text{Br}_2 \) is calculated to the nearest integer.