Step 1: Write the reaction.
Pentene reacts with bromine by addition reaction:
\[
C_5H_{10} + Br_2 \rightarrow C_5H_{10}Br_2
\]
Step 2: Determine mole ratio.
From the equation:
\[
1 \text{ mole of pentene reacts with } 1 \text{ mole of } Br_2
\]
Step 3: Calculate molar mass of pentene.
\[
M(C_5H_{10}) = 5 \times 12 + 10 \times 1 = 60 + 10 = 70 \, \text{g/mol}
\]
Step 4: Calculate moles of pentene.
\[
\text{Moles} = \frac{5}{70} = \frac{1}{14}
\]
Step 5: Use mole ratio.
Moles of \( Br_2 \) required = \( \frac{1}{14} \)
Step 6: Calculate molar mass of bromine.
\[
M(Br_2) = 2 \times 80 = 160 \, \text{g/mol}
\]
Step 7: Find mass of bromine.
\[
\text{Mass} = \frac{1}{14} \times 160 = 11.43 \, \text{g}
\]
\[
\boxed{11.4 \, \text{g}}
\]