Step 1: Identify the substrate type.
1-bromohexane \( CH_3(CH_2)_4CH_2Br \) is a primary alkyl halide (halogen on a terminal carbon).
Step 2: Predict the mechanism.
Primary alkyl halides are not sterically hindered. They react with nucleophiles like \( OH^- \) by the \( S_N2 \) mechanism (bimolecular nucleophilic substitution).
Step 3: Write the rate law for SN2.
In \( S_N2 \), both reactants take part in the rate-determining step simultaneously: \[ \text{Rate} = k[\text{1-bromohexane}][OH^-] \]
Step 4: Determine the overall order.
First order in \( [RBr] \) + first order in \( [OH^-] \) = second order overall.
Step 5: Compare with SN1.
\( S_N1 \) would give first order kinetics. The \( S_N2 \) pathway of a primary halide gives second order kinetics.
Step 6: State the answer.
The reaction follows second order kinetics. \[ \boxed{\text{Second order kinetics}} \]