Two alkyl bromides undergo bimolecular nucleophilic substitution (SN2) with hydroxide ion in separate aqueous solutions at 298 K:
Reaction 1: CH3Br + OH⁻ → CH3OH + Br⁻ (primary substrate)
Reaction 2: (CH3)3CBr + OH⁻ → (CH3)3COH + Br⁻ (tertiary substrate)
Experimental data:
• Both reactions have identical activation energies of 74 kJ mol⁻¹.
• The measured rate constants are k1=1.6×106 L mol⁻¹ s⁻¹ and k2=4.0×102 L mol⁻¹ s⁻¹, respectively.
• The pre-exponential factor A in the Arrhenius equation can be written as A=PZ, where Z is the theoretical collision frequency calculated from kinetic theory and P is an empirical orientation factor.
Assume that Z is the same for both reactions at 298 K.
(a) Derive an expression for the ratio P2P1 in terms of the given rate constants and activation energy.
(b) Use the experimental data to calculate the numerical value of P2P1.
(c) Interpret your result from part (b) in terms of steric hindrance around the reactive carbon centers.
(d) Propose one structural modification to the tertiary substrate that would increase P2 while retaining the same leaving group. Justify your proposal based on molecular geometry.