A three-step gas-phase reaction converts species R (energy reference = 0 kJ mol⁻¹) to species P. A textual description of the potential-energy profile is given.
• Transition State 1 (TS₁) peaks at 120 kJ mol⁻¹ and leads to Intermediate 1 (Int₁) at +40 kJ mol⁻¹.
• Transition State 2 (TS₂) peaks at 90 kJ mol⁻¹ and leads to Intermediate 2 (Int₂) at +30 kJ mol⁻¹.
• Transition State 3 (TS₃) peaks at 110 kJ mol⁻¹ and drops to products P at –20 kJ mol⁻¹.
Assume each peak corresponds to one elementary step and that no other processes occur.
(a) Calculate the forward activation energy for each of the three elementary steps.
(b) Determine the overall enthalpy change ΔHoverall for the conversion R → P.
(c) Compute the activation energy for the reverse direction of the second elementary step (Int₂ → TS₂ → Int₁).
(d) Identify which elementary step controls the rate in (i) the forward direction and (ii) the reverse direction. Justify each choice based on numerical values from parts (a) and (c).