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The transition state represents the single highest-energy configuration at the peak of the energy barrier. The activated complex refers to the collection of species near the transition state, forming a transient equilibrium with reactants. Once the transition state is reached, the system may revert to reactants or proceed to products.

A reaction profile plots potential energy against the reaction coordinate, showing how energy changes as reactants approach each other. As reactants interact, potential energy increases due to repulsive forces and structural distortions until reaching a maximum. This maximum represents the activation energy barrier that must be overcome for the reaction to proceed.

The Eyring equation links the rate constant to the transmission coefficient, Boltzmann's constant, temperature, the transition-state equilibrium constant, standard concentration, and Planck's constant. It can also be expressed using the Gibbs free energy of activation, connecting reaction kinetics with thermodynamic quantities and showing how temperature, entropy, and enthalpy influence reaction rates.

Transition state theory is called activated-complex theory because it focuses on the formation of a short-lived, high-energy activated complex during a reaction. This theory explains reaction rates in both gas-phase and solution-phase reactions by considering the molecular-level formation of this transient configuration at the energy barrier peak.

The equilibrium constant for activated complex formation is related to the Gibbs free energy of activation. The Eyring equation expresses the rate constant as kr = κ(kT/hc°)e^(-ΔG‡/RT), where ΔG‡ is the activation Gibbs free energy. This formulation demonstrates how thermodynamic properties directly determine reaction rates.

Once reactants reach the transition state at the peak of the energy barrier, the system can follow two pathways. The transition state can either collapse back into the reactants, returning to the starting materials, or decay into products, completing the forward reaction.

Transition state theory explains reaction rates in both solution and gas phases, such as precipitation in solution and ammonia synthesis in gases. By describing how reactants form high-energy activated complexes and overcome energy barriers, the theory provides a unified molecular-level explanation for rate laws and equilibrium constants for elementary reactions across different reaction environments.