2 HI in the hydrogen-iodine reaction. In cases where a termolecular step might plausibly be proposed, one of the reactants is generally present in high concentration (e.g., as a solvent or diluent gas). Relationship to other parameters For a first-order reaction (including a unimolecular one-step process), there is a direct relationship between the unimolecular rate constant and the half-life of the reaction: . Transition state theory gives a relationship between the rate constant and the Gibbs free energy of activation a quantity that can be regarded as the free energy change needed to reach the transition state. In particular, this energy barrier incorporates both enthalpic and entropic changes that need to be achieved for the reaction to take place: The result found from transition state theory is where h is the Planck constant and R the molar gas constant. As useful rules of thumb, a first-order reaction with a rate constant of 10−4 s−1 will have a half-life (t1/2) of approximately 2 hours. For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (ΔG‡) is approximately 23 kcal/mol. Temperature dependence The Arrhenius equation is an elementary treatment that gives the quantitative basis of the relationship between the activation energy and the reaction rate at which a reaction proceeds. The rate constant as a function of thermodynamic temperature is then given by and the reaction rate by where Ea is the activation energy, and R is the gas constant, and m and n are experimentally determined partial orders in [A] and [B], respectively. Since at temperature T the molecules have energies according to a Boltzmann distribution, one can expect the proportion of collisions with energy greater than Ea to vary with e. The constant of proportionality A is the pre-exponential factor, or frequency factor (not to be confused here with the reactant A) takes into consideration the frequency at which reactant molecules are colliding and the likelihood that a collision leads to a successful reaction. Here, A has the same dimensions as an (m + n)-order rate constant (see Units below). Another popular model that is derived using more sophisticated statistical mechanical considerations is the Eyring equation from transition state theory: where ΔG‡ is the free energy of activation, a parameter that incorporates both the enthalpy and entropy change needed to reach the transition state. The temperature dependence of ΔG‡ is used to compute these