Appendix 3.A.Reaction rate under non-equilibrium conditions On a microscopic,molecular level,we can write for a state selected and state resolved reaction F+HCI()→CI+HF() where i and j label the different internal states.We assume here that the kinetic energy has a thermal distribution.The observed bulk reaction rate at complete thermal equilibrium is then a sum over the rates of reaction of the HCI molecules,in all possible states,with F atoms, -∑k(TEHC6] (A.3.1) dt Here k(T)is the reaction rate constant for a selected state of the reactants.Whether the system is in thermal equilibrium over the internal states of HCl or not,we can rewrite(A.3.1) as 四-∑k(D [HCID HCI=K(TXFIHCI] (A.3.2) dt [HCI] where [HCI]is the total concentration of HCl.By comparison to equation(3.1)this defines a reaction rate constant,k(T)as k(T)=∑nHC0=∑P,k(D (A.3.3) [HCI] i Here Pi,as defined by equation(A.3.3),is the relative population (=mol fraction)of HCI molecules in the state i [HCI(O] Pi= (A.3.4) [HCI] In general pi can depend on time and so equation(A.3.3)does not necessarily define a rate constant.If however the system is in thermal equilibrium at the temperature T then pi is the MRD Chapter 3 page 15 ©R D Levine(2003)Appendix 3.A. Reaction rate under non-equilibrium conditions On a microscopic, molecular level, we can write for a state selected and state resolved reaction F + HCl(i) → Cl + HF( j) where i and j label the different internal states. We assume here that the kinetic energy has a thermal distribution. The observed bulk reaction rate at complete thermal equilibrium is then a sum over the rates of reaction of the HCl molecules, in all possible states, with F atoms, − d[F] dt = ki(T)[F][HCl(i)] i ∑ (A.3.1) Here ki(T) is the reaction rate constant for a selected state of the reactants. Whether the system is in thermal equilibrium over the internal states of HCl or not, we can rewrite (A.3.1) as − d[F] dt = ki(T)[F][HCl(i)] [HCl] [HCl] i ∑ = k(T)[F][HCl] (A.3.2) where [HCl] is the total concentration of HCl. By comparison to equation (3.1) this defines a reaction rate constant, k(T) as k(T) = ki(T) [HCl(i)] [HCl] i ∑ ≡ pi i ∑ ki(T) (A.3.3) Here pi , as defined by equation (A.3.3), is the relative population (=mol fraction) of HCl molecules in the state i pi = [HCl(i)] [HCl] (A.3.4) In general pi can depend on time and so equation (A.3.3) does not necessarily define a rate constant. If however the system is in thermal equilibrium at the temperature T then pi is the MRD Chapter 3 page 15 © R D Levine (2003)