Thermodynamics and kinetics of transformation reactions Chapter 12

Chemical transformation reactions bonds breaking and forming 3 types: chemical photochemical biological

Questions Can a given compound be transformed in the environment by one or more pathways? what are the reaction products? what are the kinetics? what is the influence of variables such as pH, light intensity, redox condition, ionic strength, etc, on products and kinetics?

Thermodynamics vs. Kinetics We have already discussed one type of transformation reaction: proton transfer. Proton transfer was considered to be fast and reversible, i.e. equilibrium was established. We could therefore ignore kinetics and deal only with products and equilibrium. the reactions we will now discuss will generally be under kinetic control, therefore focus on kinetics, not equilibrium (although eqbm considerations may be useful in predicting kinetics!)

Thermodynamics Use infinite dilution state in water as reference reference state,  o’ i  1

General reversible chemical reaction where A, B, P, Q are chemical species and a, b, p, q are stoichiometric coefficients The free energy change of this reaction is equal to the free energies of the products minus reactants: This is related to the standard free energies of the product minus the reactants:

Reaction quotient, Q r at equilibrium,  r G = 0, and Q is equal to the equilibrium constant:

Temperature dependence of K as with ALL equilibrium constants, K is dependent on temperature via the enthalpy of the reaction: enthalpies of chemical reactions can be MUCH larger than those of phase transfer processes. go through example 12.2 page 467

KINETICS Rate law = a mathematical function describing the turnover rate of the compound of interest as a function of the concentrations of the various species participating in the reaction May or may NOT have a theoretical basis For example: a, b, c indicate the order of the reaction with respect to each species overall reaction order = a+b+c

First order reactions

Pseudo first order reactions pseudo-first order: concentration of one reactant remains essentially constant over time (often because it is in large excess compared to the other reagent)

First order reaction with back reaction Example: conversion of aldehyde (A) to diol (D) At equilibrium

For formaldehyde, thus at pH7 at equilibrium, formaldehyde is 99.8% in the diol form the time to steady state is the sum of the forward and back rate constants:

Catalyzed Reactions Characterized by: first-order kinetics at low concentration zero-order kinetics at high concentration Michealis-Menton kinetics Where J = max reaction rate = k E [E] tot k = pseudo first order rxn rate constant

Michealis-Menton kinetics Where J = max reaction rate = k E [E] tot k = pseudo first order reaction rate constant = k E [E] tot K E Reaction at a limited number of reactive sites (enzymes) [E] tot which have affinity for binding the substrate of K E

Arrhenius Equation and Transition State Theory reactions occur as a sequence of elementary steps. usually one of these steps is much slower than the others  Rate Determining Step empirically, the effect of T on the rate of this reaction step (and therefore on the overall reaction rate) is described by the Arrhenius equation: pre-exponential factor or “frequency factor” describes collision frequency and the orientation probability Activation energy describes the fraction of species with energy greater than E a

Temperature dependence of reaction rate constant is: E a is therefore analogous to the  H of a phase transfer process E a is usually 40 to 130 kJ/mol, i.e. usually bigger than  H for phase transfer processes. Reaction rates are more sensitive to temperature than partitioning A = – for unimolecular reactions A = 10 7 – for bimolecular processes

k = Boltzmann constant h = Plank’s constant E a = potential energy of activation,  H ‡ is the total: “Activated complex” or “transition state” theory: B + C  BC ‡  D + E BC ‡ is the activated complex or transition state maximum energy barrier

The well mixed reactor aka The one-box model aka The CSTR volume V Input I Flow Q Output O Flow Q mass M concentration C = M/V Reaction R tot lost mixing R tot = total reaction rate (sum of all individual reactions)

Mass balance on the reactor mass per time If volume is constant: Now we have to make some simplifying assumptions: Assume 1: k w = Q/V = flushing or dilution rate Assume 2: all reactions are first order

Mass balance becomes: steady state concentration: time to steady state: If I = QC in

Problem 12.1 Consider the transformation of hexachloroethane (HCA) to tetrachloroethene (PCE) in an acidic (why acidic?) aqueous solution at 25C containing 0.5 mM Fe 2+ (aq), 5 mM Fe 3+ (aq), 20 mM Cl - and 1  M HCA: HCA + 2Fe 2+  PCE + 2Fe Cl - What type of reaction is this? To what extent is HCA transformed to PCE?  f Gº given in either aqueous or gas phase