Concepts in Environmental Behavior of Trace Metals 1. CHEMICAL KINETICS AND SORPTION: A REVIEW

LAW OF MASS ACTION At equilibrium, the rate of forward reaction becomes equal to the rate of the reverse reaction and k = 0. k forward *[A] a [B] b = k reverse *[C] c [D] d

ELEMENTARY REACTIONS They occur in a single step. For these reactions, the law of mass action holds. Bimolecular elementary reactions are common in the environment: Tri-molecular elementary rxns are less common but do exist. Complicated stoichiometric equations than tri-molecular do not occur (it is highly improbable that more than 3 molecules collide simultaneously to effect a reaction)

RATE CONSTANT AND TEMPERATURE Arrhenius equation relates reaction rate k and temperature (T) Biological reactions work on the basis of enzyme and have a surprisingly small range of activation energies in natural systems. Q10 rule in biology = The rate of a reaction will approximately double as T increases by 10 0 C increments Linearization conversion of a rate constant from a known or reference temperature to a second temperature

REACTION ORDERS AND TESTING REACTION RATE EXPRESSIONS Most elementary reactions are either zero, first, or second order. Fractional order reactions (e.g. 0.5, 1.5, etc. ) are also observed.

Zero-Order Reactions Heterogeneous complex reactions that occur in many steps in natural waters, methane production and release of hydrolysis products (e.g. NH 3, PO 4 3- ) from anaerobic sediments are examples zero-order reactions [A] Time Linearization and plot k0k0

First-Order Reactions

First-Order Reactions (Cont’d) Example first order reactions: Radioisotope decay, BOD, re-areation and gas transfer, log growth phase of microorganisms, sedimentation of non- coagulating solids, death and respiration rates for bacteria and algae

Second-Order Reactions 1.Zooplankton death rate, atmospheric gas phase reactions 2.Microbial kinetics (substrate-cells), sorption rxns, aquatic redox rxns 3.Autocatalytic rxns = nucleation/crystal growth, some photo redox reactions, microbial division, etc.

Second-Order Reactions (Cont’d) Linearization For autocatalytic reactions, one needs to know the stoichiometry or yield and linearization would lead to a plot similar to #2 above.

Other Reaction Orders Many times a reaction is not elementary (i.e. single step), and the rate expression is not simply zero, first or second order. In this case, the change in reaction rate can be plotted against concentration (on a log-log plot) to get an estimate of the order of reaction (also known as Van’t Hoff Plot) It may be fractional Fractional order reactions occur in precipitation and dissolution reactions Log[C] Logk Log(-dC/dt)] n = 1 n = 2 n =3 Van’t Hoff Plot [C] Time (t) n=2 n=3

SORPTION / ADSORPTION A. SORPTION: This term denotes the distribution of a compound into/onto a sorbent without considering a specific mechanism. Therefore, sorption is a more inclusive and less definitive term and is a more appropriate designator for the distribution of chemicals between solid and aqueous phases Soils/sediments are so complex that several mechanisms are usually active in sorption

B. ADSORPTION: A substance is said to adsorb if the concentration in a boundary region is higher than in the interior of the contiguous phase. Adsorbent: adsorbing surface Asorbate: compound that adsorbs from solution Physio-sorption (e.g. London vdW forces) Chemi-sorption (chemical bonds)

SORPTION ISOTHERMS An isotherm describes the relationship of the concentrations of a solute between two separate phases at equilibrium at constant temperature An adsorption isotherm expresses the relationship between amount of vapor or solute adsorbed as a function of the equilibrium concentration of of the vapor or solute in solution A sorption isotherm describes the same process without reference to the mechanisms DEFINITIONS

Langmuir Isotherm Primarily for gases and based on the following assumptions 1.The energy of adsorption is constant and independent of the extent of surface coverage 2.The adsorption is on localized sites and there is no interaction between the adsorbed molecules 3.The maximum adsorption possible is that of a complete monolayer X = mole of solute adsorbed per gram of adsorbent C = equilibrium conc. of solute in solution X m = Number of moles adsorbed/g of adsorbent to give a complete monolayer b = constant related to the energy of adsorption

Freundlich Isotherm Empirical relation used to express the relation between the amount of compound sorbed and Keq Where x/m = amount of compound sorbed And C e = equilibrium concentration The use of this relation to evaluate experimental data is essentially “curve fitting” and has no mechanistic base. 1. K provides an index of the extent of sorption and is often listed w/o units 2. n = indicates whether the relation between x/m and Ce is linear (n=1) or concave down (n 1) – and when n = 1, K equals the distribution coefficient

Isotherm types that are commonly observed in environmental sciences q q CeCe CeCe L-curve isotherm Solute has a relatively high affinity for the sorbent surface at low surface coverage - Affinity sorbate-sorbent decreases with increasing coverage H-curve isotherm Very high affinity sorbate-sorbent. Probability of inner sphere complexes formation C-curve isotherm Characteristics of non-ionic and hydrophobic compounds Constant partitioning S-curve isotherm Affinity of sorbent for sorbate is less than of solution at low solute concentration. As the concentration of solute increases and exceeds the retention capacity of the solution, sorption peaks up. q

SORPTION KINETICS Batch Studies Column Studies Distribution defined by sorption - not desorption Common 24-hr equilibration batch experiments Rapid removal from solution: >99% in 2 to 3 hrs True equilibrium usually not attained Movement of pollutant monitored as a function of sorbent type (e.g. soil), column dimensions, flow rates, and ionic strength. Water used as eluent Principles of chromatography can be used Data used to analyze sorption kinetics by 2-site Freundlich relation and where S = amount sorbed at respective site (f=fraction of S1 and 1-f=fraction S2) C= concentration in solution k= rate constant K and n are Freundlich parameters from batch experiments and K 1 =Kf and K 2 =K(1-f)