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Electrochemistry CE 541

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Electrochemistry is the relationship between Chemical Phenomena and Electrical Phenomena It is needed in Environmental Engineering to understand: Corrosion Corrosion Electrochemical oxidation of wastes Electrochemical oxidation of wastes Analytical procedures Analytical procedures Automatic monitoring of waste streams Automatic monitoring of waste streams Oxidation-reduction reactions Oxidation-reduction reactions

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Current Flow in Solution Current can flow through: Solution of electrolyte Solution of electrolyte Metallic conductors Metallic conductors Characteristics of current flow through a metal: Chemical properties of metal are not changed Chemical properties of metal are not changed Current is carried by electrons Current is carried by electrons Increase in temperature increases resistance Increase in temperature increases resistance

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Characteristics of current flow through a solution: Chemical change occurs in solution Chemical change occurs in solution Current is carried by ions Current is carried by ions Increase in temperature decreases resistance Increase in temperature decreases resistance Resistance is normally greater than that with metals Resistance is normally greater than that with metals

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Conductivity of Solution "Is its ability to carry an electrical current" Conductivity can be measured by a conductivity meter and it is affected by: Number of ions Number of ions Type of ions Type of ions E = IR Where: E = electromotive force (volts) E = electromotive force (volts) I = current (amperes) I = current (amperes) R = resistance (ohms) R = resistance (ohms)

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AndWhere l = length of conductor l = length of conductor A = cross-sectional area of conductor A = cross-sectional area of conductor = specific resistance of conductor (ohm-cm) = specific resistance of conductor (ohm-cm) k = specific conductance (1 / ohm-cm) or siemens (S) k = specific conductance (1 / ohm-cm) or siemens (S) Specific conductance is conductance afforded by 1 cm 3 of an electrolyte solution

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Conductivity cells are calibrated by determining the resistance of a standard solution (R s ) and the cell constant (C) can be found. C = k s R s In such cases N KCl is used in calibrating conductivity cells. For N KCl: k s = S = 25 C So, Specific Conductance of a Solution = C / R R needs to be determined

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Equivalent Conductance ( ) Where N = normality of the solution N = normality of the solution k = specific conductance k = specific conductanceor, and are equivalent ionic conductance of cations and anions, respectively and are equivalent ionic conductance of cations and anions, respectively

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Table 3-3 shows equivalent ionic 25 C in S-cm 3 /equivalent. Only ions can carry current. Un-ionized species of weak acids or bases will not carry current. Also uncharged soluble organics (ethanol and glucose) can not carry current. Study Example page 80

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What is the approximate specific conductance at 25 C of a solution containing 100 mg/l of CaCl 2 and 75 mg/l of Na 2 SO 4

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Current and Chemical Change Chemical change depends on: Nature of solution (composition) Nature of solution (composition) Nature of electrodes Nature of electrodes Magnitude of electromotive force imposed Magnitude of electromotive force imposed

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HCl H+H+ e-e- Cathode (-) Cl - Anode (+) Platinum Electrodes Applying a voltage of 1.3 v H 2 evolves at Cathode Cl 2 evolves at Anode

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To bring about 1 equivalent of chemical change at an electrode: An Avogadro No of electrons must flow through the external circuit An Avogadro No of electrons must flow through the external circuit This quantity of electrons is called the faraday (F) This quantity of electrons is called the faraday (F) The rate of flow of electrons gives the current (I) in amperes The rate of flow of electrons gives the current (I) in amperes 1 F is equivalent to an ampere of current flowing for seconds 1 F is equivalent to an ampere of current flowing for seconds An ampere is defined as a Coulomb per second An ampere is defined as a Coulomb per second 1 F = Coulomb 1 F = Coulomb Study Example page 78

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What weight of silver will pass into solution from a silver anode by the passage of 0.02 A of current through the solution for 24 hours?

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Electrochemical Cell two electrodes will be connected by metallic conductor electrons will flow chemical change begins electromotive force (emf) will be generated by the cell this emf is a measure of the driving force of the chemical reaction occurring in the solution the driving force represents the chemical potential or free energy of the reaction

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Based on that, a relationship between electrical potential and chemical free energy can be found: Electrical Energy = EIt E = emf in volts E = emf in volts I = current in amperes I = current in amperes t = time in seconds t = time in seconds Electrical energy is expressed in Volt-Coulomb or Joule Electrical energy required to produce one mole of chemical change = zEF Where z = number of electron-equivalent per mole z = number of electron-equivalent per mole E = emf in volts E = emf in volts F = faraday or coulombs per equivalent F = faraday or coulombs per equivalent

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If reaction proceeds (E is +ve), then: where G is the free energy G is the free energy -zEF is the electrical energy -zEF is the electrical energy

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Consider the following reaction: aA + bB cC + dD Substituting in: we get:

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The value of R in electrical units is: R = J / K-mol At 25 C and converting ln to log

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The emf can be found in Tables (Table 3-4) just like free-energy and enthalpy. The values in the table are for a reaction written for 1 mole of e - change, such as: If an electrochemical cell reaches the state of equilibrium, then: no current can flow no current can flow emf is zero emf is zero

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In this case: sinceor log K = 16.9zE Study Examples page 85

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Estimate the solubility-product constant for Mg(OH) 2 (s) at 25 C from standard electrode potential?

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Chemical Kinetics Chemical kinetics deal with speed of reactions. If then, the rate of reaction could be: first – order reaction (exponent 1) kC a kC a second – order reaction (exponent 2) kC a 2 kC a 2 kC a C b kC a C b third – order reaction (exponent 3) kC a 3 kC a 3 kC a 2 C b kC a 2 C b kC a C b C c kC a C b C c Ca, Cb, and Cc = concentrations of A, B, and C, respectively Ca, Cb, and Cc = concentrations of A, B, and C, respectively k = rate constant k = rate constant

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These are simple reaction rates, but in reality there are more complex equations. The unit of k depends on the reaction order and units of concentration of A, B, and C. The reaction rates are required in: Microbial growth Microbial growth Aeration Aeration Disinfection Disinfection Radioactive decay Radioactive decay

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Zero-Order Reactions They are independent of concentration They are independent of concentration Most of biological growth occur in linear relationship over a range of concentrations of substance (C). Most of biological growth occur in linear relationship over a range of concentrations of substance (C).

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First-Order Reactions The rate is directly proportional to the concentration The rate is directly proportional to the concentration if we are dealing with a decay or decomposition reaction, then the rate can be expressed as if we are dealing with a decay or decomposition reaction, then the rate can be expressed as Unit of k is (1/time) and the –ve sign indicates the loss of material with time. Unit of k is (1/time) and the –ve sign indicates the loss of material with time.

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Integrating the above equation: Converting to log 10

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k = - slope of line [t versus ln(C/C 0 )] k = -slope [t versus log 10 (C/C 0 )] Half-life (t 1/2 ) In this case, t = t 1/2 andC = (1/2)C 0 Then Applications of 1st order reactions in Environmental Engineering: Dissolution of gases in water Dissolution of gases in water Removal of gases from water Removal of gases from water Rate of death of microorganisms Rate of death of microorganisms Decomposition of organic matters (BOD5 test) Decomposition of organic matters (BOD5 test) Study Example page 89

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The radioactive nuclide P32 has a half-life of 14.3 days. How long would a waste containing 10 mg/l of this nuclide have to be stored in order to reduce the concentration to 0.3 mg/l?

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Second-Order Reactions The rate of reaction is proportional to the square of the concentration of one of the reactants or to the product of concentrations of two different reactants.

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C a and C b are concentrations of A and B, respectively. Integrating (1) and (2), we obtain:

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Consecutive Reactions If rates of reactions are 1 st order, then:

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Integrating between t = 0 to t = t

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Examples of consecutive reactions in Environmental Engineering

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Enzyme Reactions Are used to describe the rate of biological waste treatment. The relationship between Substrate (S) and the rate of utilization per unit mass of enzyme or bacteria (V/E) Michaelis – Menton Relationship E f = free enzyme E f = free enzyme S = substrate S = substrate E c S = enzyme-substrate complex E c S = enzyme-substrate complex Total enzyme concentration in the system = E = [E f ] + [E c S]

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The rate of formation of enzyme-substrate complex is: The rate of complex formation rate of overall reaction. Therefore, d[E c S] / dt can be considered as ZERO when overall reaction rate is required to be determined. So:

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Or The rate of product formation = overall rate of reaction Rate of product formation V = k[E c S]

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ThenWhere k is the maximum rate k is the maximum rate Ks is the substrate concentration at arte = (1/2)k Ks is the substrate concentration at arte = (1/2)k Ks is called the "half velocity" constant Ks is called the "half velocity" constant V/E k'S when S<< K s (1st order with respect to S) V/E k when S >> K s (zero order with respect to S) Study Example page 95

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Temperature Dependence of Reaction Rates "rates increase with increase in temperature" Rate doubles for each 10 C rise. Using Arrehenius equation: Where T = temperature, K T = temperature, K R = universal gas constant R = universal gas constant E a = constant E a = constant

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Integrating k 2 and k 1 are rate constants at T 2 and T 1. In environmental engineering processes, the range of temperature is small. So T 2 T 1 can be assumed constant.

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Therefore

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Adsorption "sorption is the concentration or movement of contaminants from one place to another" "adsorption involves partitioning of contaminants from one phase to another" "adsorption is the process by which ions or molecules present in one phase tend to condense and concentrate on the surface of another phase"

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AdsorptionPhysical Weak Weak multi-layers multi-layers free moving free moving reversible reversibleChemical Strong Strong mono-layer mono-layer no movement no movement non-reversible in most cases non-reversible in most cases Ion exchange electrical attraction electrical attraction smaller particles smaller particles have stronger attraction have stronger attraction trivalent have stronger attraction than monovalent ions trivalent have stronger attraction than monovalent ions

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Activated Carbon 1 gram has surface area of 1000 m2 1 gram has surface area of 1000 m2 Pore size ranges between 10 to 1000 A Pore size ranges between 10 to 1000 A Adsorption of gas increases wit the increase I pressure Adsorption of gas increases wit the increase I pressure Adsorption depends on: Nature of materials Nature of materials Concentration Concentration Temperature Temperature

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Freundlich Isotherm Freundlich found that: Where q = mass of contaminant per unit weight of the adsorbent q = mass of contaminant per unit weight of the adsorbent C = concentration of solute after adsorption C = concentration of solute after adsorption K and n = constants (they should be evaluated for each soluble and temperature) K and n = constants (they should be evaluated for each soluble and temperature) Freundlich isotherm can be expressed as:

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Langmuir Isotherm Langmuir isotherm is also used to describe adsorption of single layer: qm = maximum adsorption that can take place in grams of adsorbate per gram of adsorbent qm = maximum adsorption that can take place in grams of adsorbate per gram of adsorbent a = constant a = constant

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BET Isotherm A third isotherm is BET (Brunauer, Emmett, and Teller) which can be used to describe multi-layer adsorption Assumptions Multi-layers of adsorbent accumulate at the surface of adsorbent Multi-layers of adsorbent accumulate at the surface of adsorbent Each layer can be described by Langmuir isotherm Each layer can be described by Langmuir isotherm Cs = saturation concentration for the adsorbate in solution Cs = saturation concentration for the adsorbate in solution

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If C > C s then the solute precipitates or condenses from solution as solid or liquid and concentrates on the surface BET equation can be put in this form: If we have data, then we have to find the best isotherm that can be used to describe the data (get straight line)

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Study Examples Page 104

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