1. Physical Chemistry CE 541

2. What is Physical Chemistry Is the science that deals with laws that is related (or that govern) chemical phenomena such as: Gas laws Gas laws Oxidation-reduction reactions Oxidation-reduction reactions Equilibrium relationship Equilibrium relationship

3. Thermodynamics Is the study of energy changes accompanying physical or chemical processes

4. Thermodynamics (a). Heat and Work Heat Is a form of energy passing from one body to another as a result of temperature difference Heat Units Calorie [heat required to raise the temperature of one gram of water one degree Celsius,  C] Calorie [heat required to raise the temperature of one gram of water one degree Celsius,  C] British thermal unit (Btu) [heat required to raise the temperature of one pound of water by one degree Fahrenheit,  F] British thermal unit (Btu) [heat required to raise the temperature of one pound of water by one degree Fahrenheit,  F] Btu = 252 Calories = 1,054 Joules (J)

5. Specific heat of a substance [heat required to raise the temperature of 1 gram of the substance by one degree Celsius,  C] Where C = specific heat C = specific heat q = heat added in Calories or Joules q = heat added in Calories or Joules M = weight of the substance, grams M = weight of the substance, grams  T = raise in temperature,  C  T = raise in temperature,  C

6. For water at 15  C C = 1.000 Cal or 4.184 J / gram-degree C Heat of fusion : heat required to melt a substance at its normal melting temperature. Heat of vaporization : heat required to evaporate a substance at its normal temperature of boiling

7. Work Measured in: Force  Distance Work (dw) is equivalent to: Pressure  Volume Change Then, (dw) = P  dV Work Units foot – pounds (ft-lb) foot – pounds (ft-lb) Joules ( 1 Cal = 4.184 J) Joules ( 1 Cal = 4.184 J) Btu (1 Btu = 778 ft-lb) Btu (1 Btu = 778 ft-lb)

8. Work and Heat are forms of Energy. Therefore, Work = Heat

9. Thermodynamics (b). Energy Conservation-of-energy Law "Any heat or work which flow into or out of the system must result in a change in the total energy stored in the system"  E = q -   E = change in energy  E = change in energy q = heat flowing into the system q = heat flowing into the system  = work done by the system  = work done by the system

10. q is positive (+ve) if the system absorbs the heat q is positive (+ve) if the system absorbs the heat q is negative (-ve) if the system gives off the heat q is negative (-ve) if the system gives off the heat  is +ve if the system does the work  is +ve if the system does the work  is –ve if the surroundings do the work on the system  is –ve if the surroundings do the work on the system

11. If the chemical system does not expand or contract (volume is constant), then:  E = q v q v = heat absorbed in a constant-volume system q v = heat absorbed in a constant-volume system In Environmental Engineering Applications, most of the systems are open, so they operate under constant pressure rather than constant volume

12. Thermodynamics (c). Enthalpy (H) H = E + PV Where H = enthalpy H = enthalpy E = internal energy of the system E = internal energy of the system P = pressure on the system P = pressure on the system V = volume of the system V = volume of the system

13. Enthalpy A thermodynamic function of a system, equivalent to the sum of the internal energy of the system plus the product of its volume multiplied by the pressure exerted on it by its surroundings.

14. At constant pressure system, Heat absorbed by the system = q p Work done by the system can be obtained by integrating dw = P dv   = P (V 2 – V 1 ) then, change in internal energy is:  E = E 2 - E 1 = q p -  = q p – [P (V 2 – V 1 )] Or (E 2 + PV 2 ) – (E 1 + PV 1 ) = q p

15. (E 2 + PV 2 ) is the final enthalpy (E 1 + PV 1 ) is the initial enthalpy So, H 2 – H 1 = q p   H = q p (T and P are constant) +ve heat means endothermic reaction (absorbs heat) +ve heat means endothermic reaction (absorbs heat) -ve heat means exothermic reaction (evolves heat) -ve heat means exothermic reaction (evolves heat) Change of enthalpy or heat of a given reaction can be found in Tables such as (Table 3-1)

16. To calculate heat of a reaction: Write a balanced equation Write a balanced equation Find standard enthalpy of reactants Find standard enthalpy of reactants Find standard enthalpy of products Find standard enthalpy of productsThen, Heat = (products) – (reactants)

17. Example (Problem 3.1) Determine the heat of combustion of ethane gas. The enthalpy of a chemical element (at its standard state) at 25  C and 1 atm is zero. For example, at standard states, O 2 is gas, Mercury is liquid, Sulfur is crystal. Study Examples A and B on page 54

18. Thermodynamics (d) Entropy Is based on the second law of thermodynamics, which states "All systems tend to approach a state of equilibrium" In chemistry, we are interested in entropy to check the position of the equilibrium of a chemical process. Where S = entropy of the system S = entropy of the system T = absolute temperature T = absolute temperature q rev = amount of heat that the system absorbs if a chemical change is brought about in an infinitely slow reversible manner q rev = amount of heat that the system absorbs if a chemical change is brought about in an infinitely slow reversible manner

19. +ve  S indicates that change can occur spontaneously +ve  S indicates that change can occur spontaneously -ve  S indicates that change tends to occur in reverse direction -ve  S indicates that change tends to occur in reverse direction Zero  S indicates that system is at equilibrium Zero  S indicates that system is at equilibrium

20. Entropy For a closed thermodynamic system, entropy is a quantitative measure of the amount of thermal energy not available to do work.

21. Thermodynamics (e). Free Energy In environmental engineering processes, both entropy and energy are needed in order to determine which processes will occur spontaneously. G = H – TS Where G = free energy G = free energy H = enthalpy (J) H = enthalpy (J) T = absolute temperature (  K) [  K =  C + 273] T = absolute temperature (  K) [  K =  C + 273] S = entropy (J /  K) S = entropy (J /  K)

22. At constant temperature and pressure:  G =  H - T  S Since H = E + PV Then  H = H 2 – H 1 = (E 2 + P 2 V 2 ) – (E 1 + P 2 V 1 )

23. At constant P  H =  E + P  V Since  E = q -  Then  H = q -  + P  V

24. From At constant T T  S = q rev If the system change is very slow, then energy loss is MINIMUM q = q rev  =  max

25. In this case, P  V represents the work that is wasted during the expansion of the system. Therefore:-  G is the difference between the maximum work and the wasted work, which can be described as the useful work available from the system change. So:

26. If a system changes from a to b, then: -ve  G means that the system or process can proceed -ve  G means that the system or process can proceed +ve  G means that the system or process can proceed in the reverse direction (b to a) +ve  G means that the system or process can proceed in the reverse direction (b to a) Zero  G means that the system or process is at equilibrium and can not proceed in either direction. Zero  G means that the system or process is at equilibrium and can not proceed in either direction. At standard state of elements and at 25  C and 1 atm, the free energy ( ) is zero. For values of, see Table 3-1. For values of, see Table 3-1.

27. Consider the following reaction: aA + bB  cC + dD Taking into consideration the concentration of reactants and products:

28. Where  G = reaction free-energy change (J)  G = reaction free-energy change (J) = standard free-energy change (J) = standard free-energy change (J) R = universal gas constant = 8.314 J / K-mol = 1.99 cal / K-mol R = universal gas constant = 8.314 J / K-mol = 1.99 cal / K-mol T = absolute temperature in Kelvin (  K) T = absolute temperature in Kelvin (  K) [ ] = activities of A, B, C, and D [ ] = activities of A, B, C, and D and and

29. At equilibrium;  G = zero So, At equilibrium K = equilibrium constant K = equilibrium constantTherefore,

30. Comparison between Q and K Q < K means the reaction proceeds from left to right Q < K means the reaction proceeds from left to right Q > K means the reaction proceeds from right to left Q > K means the reaction proceeds from right to left Q = K means the reaction is at equilibrium Q = K means the reaction is at equilibrium Study Examples A, B, C, and D page 58-59.

31. Thermodynamics (f). Temperature Dependence of K From relationship between  G and K  G and K  G and H  G and H In environmental engineering practices, the temperature range is limited and, therefore,  H  is constant. So, Study Example page 60

32. Osmosis Flow direction from dilute solution to concentrated solution is more rapidly than the other direction (concentrated  diluted)

33. In order to oppose that flow, pressure to the salt solution can be applied to produce equilibrium. That pressure is called osmotic pressure (  )  = osmotic pressure, atm  = osmotic pressure, atm R = 0.0882 l-atm / mol-K R = 0.0882 l-atm / mol-K T = absolute temperature,  K T = absolute temperature,  K V A = volume per mole of solvent = 0.018 liter ( for water) V A = volume per mole of solvent = 0.018 liter ( for water) P  A and P A = vapor pressure of solvent in the dilute and concentrated solutions, respectively P  A and P A = vapor pressure of solvent in the dilute and concentrated solutions, respectively

34. For dilute solutions, the reduction in vapor pressure of a solvent is directly proportional to the concentration of particles in solution. So, c = molar concentration of particles c = molar concentration of particles In environmental engineering Reverse Osmosis is used to demineralized brackish waters

35. Dialysis and Electro-Dialysis Dialysis is a phenomena that is related to the principle of OSMOSIS

36. Main Membrane Processes Are used to separate substances (solutes) from a solution (solvent) Are used to separate substances (solutes) from a solution (solvent) The main membrane processes are The main membrane processes are Dialysis Dialysis Electro-dialysis Electro-dialysis Reverse osmosis Reverse osmosis Driving forces that cause mass transfer of solutes are: Driving forces that cause mass transfer of solutes are: Difference in concentration (dialysis) Difference in concentration (dialysis) Difference in electric potential (electro-dialysis) Difference in electric potential (electro-dialysis) Difference in pressure (reverse osmosis) Difference in pressure (reverse osmosis)

40. Dialysis Consists of : Consists of : Separating solutes of different ionic or molecular size Separating solutes of different ionic or molecular size Solution Solution Selectively permeable membrane Selectively permeable membrane The driving force is the difference in the solute concentration across the membrane The driving force is the difference in the solute concentration across the membrane

43. Batch Dialysis Cell Solution to be dialyzed is separated from solvent by a semi-permeable membrane Solution to be dialyzed is separated from solvent by a semi-permeable membrane Small ions and molecules pass from solution to solvent Small ions and molecules pass from solution to solvent Large ions and molecules do not pass due to relative size of membrane pore Large ions and molecules do not pass due to relative size of membrane pore The mass transfer of solute through the membrane is given by The mass transfer of solute through the membrane is given by M = mass transferred per unit time (gram/hour) M = mass transferred per unit time (gram/hour) K = mass transfer coefficient [gram/(hr-cm 2 )(gram/cm 3 )] K = mass transfer coefficient [gram/(hr-cm 2 )(gram/cm 3 )] A = membrane area (cm 2 ) A = membrane area (cm 2 )  C = difference in concentration of solute passing through the membrane (gram/cm 3 )  C = difference in concentration of solute passing through the membrane (gram/cm 3 )

44. Applications of Dialysis Sodium hydroxide was recovered from textile wastewater at: Sodium hydroxide was recovered from textile wastewater at: Flowrate = 420 – 475 gal/day Flowrate = 420 – 475 gal/day Recovery of 87.3 to 94.6% Recovery of 87.3 to 94.6% Dialysis is limited to small flows due to small mass transfer coefficient (K) Dialysis is limited to small flows due to small mass transfer coefficient (K)

45. Electro-Dialysis The driving force is an electromotive force The driving force is an electromotive force If electromotive force is applied across the permeable membrane: If electromotive force is applied across the permeable membrane: An increased rate of ion transfer will occur An increased rate of ion transfer will occur This results in decrease in the salt concentration of the treated solution This results in decrease in the salt concentration of the treated solution The process demineralizes The process demineralizes Brackish water and seawater to produce fresh water Brackish water and seawater to produce fresh water Tertiary effuents Tertiary effuents

46. How it Works? When direct current is applied to electrodes: When direct current is applied to electrodes: All cations (+vely charged) migrate towards cathode All cations (+vely charged) migrate towards cathode All anions (-vely charged) migrate towards anode All anions (-vely charged) migrate towards anode Cations can pass through the cation-permeable membrane (C) but can not pass through (A) Cations can pass through the cation-permeable membrane (C) but can not pass through (A) Anions can pass through the anions-permeable membrane (A) but can not pass through (C) Anions can pass through the anions-permeable membrane (A) but can not pass through (C) Alternate compartments are formed Alternate compartments are formed Ionic concentration in compartments is less than or greater than that in the feed solution Ionic concentration in compartments is less than or greater than that in the feed solution

52. The Membrane Membranes used in electro-dialysis are: Membranes used in electro-dialysis are: Porous Porous Sheet-like Sheet-like Its structural matrix is made of synthetic ion exchange resin Its structural matrix is made of synthetic ion exchange resin

53. Current Requirement Can be calculated from Faraday’s laws of electrolysis: Can be calculated from Faraday’s laws of electrolysis: One Faraday (F) of electricity (96,500 ampere-seconds or coulombs) cause one gram equivalent weight of a substance to migrate from one electrode to another One Faraday (F) of electricity (96,500 ampere-seconds or coulombs) cause one gram equivalent weight of a substance to migrate from one electrode to another I = current in amperes I = current in amperes F = Faraday’s constant (96,500 ampere-seconds per gram equivalent weight removed) F = Faraday’s constant (96,500 ampere-seconds per gram equivalent weight removed) Q = solution flowrate (liters/second) Q = solution flowrate (liters/second) N = normality of the solution (gram eq weight per liter) N = normality of the solution (gram eq weight per liter) Er = electrolyte removal as a fraction Er = electrolyte removal as a fraction Ec = current efficiency as a fraction Ec = current efficiency as a fraction

54. Current Requirement If the number of cells in a stack = n, then If the number of cells in a stack = n, then Electro-dialysis stack usually have 100 to 250 cells (200 to 500 membranes) Electro-dialysis stack usually have 100 to 250 cells (200 to 500 membranes) E c for a electro-dialysis stack and feed water must be determined experimentally E c for a electro-dialysis stack and feed water must be determined experimentally Ec is 0.90 or more Ec is 0.90 or more Er is usually 0.25 to 0.50 Er is usually 0.25 to 0.50

55. Cell Capacity The capacity of the cell to pass an electric current depends on: The capacity of the cell to pass an electric current depends on: Current density [ = current / membrane area (ma/cm2)] Current density [ = current / membrane area (ma/cm2)] Normality of the feed (number of gram equivalent weight per liter of solution) Normality of the feed (number of gram equivalent weight per liter of solution) Current density / normality ratio Current density / normality ratio This ratio may vary from 400 to 700 This ratio may vary from 400 to 700

56. Power Requirement The resistance (R) of an electro-dialysis stack treating a particular feed must be determined experimentally The resistance (R) of an electro-dialysis stack treating a particular feed must be determined experimentally If resistance (R) and current (I) are known: If resistance (R) and current (I) are known: Required Voltage, E = RI Required Voltage, E = RI Required Power, P = RI 2 Required Power, P = RI 2 R = ohms; I = amperes; E = volts; and P = watts R = ohms; I = amperes; E = volts; and P = watts

57. Applications Electrical energy requirement is directly proportional to the amount of salt removed Electrical energy requirement is directly proportional to the amount of salt removed So, electrical cost is governed by So, electrical cost is governed by Dissolved salt content of the feed water Dissolved salt content of the feed water The desired dissolved solids content of the product water The desired dissolved solids content of the product water Energy consumption increases with deposition of scale upon the membrane Energy consumption increases with deposition of scale upon the membrane Consequently, electro-dialysis is not used to deionize seawater Consequently, electro-dialysis is not used to deionize seawater

58. Applications Electro-dialysis is used in demineralization of brackish water Electro-dialysis is used in demineralization of brackish water Brackish water having TDS concentration of 500 mg/l can be de- mineralized using electro-dialysis to produce a product water of 500 mg/l TDS Brackish water having TDS concentration of 500 mg/l can be de- mineralized using electro-dialysis to produce a product water of 500 mg/l TDS Membrane replacement and power costs are about 40% of total cost Membrane replacement and power costs are about 40% of total cost Electro-dialysis have been used to de-mineralize secondary effluents Electro-dialysis have been used to de-mineralize secondary effluents Scale formation Scale formation Organic fouling Organic fouling 25 to 50% TDS can be removed in single pass 25 to 50% TDS can be removed in single pass Coagulation, settling, filtration and activated carbon adsorption can used as pre-treatment processes to reduce organic fouling OR by cleaning the membrane using an enzyme detergent solution Coagulation, settling, filtration and activated carbon adsorption can used as pre-treatment processes to reduce organic fouling OR by cleaning the membrane using an enzyme detergent solution Scale formation can be reduced by adding small amount of acid to the feed Scale formation can be reduced by adding small amount of acid to the feed

59. Electro-Dialysis Installations

64. Reverse Osmosis Diffusion is the movement of molecules from a region of higher concentration to a region of lower concentration. Osmosis is a special case of diffusion in which the molecules are water and the concentration gradient occurs across a semipermeable membrane. The semipermeable membrane allows the passage of water, but not ions (e.g., Na+, Ca2+, Cl-) or larger molecules (e.g., glucose, urea, bacteria). Diffusion and osmosis are thermodynamically favorable and will continue until equilibrium is reached. Osmosis can be slowed, stopped, or even reversed if sufficient pressure is applied to the membrane from the 'concentrated' side of the membrane.

70. Reverse Osmosis Reverse osmosis occurs when the water is moved across the membrane against the concentration gradient, from lower concentration to higher concentration. To illustrate, imagine a semipermeable membrane with fresh water on one side and a concentrated aqueous solution on the other side. If normal osmosis takes place, the fresh water will cross the membrane to dilute the concentrated solution. In reverse osmosis, pressure is exerted on the side with the concentrated solution to force the water molecules across the membrane to the fresh water side.

74. Reverse Osmosis Reverse osmosis is often used in commercial and residential water filtration. It is also one of the methods used to desalinate seawater. Sometimes reverse osmosis is used to purify liquids in which water is an undesirable impurity (e.g., ethanol).

75. Reverse Osmosis - Pros and Cons The semi-permeable membrane used in reverse osmosis contains tiny pores through which water can flow. The small pores of this membrane are restrictive to such organic compounds as salt and other natural minerals, which generally have a larger molecular composition than water. These pores are also restrictive to bacteria and disease-causing pathogens. Thus, reverse osmosis is incredibly effective at desalinating water and providing mineral-free water for use in photo or print shops. It is also effective at providing pathogen-free water. In areas not receiving municipally treated water or at particular risk of waterborne diseases, reverse osmosis is an ideal process of contaminant removal.

76. Reverse Osmosis - Pros and Cons The reverse osmosis process contains several downsides which make it an inefficient and ineffective means of purifying drinking water. The small pores in the membrane block particles of large molecular structure like salt, but more dangerous chemicals like pesticides, herbicides, and chlorine are molecularly smaller than water (Binnie et al, 2002). These chemicals can freely pass through the porous membrane. For this reason, a carbon filter must be used as a complimentary measure to provide safe drinking water from the reverse osmosis process. Such chemicals are the major contaminants of drinking water after municipal treatment.

77. Reverse Osmosis - Pros and Cons Another downside to reverse osmosis as a method of purifying drinking water is the removal of healthy, naturally occurring minerals in water. The membrane of a reverse osmosis system is impermeable to natural trace minerals. These minerals not only provide a good taste to water, but they also serve a vital function in the body’s system. Water, when stripped of these trace minerals, can actually be unhealthy for the body.

78. Reverse Osmosis - Pros and Cons Reverse osmosis also wastes a large portion of the water that runs through its system. It generally wastes two to three gallons of water for every gallon of purified water it produces. Reverse osmosis is also an incredibly slow process when compared to other water treatment alternatives.

79. Module Types Spiral Wound Spiral Wound Hollow Fiber Hollow Fiber Tubular Tubular

89. Membrane Installations

97. Costs

100. Principles of Solvent Extraction Objectives: To recover valuable constituent To recover valuable constituent For analytical purposes For analytical purposes Solvents are used (immiscible) Petroleum ether Petroleum ether Diethyl ether Diethyl ether Benzene Benzene Hexane Hexane Dichloromethane Dichloromethane Others Others

101. Solute will be distributed based on their solubilities in water and solvent K = distribution coefficient K = distribution coefficient Usually a solvent is selected so that K is greater than 1

102. If K = 9 and volumes of water and solvent are equal, then: In the first extraction step 90% will be extracted In the first extraction step 90% will be extracted After 3 extraction steps with fresh solvent, 99.9% of the solute will be extracted After 3 extraction steps with fresh solvent, 99.9% of the solute will be extracted The mathematics are simple

103. In practice, it may be unjustified to use equal volumes of water and solvent. In such cases: W 0 = weight of solute in water (originally) W 0 = weight of solute in water (originally) W 1 = weight of solute in water (remained after one extraction) W 1 = weight of solute in water (remained after one extraction) V s = volume of solvent V s = volume of solvent V w = volume of water V w = volume of water

104. In the second step of extraction In terms of the original sample

105. After n extractions W n = remaining weight of solute in water after n extractions W n = remaining weight of solute in water after n extractions