{"id":23,"date":"2019-03-06T05:23:03","date_gmt":"2019-03-06T05:23:03","guid":{"rendered":"http:\/\/esp16.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=23"},"modified":"2022-01-07T10:52:57","modified_gmt":"2022-01-07T10:52:57","slug":"environmental-chemical-thermodynamics","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/esp16\/chapter\/environmental-chemical-thermodynamics\/","title":{"rendered":"Environmental Chemical Thermodynamics"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n \r\n\r\nContents<\/strong>\r\n\r\n1. Introduction\r\n\r\n2. Thermodynamic Terms\r\n\r\n3. Heat and Work\r\n\r\n4. First Law of Thermodynamics\r\n\r\n5.Internal Energy\r\n\r\n6. Enthalpy\r\n\r\n7. Heats of Reaction\r\n\r\n8. Second Law of Thermodynamics\r\n\r\n9. Entropy\r\n\r\n10. Third Law of Thermodynamics\r\n\r\n11. Gibbs Free Energy\r\n\r\n12. Chemical Potential\r\n\r\n13. Free Energy, Chemical Potential, and Pressure\r\n\r\n14. Thermodynamic Conditions for Equilibrium\r\n\r\n15. Equilibrium between two Phases\/States of a Single Component\r\n\r\n16. Suggested Reading\r\n\r\n17. Other interesting material\r\n\r\n \r\n\r\nIntroduction<\/strong>\r\n

Thermodynamics deals with changes in various forms of energy. Energy has various forms such as kinetic energy, potential energy, chemical energy, heat etc. Thermodynamics is the study of the changes in energy of a system. It is of fundamental importance in understanding not only environmental chemical and physical processes but also the ecological processes. For an understanding of the subject, it is necessary to understand the terms frequently encountered.<\/p>\r\n \r\n\r\nThermodynamic Terms<\/strong>\r\n

System <\/strong>- The part of the universe selected for study is called as system. For example, a cloud selected for study would be a system.<\/p>\r\n \r\n\r\nSurroundings <\/strong>\u2013 The area adjoining the system is taken as surroundings or the part of the universe other than system. For example, the air around the cloud shall form surroundings. Universe <\/strong>\u2013 Systems and surroundings together form universe.\r\n\r\n \r\n\r\nAdiabatic Process <\/strong>\u2013 In this process, there is no exchange of energy between the system and surroundings. For example, a rising parcel of air, while deriving expression for lapse rate, is considered to undergo adiabatic process.\r\n\r\n \r\n\r\nIsothermal Process <\/strong>\u2013 A process in which temperature remains constant throughout the process. For isothermal processes dT = 0.\r\n\r\n \r\n\r\nIsobaric Process <\/strong>\u2013 When there is no change in the pressure of the system during operations, the process is isobaric. Environmental chemical processes are mostly isobaric.\r\n\r\n \r\n\r\nIsolated System <\/strong>\u2013 In such a system, there is no exchange of energy and matter with the surroundings. Open System <\/strong>\u2013 Such systems can exchange both matter and energy with the surroundings. Oceans and lakes are good examples of this type.\r\n\r\n \r\n\r\nClosed System <\/strong>\u2013 It can exchange energy but not matter with the surroundings. A sealed aluminum can containing a cold drink is an example of this type.\r\n\r\n \r\n\r\nThermodynamic Variables - <\/strong>The thermodynamic macroscopic state of a system is defined by four measurable properties: composition, pressure, P; volume, V; and temperature, T. Since, P, V and T are interdependent (Please see Ideal gas equation: PV = nRT), therefore only two of these variables are required to specify the state of a system. For thermodynamic studies, generally P and T variable are considered as these are independent variables.\r\n\r\n \r\n\r\nExtensive Properties <\/strong>\u2013 These properties depend up on the quantity of the matter, e. g., mass and volume.\r\n\r\n \r\n\r\nIntensive Properties \u2013 <\/strong>These properties being the characteristics of the system do not depend on the quantity of the matter, e. g., temperature, density etc. [ the property which is based on the ratio of two extensive properties is intensive in nature]. For example: density is ratio of mass and volume. Mass and volume, both are extensive properties, but their ration, density, is intensive property. Other example is specific heat capacity.\r\n\r\n \r\n\r\nState Functions <\/strong>\u2013 The values of these functions, e.g., enthalpy, entropy and internal energy depend up on the initial and final state of the system only and independent of the path taken to reach the final state.\r\n\r\n \r\n\r\nHeat and Work<\/strong>\r\n\r\nHeat and work are two forms of energy. Whereas heat is the transfer of the energy due to temperature difference, work is transfer of energy owing to force acting via a distance. Heat and work are not state functions as these depend up on the path. Work, w, is defined by Eq. 1.\r\n\r\n\"\"\r\n\r\nThe environmental chemical reactions generally occur at a fixed pressure, so we need to consider only work of expansion of gases at a fixed pressure. In this case, force is equal to pressure P and distance moved is equal to the change in the volume. Eq.2 gives work.\r\n\r\n\"\"\r\n\r\n\u00a0 First Law of Thermodynamics<\/strong>\r\n\r\nThe first law states that energy can neither be created nor destroyed but one form of energy an change into another form. So the total energy of an isolated system remains unchanged although the form of the energy may change. The heat, q, given to a system used partly to increase its internal energy by E and to do work, w,<\/em> then according to first law:\r\n\r\n\"\"\r\n\r\n\u00a0 \u00a0 Sign Conventions<\/strong>\r\n\r\nThe work done by a has a negative sign (- w).\r\n\r\nThe work on a system has a positive sign (+ w).\r\n\r\nHeat absorbed by a system has a positive sign (Endothermic Reaction, +<\/em><\/strong>\u00a0 H)<\/em><\/strong>.\r\n\r\nHeat evolved\/<\/strong>released by a system has a negative sign (Exothermic Reaction, -<\/em><\/strong>\u00a0 H )<\/em><\/strong>.\r\n\r\n \r\n\r\nInternal Energy<\/strong>\r\n\r\nIt is the characteristic property of a system. It is sum total of all energies associated with a system comprising kinetic energy, potential energies, relativistic energy due to mass (E = mc2) etc. It is a state a function. The absolute value of internal energy can not be calculated because it contains, so many different energies that value of all energies can not be calculated. But change in internal energy of a system ( E ) can be calculated. When a system undergoes a change from initial state (defined by P1, V1, T1) to final state (defined by P2, V2, T2) having internal energies E1 and E2, respectively, then the change in internal energy,E, is given by Eq. 6.\r\n\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\nSince E, P and V are all state functions, and so qP is also a state function. The extensive thermodynamic property qP is called enthalpy and is defined by Eq. 11. It is represented by the symbol, Hp, or simply H.\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\nwhere HA, HB, HC and HD are standard enthalpies of reactants and products and \u03a3HP and \u03a3HR the enthalpies of products and reactants.\r\n\r\n \r\n\r\nHeats of Formation, H<\/em><\/strong>f<\/em><\/strong>, - The standard heat of formation is the change in enthalpy when one mole of a substance is formed from the elements in their standard states. For example, the heat of formation of CO2 is the enthalpy change in the reaction: C(s) + O2 = CO2 (g); all the reactants and products are in their standard state. The heats of formation,Hf<\/em><\/strong>, of elements in their standard states are assumed to be zero.\r\n\r\n \r\n\r\nProblem <\/strong>1. Whenever food is cooked by heating, N2 and O2 combine to form NO. Given that the standard heat of formation of NO is 90.4 kJ mol-1, Calculate the standard heat of the reaction: N2 + O2 = 2NO.\r\n\r\nSolution<\/strong>. The heat of the reaction is:\r\n\r\nH = (2HNO) \u2013 (HN2 + HO2)\r\n\r\nThe values of both HN2 and HO2 are zero because both should be in their standard state. Using HNO\r\n\r\nH = (2\u00d790.4) \u2013 (0 + 0) = 180.8 kJ\r\n\r\n \r\n\r\n \r\n\r\nProblem 2. <\/strong>The standard heats of formation of CO and CO2 are HfCO = 110.5 and HfCO2= 412.9 kJ mol-1, respectively. Calculate the standard heat of the combustion of CO.\r\n\r\nSolution<\/strong>. The combustion reaction is: CO + 0.5 O2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 CO2\r\n\r\nHeat of combustion,\u00a0\u00a0 H, is given by:\r\n\r\nH = HfCO2 \u2013 (HfCO \u2013 0.5 HfO2)\r\n\r\nH = 412.9 \u2013 (-110.5 \u2013 0.5\u00d70) = -302.4 kJ mol-1.\r\n\r\nThe reaction is exothermic.\r\n\r\n \r\n\r\nSecond Law of Thermodynamics<\/strong>\r\n\r\nThis law states that in a reversible change the entropy of the universe does not increase, and in an irreversible change the entropy of the universe increases. This law helps in predicting the direction of the reaction under given conditions. All natural or spontaneous processes lead to an increase in the entropy of the universe. Evaporation, flow of water in rivers, heat flow from higher temperature to lower temperature are all spontaneous processes and therefore accompanied by increase in entropy.\r\n\r\n \r\n\r\n\"\"\r\n\r\nWhen the system and surroundings are at different temperatures, the process becomes irreversible. Consider a thermostat (system), which maintains its temperature constant at T2, whereas its surroundings are at a lower temperature T1. Assuming that the heat q is lost reversibly by thermostat at T2 and is received by surroundings reversibly at temperature T1, the entropy changes of system and surroundings are given by:\r\n\r\n\"\"\r\n\r\nSince T2 > T1 so 1\/<\/strong>T1 is greater than1\/<\/strong>T2, hence Sunivers,> 0. This shows the entropy of the universe to increase in an irreversible process.\r\n\r\n \r\n\r\nPhysical Interpretation of Entropy <\/em><\/strong>\u2013 Entropy is related to the complexion of the system. That is it is related to the probability or the randomness of the system, W, as in Eq.(18) in which k is Boltzmann constant. Greater is the randomness greater is the entropy of the system.\r\n\r\n\"\"\r\n\r\nProblem 3<\/strong>. The heat of fusion of water is 6.0\u00a0 kJ mol-1. Calculate the entropy change during fusion.\r\n\r\nSolution. <\/strong>Water fuses at 0oC or 298 K. The entropy change,S, is given by Eq.:\r\n\r\nSfusion =\u00a0\u00a0\u00a0\u00a0\u00a0 Hfusion \/<\/strong> T\u00a0 =\u00a0\u00a0\u00a0 6.0 kJ mol-1\/ 298 K = 6000 J mol-1\/<\/strong>298 K = 20.1 J mol-1 K-1.\r\n\r\n \r\n\r\nThird Law of Thermodynamics<\/strong>\r\n\r\nThis law is concerned with the absolute values of the entropy of the substances and is helpful in determining these values. According to this law \u2018every substance has a finite entropy, but at absolute<\/em> zero the entropy may become zero, and in case of perfectly crystalline substances it really become<\/em>s zero\u2019. The entropy of any substance at temperature T and the pressure P can be stated mathematically as follows.\r\n\r\n\"\"\r\n\r\nwhere So is the entropy at absolute zero. Knowing the value of So, it would be possible to calculate entropy S at any required temperature from heat capacity data.\r\n\r\n \r\n\r\nGibbs Free Energy, G<\/strong>\r\n\r\nOut of the energy given to a system, only a part is used in doing work and the remainder is used in entropy change. The energy available to do work is Gibbs free energy or simply free energy. It is given a symbol, G, for absolute value, and G for change. If H is the heat supplied at constant\r\n\r\n\"\"\r\n\r\n\"\"any process to occur, whether chemical or physical, this is the most important criterion. In other words only, those processes shall be able to occur for which the free energy decreases. Since most of the processes occur at constant temperature and pressure in environment, G is of great importance.\r\n\r\n \r\n\r\nHelmholtz Free Energy, A<\/em><\/strong>\r\n\r\nFor the processes occurring at constant temperature and volume, the term Helmholtz free energy, A, is used. It is defined by Eq. 21. As with G, those processes would be spontaneous, for which A< 0.\r\n\r\n\"\"\r\n\r\nThus, Gibbs free energy is defined under constant pressure and constant temperature, and Helmholtz free energy is defined under constant volume and constant temperature.\r\n\r\n \r\n\r\nStandard Free Energy<\/em><\/strong>\r\n\r\nStandard free energy change of a substance is the free energy change for the reaction by which the substance is obtained from the elements in their standard states at one atmospheric pressure.\r\n\r\n \r\n\r\nProblem 4<\/strong>. At 27oC, the enthalpy change, Ho, for a reaction is 25 kJ mol-1 and entropy change, So, is 100 J mol-1 K-1. Find whether the reaction is spontaneous.\r\n\r\nSolution. To test the spontaneity of the reaction, calculate<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0 G by Eq.:\r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n

\r\n\r\nChemical Potential\/ Partial Molar Free Energy<\/strong>\r\n\r\nConsider a multi-component system. Its free energy G is a function of T, P and amounts of components, n1, n2, ------ ni.\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n \r\n\r\nAccording to Eq. 24, chemical potential of a particular constituent in a mixture is the increase in the property G of the system due to the addition of one mole of that substance at constant temperature and pressure to such a large quantity of the constituents that its composition remains virtually unchanged. It may be pointed out that the value of \u00b5i in a mixture is not same as in the pure state. Thus, value of \u00b5i varies with composition of the system.\r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n<\/div>\r\n
\r\n\r\nThermodynamic Conditions for Equilibrium<\/strong>\r\n\r\nAt constant temperature and pressure, the conditions for equilibrium are as follows.\r\n\r\n1. For a system of one of component, dG =0.\r\n\r\n2. For a multi-component system, the chemical potential of each component must be same in all the phases,\u00a0 i. e., \u00b5(a) = \u00b5(b) = \u00b5(c) where a, b and c are different phases.\r\n\r\n<\/div>\r\n\"\"\r\n\r\nSuppose that a small amount of liquid water is transferred to water vapor. If Gvapor and Gliquid be the molar free energies of water in vapor and liquid state, respectively, the transfer of one mole from liquid state to vapor state shall entail the change in free energy, \u2206G, given by Eq. 28.\r\n\r\n\"\"\r\n\r\nSince the two phases are in equilibrium, \u2206G = 0, and so Gvapor = Gliquid . It is concluded, therefore, that whenever two (or more) phases of the same substance alone are in equilibrium at a fixed P and T, the molar free energy would be the same in all phases. An interesting application of aspect is in cloud physics.\r\n\r\n\r\n\r\n
you can view video on Environmental Chemical Thermodynamicsy<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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Reference<\/strong><\/h3>\r\n
    \r\n \t
  1. S. Glasston, Thermodynamics for Chemists<\/em>, East- West, New Delhi.<\/li>\r\n \t
  2. R. P. Rastogi and R. R. Mishra, An Introduction to Thermodynamics<\/em>, Vikas Publishing House New Delhi, 2001<\/li>\r\n \t
  3. P. W. Atkins, Physical Chemistry<\/em>, Oxford University Press, 1998.<\/li>\r\n \t
  4. Chemistry I for Class XI<\/em>, NCERT, New Delhi<\/li>\r\n \t
  5. A Bahl, B. S. Bahl and G. D. Tuli(2012), Essentials of Physical Chemistry, <\/em>S. Chand, New Delhi<\/li>\r\n \t
  6. Philip Matthews(2013), Advanced Chemistry,<\/em> Cambridge, New Delhi<\/li>\r\n \t
  7. P. V. Hobbs(2000), Basic Physical Chemistry for the Atmospheric Sciences<\/em>, Cambridge, UK<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n
    \r\n

    Other interesting material<\/strong><\/h3>\r\n
      \r\n \t
    1. S. E Jorgenson, B. D. Fath,<\/strong> Applications of thermodynamic Principles to ecology, Ecological Complexity, 1, 267- 280(2004).<\/li>\r\n \t
    2. A. C. Werner, C. L. Q. Rodes, T. Huynh, F. Lubben, Ecosystem Theories: Thermodynamics, Web site \u2013 open Landscapes.org<\/em><\/li>\r\n \t
    3. R. F. Mueller, Thermodynamics of Environmental Degradation, Annual Meeting off<\/em> American Geophysical Union<\/em>, Washington, D. C., 1971.<\/li>\r\n \t
    4. Isodoro Martinez, Environmental Thermodynamics: http:\/\/webserver.dmt.upm.es\/~isidoro\/Env\/Introduction%20to%20environmental%20thermo<\/a> dynamics.pdf<\/a><\/li>\r\n \t
    5. Atmospheric Thermodynamics: www.ess.uci.edu\/~yu\/class\/ess55\/lecture.2.thermodynamics<\/strong>.all.pdf<\/li>\r\n<\/ol>\r\n<\/div>\r\n ","rendered":"
      \"epgp<\/a>
      \n<\/span><\/div>\n

       <\/p>\n

      Contents<\/strong><\/p>\n

      1. Introduction<\/p>\n

      2. Thermodynamic Terms<\/p>\n

      3. Heat and Work<\/p>\n

      4. First Law of Thermodynamics<\/p>\n

      5.Internal Energy<\/p>\n

      6. Enthalpy<\/p>\n

      7. Heats of Reaction<\/p>\n

      8. Second Law of Thermodynamics<\/p>\n

      9. Entropy<\/p>\n

      10. Third Law of Thermodynamics<\/p>\n

      11. Gibbs Free Energy<\/p>\n

      12. Chemical Potential<\/p>\n

      13. Free Energy, Chemical Potential, and Pressure<\/p>\n

      14. Thermodynamic Conditions for Equilibrium<\/p>\n

      15. Equilibrium between two Phases\/States of a Single Component<\/p>\n

      16. Suggested Reading<\/p>\n

      17. Other interesting material<\/p>\n

       <\/p>\n

      Introduction<\/strong><\/p>\n

      Thermodynamics deals with changes in various forms of energy. Energy has various forms such as kinetic energy, potential energy, chemical energy, heat etc. Thermodynamics is the study of the changes in energy of a system. It is of fundamental importance in understanding not only environmental chemical and physical processes but also the ecological processes. For an understanding of the subject, it is necessary to understand the terms frequently encountered.<\/p>\n

       <\/p>\n

      Thermodynamic Terms<\/strong><\/p>\n

      System <\/strong>– The part of the universe selected for study is called as system. For example, a cloud selected for study would be a system.<\/p>\n

       <\/p>\n

      Surroundings <\/strong>\u2013 The area adjoining the system is taken as surroundings or the part of the universe other than system. For example, the air around the cloud shall form surroundings. Universe <\/strong>\u2013 Systems and surroundings together form universe.<\/p>\n

       <\/p>\n

      Adiabatic Process <\/strong>\u2013 In this process, there is no exchange of energy between the system and surroundings. For example, a rising parcel of air, while deriving expression for lapse rate, is considered to undergo adiabatic process.<\/p>\n

       <\/p>\n

      Isothermal Process <\/strong>\u2013 A process in which temperature remains constant throughout the process. For isothermal processes dT = 0.<\/p>\n

       <\/p>\n

      Isobaric Process <\/strong>\u2013 When there is no change in the pressure of the system during operations, the process is isobaric. Environmental chemical processes are mostly isobaric.<\/p>\n

       <\/p>\n

      Isolated System <\/strong>\u2013 In such a system, there is no exchange of energy and matter with the surroundings. Open System <\/strong>\u2013 Such systems can exchange both matter and energy with the surroundings. Oceans and lakes are good examples of this type.<\/p>\n

       <\/p>\n

      Closed System <\/strong>\u2013 It can exchange energy but not matter with the surroundings. A sealed aluminum can containing a cold drink is an example of this type.<\/p>\n

       <\/p>\n

      Thermodynamic Variables – <\/strong>The thermodynamic macroscopic state of a system is defined by four measurable properties: composition, pressure, P; volume, V; and temperature, T. Since, P, V and T are interdependent (Please see Ideal gas equation: PV = nRT), therefore only two of these variables are required to specify the state of a system. For thermodynamic studies, generally P and T variable are considered as these are independent variables.<\/p>\n

       <\/p>\n

      Extensive Properties <\/strong>\u2013 These properties depend up on the quantity of the matter, e. g., mass and volume.<\/p>\n

       <\/p>\n

      Intensive Properties \u2013 <\/strong>These properties being the characteristics of the system do not depend on the quantity of the matter, e. g., temperature, density etc. [ the property which is based on the ratio of two extensive properties is intensive in nature]. For example: density is ratio of mass and volume. Mass and volume, both are extensive properties, but their ration, density, is intensive property. Other example is specific heat capacity.<\/p>\n

       <\/p>\n

      State Functions <\/strong>\u2013 The values of these functions, e.g., enthalpy, entropy and internal energy depend up on the initial and final state of the system only and independent of the path taken to reach the final state.<\/p>\n

       <\/p>\n

      Heat and Work<\/strong><\/p>\n

      Heat and work are two forms of energy. Whereas heat is the transfer of the energy due to temperature difference, work is transfer of energy owing to force acting via a distance. Heat and work are not state functions as these depend up on the path. Work, w, is defined by Eq. 1.<\/p>\n

      \"\"<\/p>\n

      The environmental chemical reactions generally occur at a fixed pressure, so we need to consider only work of expansion of gases at a fixed pressure. In this case, force is equal to pressure P and distance moved is equal to the change in the volume. Eq.2 gives work.<\/p>\n

      \"\"<\/p>\n

      \u00a0 First Law of Thermodynamics<\/strong><\/p>\n

      The first law states that energy can neither be created nor destroyed but one form of energy an change into another form. So the total energy of an isolated system remains unchanged although the form of the energy may change. The heat, q, given to a system used partly to increase its internal energy by E and to do work, w,<\/em> then according to first law:<\/p>\n

      \"\"<\/p>\n

      \u00a0 \u00a0 Sign Conventions<\/strong><\/p>\n

      The work done by a has a negative sign (- w).<\/p>\n

      The work on a system has a positive sign (+ w).<\/p>\n

      Heat absorbed by a system has a positive sign (Endothermic Reaction, +<\/em><\/strong>\u00a0 H)<\/em><\/strong>.<\/p>\n

      Heat evolved\/<\/strong>released by a system has a negative sign (Exothermic Reaction, –<\/em><\/strong>\u00a0 H )<\/em><\/strong>.<\/p>\n

       <\/p>\n

      Internal Energy<\/strong><\/p>\n

      It is the characteristic property of a system. It is sum total of all energies associated with a system comprising kinetic energy, potential energies, relativistic energy due to mass (E = mc2) etc. It is a state a function. The absolute value of internal energy can not be calculated because it contains, so many different energies that value of all energies can not be calculated. But change in internal energy of a system ( E ) can be calculated. When a system undergoes a change from initial state (defined by P1, V1, T1) to final state (defined by P2, V2, T2) having internal energies E1 and E2, respectively, then the change in internal energy,E, is given by Eq. 6.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

      \"\"<\/p>\n

      Since E, P and V are all state functions, and so qP is also a state function. The extensive thermodynamic property qP is called enthalpy and is defined by Eq. 11. It is represented by the symbol, Hp, or simply H.<\/p>\n

      \"\"<\/p>\n

      \"\"<\/p>\n

      where HA, HB, HC and HD are standard enthalpies of reactants and products and \u03a3HP and \u03a3HR the enthalpies of products and reactants.<\/p>\n

       <\/p>\n

      Heats of Formation, H<\/em><\/strong>f<\/em><\/strong>, – The standard heat of formation is the change in enthalpy when one mole of a substance is formed from the elements in their standard states. For example, the heat of formation of CO2 is the enthalpy change in the reaction: C(s) + O2 = CO2 (g); all the reactants and products are in their standard state. The heats of formation,Hf<\/em><\/strong>, of elements in their standard states are assumed to be zero.<\/p>\n

       <\/p>\n

      Problem <\/strong>1. Whenever food is cooked by heating, N2 and O2 combine to form NO. Given that the standard heat of formation of NO is 90.4 kJ mol-1, Calculate the standard heat of the reaction: N2 + O2 = 2NO.<\/p>\n

      Solution<\/strong>. The heat of the reaction is:<\/p>\n

      H = (2HNO) \u2013 (HN2 + HO2)<\/p>\n

      The values of both HN2 and HO2 are zero because both should be in their standard state. Using HNO<\/p>\n

      H = (2\u00d790.4) \u2013 (0 + 0) = 180.8 kJ<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem 2. <\/strong>The standard heats of formation of CO and CO2 are HfCO = 110.5 and HfCO2= 412.9 kJ mol-1, respectively. Calculate the standard heat of the combustion of CO.<\/p>\n

      Solution<\/strong>. The combustion reaction is: CO + 0.5 O2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 CO2<\/p>\n

      Heat of combustion,\u00a0\u00a0 H, is given by:<\/p>\n

      H = HfCO2 \u2013 (HfCO \u2013 0.5 HfO2)<\/p>\n

      H = 412.9 \u2013 (-110.5 \u2013 0.5\u00d70) = -302.4 kJ mol-1.<\/p>\n

      The reaction is exothermic.<\/p>\n

       <\/p>\n

      Second Law of Thermodynamics<\/strong><\/p>\n

      This law states that in a reversible change the entropy of the universe does not increase, and in an irreversible change the entropy of the universe increases. This law helps in predicting the direction of the reaction under given conditions. All natural or spontaneous processes lead to an increase in the entropy of the universe. Evaporation, flow of water in rivers, heat flow from higher temperature to lower temperature are all spontaneous processes and therefore accompanied by increase in entropy.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

      When the system and surroundings are at different temperatures, the process becomes irreversible. Consider a thermostat (system), which maintains its temperature constant at T2, whereas its surroundings are at a lower temperature T1. Assuming that the heat q is lost reversibly by thermostat at T2 and is received by surroundings reversibly at temperature T1, the entropy changes of system and surroundings are given by:<\/p>\n

      \"\"<\/p>\n

      Since T2 > T1 so 1\/<\/strong>T1 is greater than1\/<\/strong>T2, hence Sunivers,> 0. This shows the entropy of the universe to increase in an irreversible process.<\/p>\n

       <\/p>\n

      Physical Interpretation of Entropy <\/em><\/strong>\u2013 Entropy is related to the complexion of the system. That is it is related to the probability or the randomness of the system, W, as in Eq.(18) in which k is Boltzmann constant. Greater is the randomness greater is the entropy of the system.<\/p>\n

      \"\"<\/p>\n

      Problem 3<\/strong>. The heat of fusion of water is 6.0\u00a0 kJ mol-1. Calculate the entropy change during fusion.<\/p>\n

      Solution. <\/strong>Water fuses at 0oC or 298 K. The entropy change,S, is given by Eq.:<\/p>\n

      Sfusion =\u00a0\u00a0\u00a0\u00a0\u00a0 Hfusion \/<\/strong> T\u00a0 =\u00a0\u00a0\u00a0 6.0 kJ mol-1\/ 298 K = 6000 J mol-1\/<\/strong>298 K = 20.1 J mol-1 K-1.<\/p>\n

       <\/p>\n

      Third Law of Thermodynamics<\/strong><\/p>\n

      This law is concerned with the absolute values of the entropy of the substances and is helpful in determining these values. According to this law \u2018every substance has a finite entropy, but at absolute<\/em> zero the entropy may become zero, and in case of perfectly crystalline substances it really become<\/em>s zero\u2019. The entropy of any substance at temperature T and the pressure P can be stated mathematically as follows.<\/p>\n

      \"\"<\/p>\n

      where So is the entropy at absolute zero. Knowing the value of So, it would be possible to calculate entropy S at any required temperature from heat capacity data.<\/p>\n

       <\/p>\n

      Gibbs Free Energy, G<\/strong><\/p>\n

      Out of the energy given to a system, only a part is used in doing work and the remainder is used in entropy change. The energy available to do work is Gibbs free energy or simply free energy. It is given a symbol, G, for absolute value, and G for change. If H is the heat supplied at constant<\/p>\n

      \"\"<\/p>\n

      \"\"any process to occur, whether chemical or physical, this is the most important criterion. In other words only, those processes shall be able to occur for which the free energy decreases. Since most of the processes occur at constant temperature and pressure in environment, G is of great importance.<\/p>\n

       <\/p>\n

      Helmholtz Free Energy, A<\/em><\/strong><\/p>\n

      For the processes occurring at constant temperature and volume, the term Helmholtz free energy, A, is used. It is defined by Eq. 21. As with G, those processes would be spontaneous, for which A< 0.<\/p>\n

      \"\"<\/p>\n

      Thus, Gibbs free energy is defined under constant pressure and constant temperature, and Helmholtz free energy is defined under constant volume and constant temperature.<\/p>\n

       <\/p>\n

      Standard Free Energy<\/em><\/strong><\/p>\n

      Standard free energy change of a substance is the free energy change for the reaction by which the substance is obtained from the elements in their standard states at one atmospheric pressure.<\/p>\n

       <\/p>\n

      Problem 4<\/strong>. At 27oC, the enthalpy change, Ho, for a reaction is 25 kJ mol-1 and entropy change, So, is 100 J mol-1 K-1. Find whether the reaction is spontaneous.<\/p>\n

      Solution. To test the spontaneity of the reaction, calculate<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0 G by Eq.:<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      \n

      Chemical Potential\/ Partial Molar Free Energy<\/strong><\/p>\n

      Consider a multi-component system. Its free energy G is a function of T, P and amounts of components, n1, n2, —— ni.<\/p>\n

      \"\"<\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      According to Eq. 24, chemical potential of a particular constituent in a mixture is the increase in the property G of the system due to the addition of one mole of that substance at constant temperature and pressure to such a large quantity of the constituents that its composition remains virtually unchanged. It may be pointed out that the value of \u00b5i in a mixture is not same as in the pure state. Thus, value of \u00b5i varies with composition of the system.<\/p>\n

       <\/p>\n

      \"\"<\/p>\n

       <\/p>\n<\/div>\n

      \n

      Thermodynamic Conditions for Equilibrium<\/strong><\/p>\n

      At constant temperature and pressure, the conditions for equilibrium are as follows.<\/p>\n

      1. For a system of one of component, dG =0.<\/p>\n

      2. For a multi-component system, the chemical potential of each component must be same in all the phases,\u00a0 i. e., \u00b5(a) = \u00b5(b) = \u00b5(c) where a, b and c are different phases.<\/p>\n<\/div>\n

      \"\"<\/p>\n

      Suppose that a small amount of liquid water is transferred to water vapor. If Gvapor and Gliquid be the molar free energies of water in vapor and liquid state, respectively, the transfer of one mole from liquid state to vapor state shall entail the change in free energy, \u2206G, given by Eq. 28.<\/p>\n

      \"\"<\/p>\n

      Since the two phases are in equilibrium, \u2206G = 0, and so Gvapor = Gliquid . It is concluded, therefore, that whenever two (or more) phases of the same substance alone are in equilibrium at a fixed P and T, the molar free energy would be the same in all phases. An interesting application of aspect is in cloud physics.<\/p>\n\n\n\n
      you can view video on Environmental Chemical Thermodynamicsy<\/strong><\/td>\n\"\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n

      Reference<\/strong><\/h3>\n
        \n
      1. S. Glasston, Thermodynamics for Chemists<\/em>, East- West, New Delhi.<\/li>\n
      2. R. P. Rastogi and R. R. Mishra, An Introduction to Thermodynamics<\/em>, Vikas Publishing House New Delhi, 2001<\/li>\n
      3. P. W. Atkins, Physical Chemistry<\/em>, Oxford University Press, 1998.<\/li>\n
      4. Chemistry I for Class XI<\/em>, NCERT, New Delhi<\/li>\n
      5. A Bahl, B. S. Bahl and G. D. Tuli(2012), Essentials of Physical Chemistry, <\/em>S. Chand, New Delhi<\/li>\n
      6. Philip Matthews(2013), Advanced Chemistry,<\/em> Cambridge, New Delhi<\/li>\n
      7. P. V. Hobbs(2000), Basic Physical Chemistry for the Atmospheric Sciences<\/em>, Cambridge, UK<\/li>\n<\/ol>\n<\/div>\n

         <\/p>\n

        \n

        Other interesting material<\/strong><\/h3>\n
          \n
        1. S. E Jorgenson, B. D. Fath,<\/strong> Applications of thermodynamic Principles to ecology, Ecological Complexity, 1, 267- 280(2004).<\/li>\n
        2. A. C. Werner, C. L. Q. Rodes, T. Huynh, F. Lubben, Ecosystem Theories: Thermodynamics, Web site \u2013 open Landscapes.org<\/em><\/li>\n
        3. R. F. Mueller, Thermodynamics of Environmental Degradation, Annual Meeting off<\/em> American Geophysical Union<\/em>, Washington, D. C., 1971.<\/li>\n
        4. Isodoro Martinez, Environmental Thermodynamics: http:\/\/webserver.dmt.upm.es\/~isidoro\/Env\/Introduction%20to%20environmental%20thermo<\/a> dynamics.pdf<\/a><\/li>\n
        5. Atmospheric Thermodynamics: www.ess.uci.edu\/~yu\/class\/ess55\/lecture.2.thermodynamics<\/strong>.all.pdf<\/li>\n<\/ol>\n<\/div>\n

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