CY1040 Basic Chemistry for Engineers PDF

CY1040: Basic Chemistry for Engineers Instructor: Dr. Yugender Goud Kotagiri Indian Institute of Technology Palakkad Email: [email protected] Introduction to the Course  Syllabus 1. Chemical Thermodynamics: [8...

CY1040: Basic Chemistry for Engineers Instructor: Dr. Yugender Goud Kotagiri Indian Institute of Technology Palakkad Email: [email protected] Introduction to the Course  Syllabus 1. Chemical Thermodynamics: [8 L+ 2T] Laws of Thermodynamics, Entropy change accompanying various processes (isothermal expansion, phase transition, heating, entropy of mixing of perfect gases); Absolute entropy and the Third Law of thermodynamics; Statistical entropy; Thermodynamic functions (A, G, U & H) and four fundamental equations, Maxwell relationships; Spontaneity of a chemical reaction and Gibbs energy; Standard Gibbs energies of formation and reactions; variation of G with T and P, Gibbs-Helmholtz equation, Chemical potential; G versus extent of reaction, Application in electrochemical cell, and Polymer Chemistry. 2. Chemical Kinetics: [3 L+ 1T] Rate law and rate equations, rate constant, Order and molecularity, Half life of a reaction, Arrhenius equation and activation energy, examples of complex reactions: Parallel, opposing and consecutive reactions; Analysing mechanisms using the steady-state approximation with one or two examples. DR. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 3  Syllabus 3. Basic Quantum Mechanics and Its Application to Molecular Spectroscopy [6L+ 2T] Postulates, Particle in a box model including Schrodinger equation, wave function, quantisation of energy, energy levels and Basics of molecular spectroscopy, Basics of Microwave, IR Spectroscopy and UV-Vis spectroscopy, quantification by Beer Lambert Law. 4. Chemical Bonding and Transition Metal Complexes: [8L+ 2T] LCAO-MO; H2 + molecule; Bonding and antibonding orbitals; Electronic structure of homonuclear diatomic molecule, bond order, paramagnetism (B2 and O2 molecules)and diamagnetism (C2, N2 and F2 molecules); Heteronuclear diatomic molecules (HF); Formation of bands in solids-metals, semiconductors and insulators. Bonding in transition metal complexes; coordination compounds; crystal field theory, octahedral, tetrahedral and square planar complexes; CFSE; Jahn-Teller theorem; Spectral, electronic and magnetic properties of coordination complexes. DR. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 4  Syllabus 5. Organic Reaction Mechanisms: [ 8L+ 2T] a) Basic reaction Mechanism: Substitution reactions, Elimination Reactions, Addition reactions. b) Aromatic, non-aromatic and anti-aromatic compounds. (Explanation using Frost Cycle energy diagram). c) Aromatic substitution reactions: Aromatic electrophilic substitution and Aromatic nucleophilic substitution reactions. Applications briefly: production of Ibuprofen and paracetamol. Application of Sanger's reagent. Dow’s process, Nylon 66 [Brief introduction on industrial applications]. DR. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 5  Learning Objectives 1. Analyse how thermodynamics and chemical kinetics are useful to chemists, for predicting the possibility of reactions, and understanding the mechanism of reactions, and quantifying the thermodynamic properties of pure substances and mixtures. 2. Employ the concepts to understand the behavior of chemical systems from the molecular level. 3. Explaining the reactivity and stability of organic molecules. 4. Analysis of the mechanisms for aromatic organic reactions, design and synthesize aromatic compounds. 5. Characterize organic systems using spectroscopic techniques. DR. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 6  Reference Textbooks Text/Reference Books: 1. Physical Chemistry, Peter Atkins and Julio de Paula, 10th Edition, Oxford University Press. ISBN: 9780199697403 2. Physical Chemistry – A Molecular Approach, Donald A McQuarie and John D Simon, Viva Books. ISBN13: 9780935702996 3. Inorganic Chemistry Principle of Structure and Reactivity, James E Huyee, Ellen A Keiter and Richard L. Keiter, HarperCollinsCollegePublisher. ISBN: 0-06-04-2995-X 4. Organic Chemistry, Paula Y Bruice, 7th Edition, Springeseverar, 2009, Pearson. ISBN-13: 978-0321819031 5. Fundamentals of Molecular Spectroscopy by C N Banwell and E M McCah, 4th Ed., Tata McGraw-Hill. ISBN:0077079760 9780077079765 Reference books: 1. Organic Chemistry, Robert Thornton Morrison and Robert Neilson Boyd, 6th Edition, Pearson. ISBN 9788131704813 2. Introduction to spectroscopy, Pavia, 4th Edition, Science Publisher, 2015. ISBN: 9780495114789 DR. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 7  Exam Pattern Total Marks: 100 1. Test I – 25 Marks 2. Test II – 25 Marks 3. Final – 50 Marks DR. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 8 Chemical Thermodynamics  Introduction to Thermodynamics ❖ Thermodynamics is the “Science of Energy Transfer” “Therme-heat Dynamics-Power” ❖ Thermodynamics is the branch of physics and physical chemistry that deals with the relationships between heat and other forms of energy, such as work, and the conversion of one form of energy into another. ❖ It encompasses the study of the principles governing the behavior of systems at macroscopic scales, focusing on concepts such as temperature, entropy, and energy transfer in various processes. ❖ Thermodynamics provides fundamental principles for understanding and predicting the behavior of matter and energy in a wide range of physical, chemical, and biological systems. ❖ Thermodynamics serves as a foundational framework for understanding the behavior of matter and energy in chemical systems, providing essential tools for chemists to analyze, predict, and control chemical processes effectively. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 10  Introduction to Thermodynamics Macroscopic Approach - Classical Microscopic Approach – Statistical Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 11  Terms used in Thermodynamics System: A specified part of the universe or a specified portion of the matter which is under experimental investigation. Eg. Reaction vessel, an engine, an electrochemical cell, a biological cell Surroundings: The rest of the universe i.e. all other matter which can interact with the system, is surroundings. Boundaries: The real/imaginary part which separates the system and surroundings. Boundary may be rigid/nonrigid and may be a conductor or non-conductor of heat. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 12  Types of system Depending on the no.of phases, systems are two types. Homogeneous: A system with a single phase is called homogeneous Ex: mixture of water and alcohol. Heterogeneous: A system with two or more phases is called heterogeneous. Ex: mixture of water and benzene. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 13  Types of system Depending on the nature of boundaries, Open system: This type of system can exchange matter as well as energy with surroundings. The boundary is not sealed and not insulated. Ex: Hot water in a glass/beaker Closed system: A system can exchange energy in form of heat, work or radiation but not matter with its surroundings. The boundary is sealed but not insulated. Ex: Hot water in closed beaker Isolated system: This type of system has no interaction with surroundings. Neither matter nor energy can be exchanged with surroundings. The boundary is sealed and insulated. Ex: Thermos flask Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 14  Types of system Macroscopic system: A system consisting of a large number of particles (molecules, atoms, ions, etc) is known as a macroscopic system. Macroscopic properties: The properties associated with a macroscopic system are called Macroscopic properties. Ex: Pressure (P), Temperature (T), Volume (V), Viscosity, Density (d) etc. State of the system: The state of the system is defined when its macroscopic properties are specified. If any one of the macroscopic properties of the system changes, the system is said to be in a different state. When a reaction takes place, one or more of the macroscopic properties of the system changes, the first and final state of the system are called initial and final state respectively. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 15  Thermodynamic properties The quantities, whose values define a system, Extensive properties: Mass-dependent properties are called extensive properties. Ex: mass, length, area, volume, no. of moles, force, enthalpy etc. Intensive properties: Mass-independent properties are called intensive properties. Ex: Sp. Gravity, density, viscosity, boiling point, melting point, pressure etc. Note: The quotient obtained by dividing any extensive property by another extensive property given an intensive property. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 16 Diathermic And Adiabatic Wall Diathermic wall Adiabatic wall Passage of heat is Passage of heat is permitted not permitted Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 17 Exothermic and Endothermic process Endothermic – Gaining of heat during a process Exothermic – Release of heat during a process Adiabatic system; Heat neither goes out or come in. Temperature reading in thermometer falls during endothermic process. Temperature rises during exothermic process. Isothermal Process; Heat is exchanged between system and surrounding depending upon the process as may be. So, “T” of the system is maintained constant. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 18  Molecular Interpretation of Heat and Work work is identified as energy transfer making use of the organized motion of atoms in the surroundings, and heat is identified as energy transfer making use of thermal motion in the surroundings. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 19 Types of Thermodynamic Processes U = internal energy Q = Heat Transfer Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 20 Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 21  Objects in thermal equilibrium The temperature, T, is the property that indicates the direction of the flow of energy through a thermally conducting rigid wall. A B If energy flows from A to B when they are in contact, then we say that A has a higher temperature than B Vice versa, If energy flows from B to A when they are in contact, then we say that B has a higher temperature than A. Thermal equilibrium is established if no change of state A B occurs when two objects A to B are in contact through a diathermic boundary. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 22 Reversible process: Def 1: A reversible process is that which is carried out infinitesimally slowly to that all changes occuring in the direct process can be exactly reversed and the system remains almost in a state of equilibrium at all times. Def 2: It may be defined as that which is carried out in stages and the driving force at every stage is only infinitesimally greater than the opposing force and which can be reversed by increasing the opposing force by an infinitesimal amount. Irreversible process: It is that which is not carried out in infinitesimally slowly steps (instead it is carried out in single step) and thus cannot be carried in the reverse order. Ex: Expansion of gas, heat flow from hot body to cold body Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 23 Reversible process: When a thermodynamic process occurs in such way that the properties of the system at any instant remains practically uniform, the process is called Reversible process. Note: A reversible process can be conceived to proceed very slowly through a succession of infinitesimal steps and its direction can be reversed at any point by making a small change in a variable like temperature, pressure etc. In this connection pressure of gas "P" applied on the piston is equal to the combined pressure applied by the weight of piston, weight of sand and atmospheric pressure i.e. Pext Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 24 The pressure on the piston is allowed by an infinitesimally small amount dp, pressure on the piston will be p-dp which is infinitesimal smaller than the pressure of the gas "P". Therefore, the piston will move upward, and gas will expand by an infinitesimally small amount. By the removal of sand particles continuously the gas can be allowed to undergo finite expansion. But each of the step in this expansion is an infinitesimal one and can be reversed by an infinitesimal change in the external conditions. At all steps the equilibrium is restored immediately. Note: A reversibe process will take infinite time and thus cannot be realized in practice. Therefore, a reversible process is only imaginary and theoretical. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 25  Reversible Process Irreversible Process It takes place slowly in infinite It takes place in one rapid number of infinitesimal small measurable step steps which is not possible in practical It is unreal It is real It is in equilibrium state at all It is in equilibrium position in stages of the operation only initial and final stages of the operation only It can be made to go any It can be made to go only one direction direction Work done is greater than Work done is lower than the irreversible process reversible process. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 26  Zeroth Law of thermodynamics: (Concept of temperature and thermal equilibrium) The Zeroth Law of Thermodynamics states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law establishes the concept of temperature and provides the foundation for temperature measurement and the definition of temperature scales. Suppose an object A (which we can think of as a block of iron) is in thermal equilibrium with an object B (a block of copper), and that B is also in thermal equilibrium with another object C (a flask of water). Then it has been found experimentally that A and C will also be in thermal equilibrium when they are put in contact. This observation is summarized by the Zeroth Law of thermodynamics: “If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A” Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 27  Zeroth Law of thermodynamics: Concept of temperature and thermal equilibrium – Adiabatic wall – Diathermal wall If TA = Tc and TB = TC Zeroth Law Provides the Basis for the thermometer function. Then, TA = TB Where mercury and the liquid in contact are separated by a diathermal wall Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 28  Applications (i) When we get very hot food, we wait to make it normal. In this case, hot food exchanges heat with surrounding and bring equilibrium. (ii) We keep things in the fridge, and the things come in equilibrium with fridge temperature. (iii) Temperature measurement with a thermometer or another device. (iv) In the HVAC system, sensors or thermostats are used to indicate the temperature. It always comes in thermal equilibrium with room temperature. Limitations (i) It does not tell us about the direction in which heat flows when they are in contact. (ii) When two bodies come in equilibrium conditions, this law is unable to tell about the final temperature or the temperature of the equilibrium conditions. (iii)It does not tell about energy conservation. (iv)If two objects are not in physical contact, there may also be a heat transfer. For example, if two objects with different temperatures placed little distance, there may be a heat transfer by radiation. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 29  First Law of Thermodynamics (Conservation of energy) First law of Thermodynamics: 1. Law of conservation of energy: Energy can neither by created nor destroyed although it can be converted from one form to another. 2. The total energy of an isolated system remains constant although it can undergo a change from one form to another. 3. Rudolf Clausius: Whenever a quantity of some form of energy disappears, an exactly equivalent amount of some other form of energy must be produced. 4. Helmholtz (1847): It is impossible to construct a perpetual motion machine, i.e. a machine which would produce work continuously without consuming energy. 5. For a system in contact with its surroundings, the sum of the energies of the system and the surroundings at a particular time remains constant, however, differently it may be shared between the two. 6. Einstein (Law of conservation of mass and energy): The total mass and energy of an isolated system remains constant in chemical thermodynamics. The concept of internal energy (E or U), Heat (q), Work(w), and enthalpy (H) follows from first law of thermodynamics. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 30  Work (W) The fundamental physical property in thermodynamics is work It is defined as the system’s displacement with the application of force. Work (W) = Force (F) X Length (L) Units: SI – Joules; CGS – Ergs; 1 J = 107 ergs Work is motion against an opposing force. ▪ Doing work is equivalent to raising a weight somewhere in the surroundings. ▪ the process of raising a weight against the pull of gravity. ▪ Another example is a chemical reaction in a cell, which leads to an electric current that can drive a motor and be used to raise a weight. ▪ expansion of a gas that pushes out a piston PV Work or Expansion of Gas (work) δW = pdv Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 31  Energy The energy of a system is its capacity to do work. When work is done on an otherwise isolated system (for instance, by compressing a gas or winding a spring), the capacity of the system to do work is increased; in other words, the energy of the system is increased. When the system does work (when the piston moves out or the spring unwinds), the energy of the system is reduced and it can do less work than before. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 32  Heat Experiments have shown that the energy of a system may be changed by means other than work itself. When the energy of a system changes as a result of a temperature difference between the system and its surroundings we say that energy has been transferred as heat. A system is like a bank: it accepts deposits in either currency (work or heat), but stores its reserves as internal energy. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 33  Internal energy: A The total energy of a system is called its internal energy, U. The internal energy is the total kinetic and potential energy of the molecules in the system. ∆U = Uf − Ui, Where, ∆U - change in internal energy ; Ui - internal energy of initial state; Uf internal energy of final state Changing state variable such as Pressure (P), Temperature(T), Volume (V) will alter the internal energy of a system. w = - P dV (doing work on the system changes the internal energy of a system) Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 34  Molecular interpretation of Internal energy A molecule has a certain number of motional degrees of freedom, such as the ability to move through space (this motion is called ‘translation’), rotate, or vibrate. Many physical and chemical properties depend on the energy associated with each of these modes of motion. For example, a chemical bond might break if a lot of energy becomes concentrated in it, for instance as vigorous vibration. The internal energy of a sample increases as the temperature is raised and states of higher energy become more highly populated. The Boltzmann distribution gives the population, Ni, of any energy state in terms of the energy of the state, εi, and the absolute temperature, T: Ni ∝ e−εi/kT Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 35  Internal energy It has been found experimentally that the internal energy of a system may be changed either by doing work on the system or by heating it. q = heat change w = work ∆U = q + w If the system absorbs heat q > 0 If systems looses heat q < 0 If system does work on surrounding w < 0 If work is done on the system w > 0 q + w = ∆U Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 36  Change in Internal energy Amount of heat supply = work done by the system + change in internal energy Q = dE + (-w) Q = dE + PdV Q = ∆E + P∆V Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 37 Isothermal Process: Internal energy of ideal gas ∞ Absolute temperature In isothermal process temperature remains constant, dE = 0 Q = dE + (-w) Q = -w dQ = -dw The amount of heat energy supplied is completely utilized for mechanical work. Adiabatic Process: Q=0 -dE = -w A system will do the work at the expense of its internal energy. When work is done on the system, internal energy increases. During adiabatic expansion, cooling takes place, while during compression heating takes place. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 38 Isochoric Process: Here volume remains constant. Q = dE The amount of heat supplied is used to increase its internal energy. Isobaric process: In this process pressure remains constant. Q = dE + PdV Q = dH Heat capacity at constant pressure is called Enthalpy. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 39 Expansion work For general case, total work done when volume goes from Vi to Vf Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 40 Varieties of work Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 41  Work done in Isothermal reversible expansion or compression of an ideal gas Work done by the gas is given by, Consider a gas enclosed in a cylinder fitted with a dw = − P − dP dV weightless and frictionless piston. The cylinder is not dw = −PdV insulated. The external pressure equals to internal 𝑉2 pressure. If the external pressure is lowered by infinitesimal amount dP i.e. it falls from P to P-dP and 𝑤𝑟𝑒𝑣 = න −𝑃𝑑𝑉 the volume changes from V to V+dV. 𝑉1 𝑉 𝑑𝑉 For ideal gas PV = nRT 𝑤𝑟𝑒𝑣 = −𝑛𝑅𝑇 ‫ 𝑉׬‬2 1 𝑉 𝑉 −𝑤𝑟𝑒𝑣 = 𝑛𝑅𝑇𝑙𝑛 𝑉2 1 𝑉 −𝑤𝑟𝑒𝑣 = 2.303𝑛𝑅𝑇𝑙𝑜𝑔 𝑉2 1 𝑃1 𝑉2 𝑃1 𝑎𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑇, 𝑃1 𝑉1 = 𝑃2 𝑉2 𝑎𝑛𝑑 = ; −𝑤𝑟𝑒𝑣 = 2.303𝑛𝑅𝑇𝑙𝑜𝑔 𝑃2 𝑉1 𝑃2 For compression, 𝑉1 𝑃2 𝑤𝑟𝑒𝑣 = 2.303𝑛𝑅𝑇𝑙𝑜𝑔 = 2.303𝑛𝑅𝑇𝑙𝑜𝑔 𝑉2 𝑃1 Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 42 Isothermal irreversible expansion: 1. Free expansion or expansion against vacuum Pext = 0, dw = 0, dE = 0, dT = 0 2. Intermediate expansion or compression Isothermal irreversible expansion or compression of an ideal gas at constant Pext. 𝑃𝑔𝑎𝑠 > 𝑃𝑒𝑥𝑡 𝑉2 −𝑑𝑤 = 𝑃𝑒𝑥𝑡 න 𝑑𝑉 𝑉1 −𝑤𝑖𝑟𝑟 = 𝑃𝑒𝑥𝑡 (𝑉2 − 𝑉1 ) Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 43 Work done in Adiabatic Reversible expansion or compression of an ideal gas Q = ∆E + (-w) ∆E = w 𝑑𝐸 Molar heat capacity at constant volume of an ideal gas is given by, 𝐶𝑉 = 𝑑𝑇 𝑉 𝑑𝐸 = 𝐶𝑉 𝑑𝑇 𝑤 = ∆𝐸 = 𝐶𝑉 𝑑𝑇 = −𝑃𝑒𝑥𝑡 𝑑𝑉 𝑓𝑜𝑟 𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑃𝑒𝑥𝑡 ≈ 𝑃 −𝑃𝑑𝑉 = 𝐶𝑉 𝑑𝑇 −𝑅𝑇 𝑅𝑇 𝑑𝑉 = 𝐶𝑉 𝑑𝑇 𝑃= 𝐹𝑜𝑟 𝑜𝑛𝑒 𝑚𝑜𝑙𝑒 𝑉 𝑉 𝑑𝑉 𝑑𝑇 −𝑅 = 𝐶𝑉 𝑉 𝑇 𝑉2 𝑇2 𝑑𝑉 𝑑𝑇 −𝑅 න = 𝐶𝑉 න 𝑉 𝑇 𝑉1 𝑇1 𝑉2 𝑇2 −𝑅 𝑙𝑛 = 𝐶𝑉 𝑙𝑛 𝑉1 𝑇1 Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 44 𝐶𝑃 − 𝐶𝑉 𝑅 𝐶𝑃 𝑅 𝑅 = , −1= , 𝐴𝑛𝑑 𝛾 − 1 = 𝐶𝑉 𝐶𝑉 𝐶𝑉 𝐶𝑉 𝐶𝑉 𝑉2 𝑇2 −(𝛾 − 1) 𝑙𝑛 = 𝑙𝑛 𝑉1 𝑇1 𝑉1 𝑇2 (𝛾 − 1) 𝑙𝑛 = 𝑙𝑛 𝑉2 𝑇1 𝛾 is the adiabatic index, or the 𝛾−1 𝑉1 𝑇2 ratio of heat capacity at = constant pressure 𝐶𝑃 to heat 𝑉2 𝑇1 capacity at constant volume 𝐶𝑉 𝛾−1 𝛾−1 𝑇1 𝑉1 = 𝑇2 𝑉2 𝑻𝑽𝜸−𝟏 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑃𝑉 𝛾−1 𝑉 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑅 𝑷𝑽𝜸 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝛾 𝑅𝑇 𝑃 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑷𝟏−𝜸 𝑻𝜸 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑃 Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 45 Work Done: 𝑑𝑤 = 𝑑𝐸 𝑑𝐸 = 𝐶𝑉 𝑑𝑇 𝑅 𝑅 𝛾−1= , 𝐶𝑉 = 𝐶𝑉 𝛾−1 𝑇2 𝑅 𝑑𝑤 = න 𝑑𝑇 𝛾 − 1 𝑇1 𝑅 𝑊𝑟𝑒𝑣 = (𝑇 – 𝑇 ) For one mole 𝛾−1 2 1 𝑛𝑅 𝑊𝑟𝑒𝑣 = (𝑇2 – 𝑇1 ) For n moles 𝛾−1 For expansion, T2 < T1 and T2 – T1 is –ve Wrev is –ve (Work done by the gas) For compression, T2 > T1 and T2 – T1 is +ve Wrev is +ve (Work done on the gas) Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 46 Adiabatic irreversible process: 1. Free expansion or expansion against vacuum Work done is zero. 2. Irreversible expansion or compression of an ideal gas at constant Pext. 𝑉2 −𝑑𝑤 = 𝑃𝑒𝑥𝑡 න 𝑑𝑉 𝑉1 −𝑤𝑖𝑟𝑟 = 𝑃𝑒𝑥𝑡 (𝑉2 − 𝑉1 ) 𝑤𝑖𝑟𝑟 = 𝑃𝑒𝑥𝑡 𝑉1 − 𝑉2 𝑅𝑇1 𝑅𝑇2 𝑤𝑖𝑟𝑟 = 𝑃𝑒𝑥𝑡 − → (1) 𝑃1 𝑃2 𝑇1 𝑇2 𝑤𝑖𝑟𝑟 = 𝑅𝑃𝑒𝑥𝑡 − 𝑃1 𝑃2 𝑤 = ∆𝐸 = 𝐶𝑉 𝑑𝑇 𝑊𝑖𝑟𝑟 = 𝐶𝑉 𝑇2 − 𝑇1 → (2) From (1) and (2) 𝑻𝟏 𝑻𝟐 𝒘𝒊𝒓𝒓 = 𝑹𝑷𝒆𝒙𝒕 − = 𝑪𝑽 𝑻𝟐 − 𝑻𝟏 𝑷𝟏 𝑷𝟐 Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 47  Enthalpy The change in internal energy is not equal to the energy transferred as heat when the system is free to change its volume, such as when it is able to expand or contract under conditions of constant pressure. Under these circumstances some of the energy supplied as heat to the system is returned to the surroundings as expansion work (Fig. 2B.1), so dU is less than dq. In this case the energy supplied as heat at constant pressure is equal to the change in another thermodynamic property of the system, the ‘enthalpy’. where p is the pressure of the system and V is its volume. The enthalpy, H, is defined as Because U, p, and V are all state functions, the enthalpy is a H = U + pV state function too. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 48  Enthalpy The enthalpy, H, is defined as H = U + pV Deriving the relation between enthalpy change and heat transfer at constant pressure + For a general infinitesimal change in the state of the system, U changes to U + dU, p changes to p + dp, and V changes to V + dV + = + + + + = + + + + + The last term is the product of two infinitesimally small quantities and can be neglected. Now recognize that U + pV = H on the right (in blue), so + = + + + = + + Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 49  Enthalpy Step 2 Introduce the definition of dU = + = + + + =− = + = = = This equation states that, provided there is no additional (non-expansion) work done, the change in enthalpy is equal to the energy supplied as heat at constant pressure. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 50  Enthalpy Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 51  Thermochemistry Δ < Δ > Δ < Δ > Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 52  Thermochemistry Δ ⦵ Δ ⦵ Δ ⦵ → Δ ⦵ =+ − → Δ ⦵ =+ − Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 53 Thermochemistry Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 54 Bond Energy/Bond Enthalpy Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 55  Hess’s Law Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 56 Limitations of first law of Thermodynamics: 1. The law does not give any information about direction in which the flow of energy takes place. 2. The law does not explain why the chemical reactions do not proceed to completion. 3. The law does explain why the natural spontaneous processes are irreversible. 4. The law does not contradict the existence of self acting refrigeration and 100% efficient engine. 5. The difference between spontaneous and non spontaneous processes is insignificant in view of the first law. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 57 1. Calculate the work done when 50 g of iron reacts with hydrochloric acid to produce FeCl (aq) and hydrogen in (a) a closed vessel of fixed volume, 2 (b) an open beaker at 25 °C. Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 58 Dr. YUGENDER, DEPARTMENT OF CHEMISTRY Sunday, January 19, 2025 59