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124 CHEMISTRY SOME IMPORTANT THERMODYNAMIC TERMS The System and The Surroundings System in thermodynamics refers to that part of universe in which observations are made and remaining universe constitute the surroundings. Universe = system + surroundings Types of System (i) Open System : In this system there is exchange of energy and matter between system and its surroundings (ii) Closed System : In this system there is no exchange of matter, but exchange of energy is possible between system and its surroundings (iii) Isolated System : In this system there is no exchange of matter and energy between system and surroundings. State of the System and State Variables The state of a thermodynamic system is described by its measurable or macroscopic properties. Variables like pressure (P), volume (V) and temperature (T) are called state variables or state functions because their values depend only on state of system and not on how it is reached. The state of a system is specified by state functions or state variables. Macroscopic System and Macroscopic Properties If a system contains a large no. of chemical species, it is called a macroscopic system. The properties of macroscopic system like temperature, pressure, volume, density, melting point, boiling point, etc are called macroscopic properties. They are further divided into two types : (i) Extensive properties They depend on quantity of matter contained in system Example : mass, volume, heat capacity etc. (ii) Intensive properties depend only on nature of substance and are independent of amount of substance present in system Example : temperature, pressure, density, etc. Thermodynamic Processes These are said to occur when a system changes from one state to another. (i) Isothermal process occurs when temperature remains constant throughout the process. (ii) Adiabatic process occurs when no heat can flow from system to its surroundings and vice-versa. (iii) Isochoric process occurs when volume of the system is kept constant. (iv) Isobaric process occurs when pressure of the system is kept constant. (v) Cyclic Process – The process in which a system proceeds via many intermediate steps and returns to the initial state. Change in internal energy (dE) = 0, change in enthalpy (dH)=0 Thermodynamic Quantities Internal energy The energy stored within a substance is called its internal energy. It is represented by ‘U’ or ‘E’. It is the sum of different types of energies associated with atoms and molecules. The change in internal energy is given by: DU = U2 – U1 . where, U2 : final state U1 : initial state The internal energy of a system changes when (i) heat passes in or out of the system. (ii) work is done on or by the system. (iii) matter enters or leaves the system. It is a state function and is an extensive property. DU is negative if energy is evolved andDU is positive if energy is absorbed. Internal energy of one mole of a monoatomic gas at ‘T’ Kelvin is 3 2 RT . Internal energy of ideal gas is a function of temperature only. In isothermal processes (T is constant), DU = 0. Work There are two types of work in Thermodynamics : (i) Electrical work = EMF × quantity of electricity (ii) Pressure – volume work W = – Pext DV (DV = V2 – V1 = Vfinal – Vinitial) Work done on the system is positive while work done by the system is negative For free expansion of an ideal gas, Pext = 0, \ W = 0 Heat It is a mode of energy exchanged between the system and the surroundings as a result of difference of temperature between them. It is represented by ‘q’, when heat is given by the system, it 6 Thermodynamics EBD_7327
Thermodynamics 125 is given negative sign. When heat is absorbed by the system, it is given positive sign. Work and heat are not state functions. FIRST LAW OF THERMODYNAMICS It is the law of conservation of energy. According to this law, energy can neither be created nor destroyed although it may be converted from one form to another or The energy of an isolated system is constant. Mathematically, DU = q + W where, q = energy absorbed by the system W = workdone on the system. SOME IMPORTANT RESULTS (i) For isothermal irreversible expansion, q = –W = Pext (V2 – V1 ) (ii) For isothermal reversible expansion or compression from volume V1 to V2 2 1 V q W nRT ln V =- = (iii) For isothermal expansion of an ideal gas against vacuum i.e. for free expansion, DU = 0, W = 0, q = 0 (iv) Since internal energy of an ideal gas is a function of temperature, for all isothermal processes involving ideal gas, DU =0, whether the process is reversible or irreversible. (v) For adiabatic change, q = 0, therefore DU = Wad. (vi) For isochoric process , W = 0 \ DU = qv + 0 i.e., heat given to system at constant volume changes internal energy. ENTHALPY, H The total heat content of a system at constant pressure is known as its enthalpy From 1st law of thermodynamics, DU = q + W As W = – P D V \ q = DU + P D V At constant volume, D V = 0, we have qV = DU At constant pressure, we have qp = DU + PDV or, qp = (U2 – U1 ) + P (V2 – V1 ) qp = (U2 + PV2 ) – (U1 + PV1 ) .... (1) The quantity (U + PV) is called heat content or enthalpy of the system. \ H U PV = + Also, H U PV 22 2 = + and H U PV 11 1 = + Putting these values in eq (1), p 21 q HH = - or, p q H = D as p q U PV =D + D \ D =D + D H U PV Enthalpy is a state function and an extensive property. Enthalpy of monoatomic gas = 5 2 RT per mole. Change in enthalpy of the products and reactants at 298 K and 1 atmospheric pressure is called standard molar enthalpy change. In a cyclic process, i.e. when the system returns to the original state after a number of changes, DU or DH = 0. Relationship between heat of reaction at constant pressure and at constant volume We know qp = DH and qv = DU, DH = DU + PDV =D + - =D + - U P V V U PV PV ( 21 2 1 ) ( ) Putting PV = n1RT, PV2 = n2RT, D =D + - H U n RT n RT ( 2 1 ) D =D +D H U n RT g or, qp = qv + Dng RT HEAT CAPACITY It is the amount of heat required to raise the temperature of a system through 1°C. It is given by: 2 1 q q C TT T = = - D \ q = C × DT Specific Heat Capacity It is the amount of heat required to raise the temperature of one gm of substance through 1°C. q = m × c × DT where m : mass of sample, c : specific heat Molar Heat Capacity It is amount of heat required to raise the temperature of 1 mole of a substance through 1°C. i.e., m C C n = Types of heat capacities or molar heat capacities (i) Heat capacity at constant volume (CV ) At constant volume, qv = Cv DT = DU (ii) Heat capacity at constant pressure (Cp ) At constant pressure, qp = Cp DT = DH Relation between Cp and Cv As D =D +D =D +D H U PV U RT ( ) ( ) DH = DU + RDT \ CP DT = Cv DT + RDT Þ CP = Cv + R or, CCR P v - = Relation between ratio Cp /Cv and atomicity of a gas (i) For monoatomic gases Cp /CV = 1.66 (ii) For Diatomic gases Cp /Cv = 1.40 (iii) For Triatomic gases Cp /CV = 1.33 EXOTHERMIC AND ENDOTHERMIC REACTIONS Exothermic reactions are those which are accompanied by evolution of heat. DH is negative for exothermic reactions Endothermic reactions are those in which heat is absorbed. DH is positive for endothermic reactions.
126 CHEMISTRY THERMOCHEMICAL EQUATION When a balanced chemical equation not only indicates the quantities of different reactants and products but also indicates the amount of heat evolved or absorbed, it is called thermochemical equation. HEAT OF REACTION OR ENTHALPY OF REACTION OR ENTHALPY CHANGE OF REACTION The amount of heat evolved or absorbed in a chemical reaction when the number of moles of reactants as represented by the chemical equation have completely reacted, is called heat of reaction or enthalpy of reaction or enthalpy change of reaction (DrH). Change in total heat of reaction at 25°C and 1 atm pressure is called standard heat of reaction Different types of heats/ enthalpies of reaction (i) Enthalpy of combustion : It is the heat evolved when 1 mole of substance is completely burnt or oxidised in oxygen. It is represented as DcH. ex: CH g 2O g CO g 2H O g 42 2 2 () () + 3⁄43⁄4® + () () DcH° is standard enthalpy of combustion i.e. combustion taking place under standard conditions, i.e., 298 K and 1 bar pressure. (ii) Enthalpy of formation : It is the heat change i.e. heat evolved or absorbed when 1 mole of the substance is formed from its elements under given conditions of T and P. It is represented by Df H. Standard enthalpy of formation arises when the substance is formed in the standard state from its elements, which is also taken in the standard state (i.e. 298 K and 1 bar pressure). It is represented by Df H° The standard enthalpy change of the reaction is: D °= D ° - D ° rf f H H products H reactants å å ( ) ( ) For elementary substances in standard state, o Df H is taken as zero. (iii) Enthalpy of Neutralization The enthalpy of neutralization of an acid by a base is defined as the heat change when one gram equivalent of the acid is neutralized by a base, the reaction being carried out in dilute aqueous solution. The enthalpy of neutralization of any strong acid with a strong base or vice-versa, is always the same, i.e. 57.1kJ. (iv) Enthalpy of solution It is defined as the enthalpy change when 1 mole of the substance is dissolved in a specified amount of the solvent. For ionic compounds, enthalpy of solution depends upon lattice enthalpy and hydration enthalpy, i.e., D °=D °+D ° sol hyd H HH lattice For most ionic compounds, D ° solH is positive and dissociation process is endothermic. Thus, solubility of most salts in water increases with increase in T. If lattice enthalpy of a salt is very high, the dissolution of the compound may not take place at all. For this reason fluorides are less soluble than chlorides. (v) Heat of hydration : The amount of heat released on complete hydration of one mole of an anhydrous substance is called heat of hydration. (vi) Lattice enthalpy and its calculation The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociates into its ions in gaseous state. Lattice energy is calculated using the Born-Haber Cycle. It is explained by taking the examples of NaCl. (a) Na(s) 3⁄43⁄4® Na (g) i.e., sublimation 1 subH 108.4kJ mol- D °= (b) Na(g) 3⁄43⁄4® Na+ (g) + e– i.e., ionization of 1 iH 496kJ mol- D °= (c) 2 () () 1 Cl g Cl g 2 3⁄43⁄4® i.e., dissociation of Cl 1 bond 1 H 121 kJ mol 2 - D °= (d) Cl g e Cl g ( ) ( ) - - + 3⁄43⁄4® i.e. gain of e– by Cl. 1 EGH 348.6 k J mol- D °=- (e) Na g Cl g Na Cl s () () ( ) + - +- + 3⁄43⁄4® and 2 1 Na(s) + Cl ( ) NaCl (s) 2 g ® 1 Δf H =–411.2kJ mol- This is the Born – Haber Cycle . Applying Hess’s law, we get DfH° = DsubH° + bond lattice 1 H° + I.E. + E. A. + H° 2 D D D °= latticeH 411.2 +108.4+121+496 – 348.6 = + 788 k J Now, D °=D °+D ° sol lattice hyd H HH = + 788 kJ mol–1 + (– 784 kJ mol–1) = + 4 kJ mol–1 . (vii) Enthalpy of Atomization When one mole of a given substance dissociates into gaseous atoms, the enthalpy change accompanying the process is called enthalpy of atomization. It is represented by DaH°. e.g., o 1 H ( ) 2H(g), H 435.0 kJ mol 2 a g ® D= - (viii) Bond Enthalpy or Bond energy It is the amount of energy released when one mole of bonds are formed from the isolated atom in gaseous state or the amount of energy required to dissociate one mole of bonds present between the atoms in gaseous molecules. It is represented by DbH or DbondH. It is expressed in kcal/mole DrH = å B.E. (Reactants) – å B.E. (Products) EBD_7327
Thermodynamics 127 Enthalpy Changes During Phase Transitions (i) Heat of sublimation : The amount of heat required to change one mole of a solid substance into vapour state is called heat of sublimation. I 2 (s) ® I2 (g) DH = +62.07 kJ/mole (ii) Heat of fusion : The amount of heat required to completely change one mole of a solid substance into liquid at its melting point is called heat of fusion. H2O(s) ––––® H2O(l) DH = 6.0 kJ (iii) Heat of vapourisation : The amount of heat required to completely change one mole of a liquid into vapours at its boiling point is called heat of vapourisation. H2O(l) ––––® H2O(g) DH = +44 k cal HESS’S LAW OF CONSTANT HEAT SUMMATION It states that the total amount of heat evolved or absorbed in a reaction is the same whether the reaction takes place in one step or in a number of steps. In other words, the total amount of heat change in a reaction depends only upon the nature of initial reactants and nature of final products and is independent of the path or manner by which this change is brought about. A B Reactant R Product, P q1 q2 q3 Q Qq q q =++ 123 SPONTANEITY A spontaneous process is an irreversible process and may only be reversed by some external agency. The tendency for a process to occur depends upon two factors: (i) tendency for minimum energy (ii) tendency for maximum randomness The resultant of the above two tendencies which gives the overall tendency for a process to occur is called driving force of the process. ENTROPY It is a measure of randomness or disorder of the system. Unit of entropy is JK–1mol–1 Greater the randomness, higher is the entropy. Entropy change during a process is given by: DS = S2 – S1 = å Sproduct – å Sreactant DS is related to q and T for a reversible process as follows: rev q S T D = In any process : Total system surrounding D =D +D SS S At equilibrium, entropy of the system is maximum and DS = 0 For irreversible process, Total system surrounding D =D +D > SS S O SECOND LAW OF THERMODYNAMICS It states that the energy of universe is constant whereas the entropy of universe is continuously increasing and tends to a maximum. GIBBS FREE ENERGY AND SPONTANEITY The available amount of energy to the system during the process which can be changed into useful work, is called free energy of the system. Gibbs energy helps in predicting the spontaneity of a process. It is denoted by ‘G’ and is given by G = H – TS The change in Gibb’s energy is given by: DG = DH – TDS The decrease in the value of Gibbs free energy during a process is equal to the maximum possible useful work that can be obtained from the system. According to Gibbs energy equation : DG = DH – TDS It combines both the factors of spontaneity, namely, energy factor DH and entropy factor TDS Spontaneity in Terms of Free Energy Change (i) If DG is negative, the process is spontaneous (ii) If DG = 0, the process does not occur or system is in equilibrium. (iii) If DG = positive, process does not occur in forward direction. It may occur in backward direction. At equilibrium, DrG° = DrH° – T Dr S° = – RT ln K = – 2.303 RT logK (K ® equilibrium constant) Relation Between DG and emf of Cell DG = – nFEcell where, Ecell = emf of the cell n = number of moles of electrons involved F = Faraday’s constant i.e., 96500 coulomb If reactants and products are in their standard state, DG° = – nFE° where E° = standard cell potential Effect of Temperature on Spontaneity of Reactions ( ) ( ) ( ) ( ) ( ) rr r H S G Description of reaction Spontaneous at all T lowT spontaneous at low T high T non-spontaneous at high T low T spontaneous at low T high T spontaneous at high T at all T non-spontaneous at all T D °D° D ° -+ - - -- - -+ + ++ + +- + -+ THIRD LAW OF THERMODYNAMICS At absolute zero temperature, the entropy of a perfectly crystalline substance is taken as zero. This law was formulated by Nernst in 1906.