CH1007 Chemistry Thermodynamics & Equlibrium PDF

Thermodynamics & Equlibrium Dr. Raghavendra Samantaray  Thermodynamics Thermodynamics: The science of heat and their inter-conversion to work or any other form of energy. Thermodynamics is governed by three major principles: Ø The first law states the conserva...

Thermodynamics & Equlibrium Dr. Raghavendra Samantaray  Thermodynamics Thermodynamics: The science of heat and their inter-conversion to work or any other form of energy. Thermodynamics is governed by three major principles: Ø The first law states the conservation of energy Energy can neither be created nor destroyed, it can merely be converted from one form to another. Ø explains the spontaneotey of various reactions processes. It introduces the concept of ‘entropy’ or ‘disorder’ or ‘randomness’ to predict the spontaneous occurrence of chemical reactions. Ø relates to the entropy basically in experimental approach The entrpy of pure crystalline is object is zero at 0  Thermodynamics: Some important terms If objects A and B are separately in thermal equilibrium with a third object C, then objects A and B are in thermal equilibrium with each other. Internal energy: Internal energy is the sum total of energy of a system. The energy is generated at molecular level, and associated to atoms and molecules. Ek, Ep stands for kinetic and potential energy Absolute value of internal energy is not calculated rather changes in E (ΔE) of a system is considered in thermodynamics. ΔE = Ef – Ei State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. Thermodynamics: Some important concepts ΔQ=0, Δn=0 ΔQ≠0, Δn=0 ΔQ≠0, Δn≠0 Extensive Intensive properties properties are those are those whose value whose value does not on depend on the the quantity of substance of substance present in present in the system. the system.  Thermodynamic Equilibrium Equlibrium: At equilibrium, the intensive properties of a system do not change with time. At equilibrium, energy (Q) or matter (n = number of moles) does not flow (seemingly) within the system or at its boundaries. Three types of equilibrium exist in the system: - Thermal equilibrium: The temperature remains same throughout the whole system - Chemical equilibrium: The composition of the system remains constant or does not change with time. The chemical equilibrium is a dynamic process in which the rates of forward and backward reactions become equal. - Mechanical equilibrium: In this equilibroum, there is no flow of matter within the system or at its boundaries.  Sign convention for Q (heat) Exothermicity Endothermicity – “out of” a system – “into” a system Surroundings Surroundings System System Energy Energy Δq < 0 Δq > 0 - In an exothermic process heat is released ( ). - In an endothermic process heat is absorbed ( )  Thermodynamic equilibrium. In a system if the state variables have constant values throughout the system is said to be in a state of thermodynamic equilibrium. For example, a gas confined in a cylinder has a frictionless piston. If the piston is stationary, the state of the gas can be specified by giving the values of pressure and volume. The system is then in a state of equilibrium. A system in which the state variables have different values in different parts of the system is said to be in a non-equilibrium state. If the gas is compressed very rapidly by moving the piston, it passes through states in which pressure and temperature cannot be specified exactly, as these properties vary throughout the gas. The gas near the piston is compressed and heated more in comparision to the far end of the cylinder is not. The gas then would be said to be in non-equilibrium state. Thermodynamic processes Ø Isobaric process (Pressure constant) Ø Isochoric process (Volume constant) Ø Isothermal process (Temperature constant) Ø Adiabatic process (No heat exchange) Ø Cyclic process Ø Reversible process Ø Irreversible process  Enthalpy Enthalpy: The heat absorbed or evolved at constant pressure H= Qp Note: All the chemical reactions occur at atmospheric pressure, hence p constant Enthalpy, denoted by H, and is an extensive property - An extensive property is one that depends on the quantity/size of substance. - Enthalpy is a state function: is independent of path in other words independent of previous history of the system  First law of thermodynamics √ First law is not hi ng but t he ge ne ral i sat i on of conservation of energy E  dQ  dW -Work done the system is -Work done the system is negative -For an isolated system ΔE = 0, as Q=W=0 -For an ΔE = 0, as Q=W (W=-ve) -At constant V, ΔE = Q -At constant Q, ΔE = -W heat transfer in heat transfer out (endothermic), +Q (exothermic), -Q ∆E = Q+ W w transfer in w transfer out On the syatem By the syatem (+w) (-w) Enthalpy and the First Law of Thermodynamics E  dQ  dW At constant pressure, ΔQ = ΔH and w = -PΔV ΔH = ΔE + PΔV 6.7  First law of thermodynamics Isothermal process, T = Constant Isobaric process, P= Constant Isochoric or isovolumatric process, V= Constant Adiabatic process, Q= constant Enthalpy (ΔH) in a Chemical Reaction H = Qp = E + PV But enthalpy is a state function H = H2 – H1 = (E2 + P2V2) - (E1 + P1V1) = (E2 - E1)+ (P2V2 - P1V1) = E + PV H = E + w As per 1st law, E = q – w Now, H = q, at constant pressure E = q, at constant volume For a chemical reaction, H = Hproduct – Hreactant H = E + PV PV2 = n2RT, PV1 = n1RT = P(V2 - V1)= (n2 - n1)RT = P V = n RT Now, H = E + n RT ΔH is positive if Hp > Hr and the process or reaction will be endothermic. and the reaction will be Enthalpy (ΔH) in a Chemical Reaction At (V = 0) constant volume, H = E - Reactions are carried out in closed vessels - Reactions gaseous components Example: - Gaseous reactions where When V ≠ 0, - In case of np > nr, Then H > E - In case of np < nr, Then H < E Enthalpy (ΔH) : Numericals  The Concept of Entropy (ΔS) Entropy is the measure of the of the system. - it is a state function, - hence it depends only on the initial and final state of the system. Thus, S = Sfinal – Sinitial When, Sfinal  Sinitial, S is positive A chemical process or reaction accompanied by an increase in entropy tends to be spontaneous  Entropy (ΔS) A change in a system which is accompanied by an increase in entropy, is spontaneous.  Clausius Definition of Entropy According to Clausius: For a reversible process taking place at a fixed temperature (T), the change in entropy (  S) is equal to heat energy absorbed or evolved divided by the temperature (T). If heat is absorbed, S is positive, increase in entropy If heat is evolved, S is negative, decrease in entropy Units: cal mol–1 K–1. (Entropy units, eu) J mol–1 K–1. (SI unit) 1eu = 4.184 Entropy  Standard Entropy (S˚) - The absolute entropy of a substance at pressure, is called the standard entropy. - The absolute entropy of elements is zero only at 0 K in a perfect crystal - standard entropies of all substances at any temperature always posses - If we know the entropies of reacants and products, then we can calculate the standard entropy change, ΔSº, for chemical reactions. - We can also calculate the value of entropy of formation of a given compound from the values of S˚ of elements. Entropy: Numericals  Entropy: Numericals Third law of Thermodynamics. In case of a perfect crystal the entropy is zero.  Entropy change of an Ideal Gas Entropy is a state function and its value depends on two of three variables T, P & V. (a) T and V as Variables Entropy change of an Ideal Gas Entropy change of an Ideal Gas, at T and P as Variables Entropy change of an Ideal Gas, at different conditions Numericals Numericals Numericals Numericals  Entropy of Mixing ü When different gases are mixed freely at constant T and P, then the entropy of the system increases. ü On mixing, the molecules of each gas are free to move in a large volume, hence their randomness (entropy) increases. ü Let us consider two ideal gases, A and B, with a number of moles nA and nB, at constant T & P and volumes of VA and VB. ü To undersatnd entropy change, let us treat this mixing as two separate gas expansions, one for gas A and another for B. From the standard definition of entropy, we know that  Entropy of Mixing Now, for each gas, the V1 is the initial volume, and V2 which is VA+VB. Now, entropy of gas A and B after expansions will be So the total entropy change for both these processes, The ideal gas law, PV = nRT, at constant T and P, The V directly proportional to n, and hence the number of moles can be substituted by volume:  Entropy of Mixing The inverse of (nA+nB)/nA is the mole fraction χA=nA/nA+nB, Hence, This equation represents the equation for the entropy change of mixing. This equation is also commonly written with the total number of moles: where the total number of moles is n=nA+ nB Numericals Numericals Numericals  Free Energy Function (G) and Work Function(A) ü The feasibility of a process or chemical reaction cannot be determined by enthalpy change or entropy change alone. ü Both ∆H and ∆S are essential to predict the spontaneity or feasibility of a chemical reaction. ü The functions which incorporate both energy and entropy change are the free energy function and work function represented by G and A respectively. ü Both these functions are state functions, that is, their value depends only on the initial and final state of the system. ü They are given by A = E  TS ∆A = ∆E  T∆S G = H  TS ∆G = ∆H  T∆S  Significance of Work Function(A) ü For an isothermal change, ∆A = ∆E  T∆S Since, T∆S = q rev ∆A = ∆E  q rev (1) From 1st Law of thermodynamics, ∆E = q + w Hence, W rev = ∆E - q rev (2) Comparing Eq (1) & Eq (2) ∆A = W rev ü Thus, at constant temperature, A is equal to reversible work done by the system. ü Work function is a mesure of maximun work obtainable from the system, also known as or Helmoltz function Significance of Energy Function (G) We know that, ∆G = ∆H  T∆S........(1) From first law q = E + W, or ∆H = ∆E + P∆V, and we also know that T∆S = q rev Substituting these values in above equation (1), ∆G = ∆E + P∆V -T∆S or ∆G = ∆A + P∆V (Since ∆A = ∆E -T∆S) But, ∆A = -w Hence ∆G = -w+ P∆V or -∆G = w- P∆V Remember P∆V is the work done due to volume expansionthus -∆G can be called as net work odone by the system, and is known as free enrgy of the system  G on variation of P and V Now G = H -TS or G = E + PV -TS (1) in differential form, or dG = dE + PdV + Vdp -TdS -SdT From first law dq = dE-dW, and in chemical systems, -dW = p∆V Now, dq = dE + PdV, but dq = TdS Putting these values in eqn 1 dG = VdP-SdT G for ideal gases  Gibbs–Helmholtz Equation We know that dG = Vdp -SdT, and at constant pressure, dG = -SdT Let the free energy at two different temperatures T1 and T2 are dG1 and dG2 , and entropy S1, and S2 respectively The change in free energy, dG1-dG2 = -(S2-S1)dT or d(ΔG) = -ΔSdT ∆ At const. P, d =− ∆ (1) But we know that ΔG = ΔH -TΔS ∆ −∆ − ∆ = (2) Now, Comparing the above equations (1) and (2) ∆ − ∆ ∆ = ∆ Rearranging, ∆ = ∆ + This is the Gibb’s Helmoltz equation in terms of energy and enthalphy at constant pressure  Gibbs–Helmholtz Equation in terms of ΔE and ΔA ∆ −∆ We know that, A = E-TS or ΔA = ΔE- TΔS or −∆ = Free energy in differential form dA= dE -TdS -SdT From first law, dq = dE + pdV, and at const V, dq = dE, and also dq = TdS Now, dA = -SdT Let the Work function at two different temperatures T 1 and T 2 are dA 1 and dA 2 , and entropy S1, and S2 respectively The change in free energy, dA1-dA2 = -(S2-S1) dT, or d(ΔA) = -ΔSdT ∆ At const. V, d =− ∆ (1) But we know that ΔA = ΔE -TΔS ∆ −∆ − ∆ = (2) Now, Comparing the above equations (1) and (2) ∆ − ∆ ∆ = ∆ Rearranging, ∆ = ∆ + This is the Gibb’s Helmoltz equation in terms of internal energy and work function at constant volume Numericals Numericals  Conditions of Equilibrium and Criterion for a Spontaneous Process (a) In Terms of Entropy Change The entropy of a system remains unchanged in a reversible change while it increases in an irreversible change, i.e., Conditions of Equilibrium and Criterion for a Spontaneous Process (a) In Terms of Enthalpy Change (a) In Terms of Free Energy Change G = H – TS G = E + PV – TS dG = dE + PdV + VdP – TdS – SdT  Van’t Hoff Isotherm § Every chemical reaction has free energy change (∆G) which is given by van’t Hoff’s reaction isotherm. § It gives the net work that can be obtained from a gaseous reactant at constant temperature when both the reactants and the products are at suitable arbitrary pressures. Let us consider a reaction, A + B C + D (1) Van’t Hoff Isotherm Van’t Hoff Isotherm  Van’t Hoff Isochore Ø It deals with the variation of equilibrium constant with temperature.  Claypeyron–Clausius Equation It finds application in one component and two-phase systems. It gives information about a system consisting of any two phases of a single substance in chemical equilibrium. It is derived from the Gibbs-Helmholtz equation Let us consider two phases A and B of the same component in equilibrium with each other at constant temperature T and pressure P. This equilibrium may be represented as  Claypeyron–Clausius Equation entropies. Claypeyron–Clausius Equation Liquid ↔ Vapour System Calculation of Latent Heat of Vaporisation Calculation of Boiling Point or Freezing Point Calculation of Vapour Pressure at another Temperature  Partial Molar Properties For studying the systems containing two or more phases or components G.N. Lewis introduced the concept of partial molar properties as in these cases both mass and composition vary (open systems). Consider any extensive thermodynamic property X of such a system, the value of which is determined by the temperature, pressure and the amounts of various constituents present. Let the system consist of J constituents and let n1, n2, n3.... nj be the number of moles of the various constituents present. Evidently X must be a function of P, T and the number of moles of various constituents present, i.e. X = f (T, P, n1, n2, n3.... nj) (i) If there is a small change in the temperature and pressure of the system as well as the amounts of its constituents, the change in the property X is given by Partial Molar Properties  By definition the chemical potential of a given substance is the change in free energy of the system produced on addition of one mole of the substance at constant temperature and pressure to a large bulk of the mixture so that its composition does not undergo any change. It is an intensive property and it may be regarded as the force which drives the chemical system to equilibrium. At equilibrium the chemical potential of the substance in the system must have the same value through the system. In other words, the matter flows spontaneously from a region of high chemical potential to low chemical potential. The chemical potential may also be regarded as the escaping tendency of that system. Greater the chemical potential of a system greater will be its escaping tendency. Gibbs Duhem Equation dG = V =S