Thermodynamic Processes and Thermochemistry

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1 General Chemistry Thermodynamic Processes and Thermochemistry 박준원교수 ( 포항공과대학교화학과 )

2 이번시간에는! Systems, states, and processes The first law of thermodynamics: internal energy, work, and heat Heat capacity, calorimetry, and enthalpy The first law and ideal gas processes Thermochemistry

3 General Chemistry Thermodynamic Processes and Thermochemistry (I-1) 박준원교수 ( 포항공과대학교화학과 )

4 Thermodynamics is a broad and general subject with applications in all branches of the physical and biological sciences and engineering; thus we limit our discussion to those aspects necessary for chemical equilibrium.

For example, with thermodynamics we can answer the following types of chemical questions: 1. If hydrogen and nitrogen are mixed, is it possible for them to react?

5 For example, with thermodynamics we can answer the following types of chemical questions: 1. If hydrogen and nitrogen are mixed, is it possible for them to react? If so, what will be the percentage yield of ammonia? 2. How will a particular change in temperature or pressure affect the extent of the reaction? 3. How can the conditions for the reaction be optimized to maximize its yield? Thermodynamics can determine whether a process is possible, but it cannot say how rapidly the process will occur.

6 1 Systems, states, and processes System: a part of universe of immediate interest in a particular experiment or study. Closed system: the boundaries prevent the flow of matter into or out of it. Open system: the boundaries permit such flow.

7 Isolated system: exchanges neither matter nor energy with the rest of the universe. Rigid walls prevent the system from gaining energy by mechanical processes such as compression. Adiabatic walls prevent the system from gaining or losing thermal energy. Diathermal walls permit thermal energy transfer. Surroundings: the portion of the remainder of the universe that can exchange energy and matter with the system. Thermodynamic universe: the system + the surroundings

8 An extensive property of the system can be written as the sum of the corresponding property in the two subsystems. Ex) volume, mass, energy An intensive property of the system is the same as the corresponding property of each of the subsystem. Ex) temperature, pressure A thermodynamic state is a macroscopic condition of a system in which the properties of the system are held at selected fixed values independent of time. A thermodynamic process changes the thermodynamic state of a system. A process may be physical, such as changing the pressure of a gaseous system or boiling a liquid. A chemical process involves a chemical reaction.

9 Suppose a gas is confined by a piston in a cylinder with volume V 1 (thermodynamic state A in Fig 12.2). If the piston is abruptly pulled out to increase the volume to V 2 (thermodynamic state B), chaotic gas currents arises (Fig 12.2 b), and the intermediate stage is not thermodynamic state because the properties are not independent of time. [ F I G U R E ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 523.

10 In contrast, a reversible process proceeds through a continuous series of thermodynamic states. The term reversible is used because an infinitesimal change in external conditions suffices to reverse the direction of motion of the system. Such a process is an idealization. If a real process is conducted slowly enough and in sufficiently small steps, the real (irreversible) process can be approximated by an idealized reversible process.

11 Certain properties of a system, called state functions, are uniquely determined by the thermodynamic state of the system. Ex) volume, temperature, pressure, and the internal energy U The change in any state function between two states is independent of path.

12 [ F I G U R E ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 524. The change of altitude, latitude, and longitude by going from Chicago to Denver is independent of path, and other properties such as the total distance traveled are dependent of path.

13 General Chemistry Thermodynamic Processes and Thermochemistry (I-2) 박준원교수 ( 포항공과대학교화학과 )

14 2 The first law of thermodynamics: internal energy, work, and heat <Work> The mechanical definition of work is the product of the external force on a body times the distance through which the force acts. w = F r f r i (force along direction of path)

15 1) Consider a block of mass, M, moving with initial velocity v i along a frictionless surface. If a constant force, F, is exerted on it in the direction of its motion, it will experience a constant acceleration, a. After a time, t, the velocity of the block will have increased from v i to v f. The work done on the block is w = F r f r i = Ma r f r i w = M v f v i t v i +v f 2 t r f r i = v i +v f 2 t = M 2 (v f v i )(v f + v i ) a = (v f v i )/t = M 2 v f 2 M 2 v i 2 = E kin The work done in the moving block from r i to r f is equal to the change in energy of the block.

16 2) Consider the work done in lifting an object in a gravitational field. To raise a mass, M, from an initial height, h i, to a final height, h f, an upward force sufficient to counteract the downward force of gravity, Mg, must be exerted. The work done on the object is w = Mg h f h i = Mg h = E pot The mechanical work done in moving a body is equal to the change in potential energy.

17 3) Imagine that a gas has pressure P i and is confined in a cylinder by a frictionless piston of cross-sectional area A and negligible mass (Fig 12.4). The piston is exerted by an external pressure P ext, and the pressure is less than the initial pressure exerted by the gas inside of the cylinder, then the gas will expand and lift the piston from h i to h f.

[ F I G U R E 1 2. 4 ] Oxtoby, D. W.; Gillis, H. P.; Campion, A.

18 [ F I G U R E ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 525.

19 The work is w = F ext (h f h i ) w = P ext A h so the work is w = P ext V [12.1] For an expansion, V > 0, thus w < 0 and the system does work. For a compression, the work is done on the system. If P ext = 0, no pressure-volume work can be performed even for the expansion (called free expansion).

20 International System of Units (SI) unit for pressure is pascals, the unit for volume is cubic meters, and the unit for their product is joules (J). For many purposes, it is more convenient to express pressures in atmospheres and volumes in liters. 1 L atm = 10 3 m kg m 1 s 2 = J

21 <Internal energy> The internal energy is defined as the total energy content of a system arising from the potential energy between molecules, from the kinetic energy of molecular motions, and chemical energy stored in chemical bonds. P V work is a means of changing the internal energy of a macroscopic system through purely mechanical interaction between the system and its surroundings.

22 <Heat> A means of increasing the internal energy of a system without mechanical interaction. The amount of energy transferred between two objects initially at different temperatures is called heat, or thermal energy. The specific heat capacity of a material is the amount of heat required to increase the temperature of a 1-g mass by 1. q = Mc s T [12.2] One calorie was defined as the amount of heat required to increase the temperature of 1 g water from 14.5 to 15.5, and the calorie is now defined as 1 cal = J (exactly)

23 <The first law of thermodynamics> In many processes, both heat and work cross the boundary of a system, and the change in the internal energy, U, is the sum of the two contributions. This statement, called the first law of thermodynamics, takes the mathematical form U = q + w [12.3] Because q and w depend on the particular process (or path) connecting states, they are not state functions. But their sum ( U) is independent of path; therefore, internal energy is a function of state. The laws of thermodynamics cannot be derived or proved; they are generalizations of the results of countless experiments on a tremendous variety of substances.

24 In any process, the heat added to the system is removed from the surroundings: thus q sys = q surr In the same way, w sys = w surr Adding these two gives U sys = U surr U univ = U sys + U surr = 0 [12.4] The total energy change of the thermodynamic universe remains unchanged (conservation of the total energy).

25 General Chemistry Thermodynamic Processes and Thermochemistry (II-1) 박준원교수 ( 포항공과대학교화학과 )

26 3 Heat capacity, calorimetry, and enthalpy <Heat capacity and specific heat capacity> Heat capacity, C, is defined as the amount of energy that must be added to the system to increase its temperature by 1 K and has units of J K 1. q = C T

27 The molar heat capacity C v is the amount of heat required to increase the temperature of 1 mol of substance by 1 K at constant volume, the molar heat capacity c p is that at constant pressure. If the total heat transferred to n moles at constant volume is q V, then q V = nc V T 2 T 1 = nc V T [12.5] If an amount q P is transferred at constant pressure, then q P = nc P T [12.6] The specific heat capacity at constant V or constant P is the system heat capacity reported per gram of substance.

28 <Heat transfer at constant volume: Bomb calorimeters> Suppose some reacting species are sealed in a small closed container (called a bomb). Because the container is sealed tightly, its volume is constant and no P V work is done. Therefore, the change in internal energy is U = q V

[ F I G U R E 1 2. 9 ] Oxtoby, D. W.; Gillis, H. P.; Campion, A.

29 [ F I G U R E ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 532.

30 <Heat transfer at constant pressure: Enthalpy> Most chemical reactions are carried out under constant pressure rather than at constant volume. Therefore, the change in internal energy is U = q P + w = q P P ext V If P ext = P internal U = q P P V q P = U + P V

31 Because P is constant, P V = (PV) The above equation becomes q P = U + PV The combination U + PV is now defined as the enthalpy H: H = U + PV [12.7a] q P = U + PV = H [12.7b] Because U, P, and V are state functions, H must be also a state function.

32 4 The first law and ideal gas processes <Heat capacities of ideal gases> The pair of molar heat capacities of c V and c P for an ideal monoatomic gas can be calculated from the results of the kinetic theory of gases and the ideal gas equation of state. U = q V = nc V T (ideal gas) c V = 3 R (monatomic ideal gas) [12.8] 2 To find the value of c P, U = q P + w nc V T = nc P T P V

33 For ideal gases, PV 1 = nrt 1 and PV 2 = nrt 2 ; thus nc V T = nc P T nr T c V = c P R, c P = c V + R c P = c V + R (any ideal gas) [12.9] For an ideal gas processes, H = U + PV = nc V T + nr T H = nc P T (any ideal gas) [12.11]

34 General Chemistry Thermodynamic Processes and Thermochemistry (II-2) 박준원교수 ( 포항공과대학교화학과 )

35 5 Thermochemistry The study of heat transfers during chemical reactions is referred to as thermochemistry. Because chemical reactions are usually studied at constant pressure, the heat transferred in each reaction (q P ) equals with the enthalpy change ( H reaction ). <Enthalpies of Reaction> When heat is given off by a reaction ( H is negative), the reaction is said to be exothermic. Reactions in which heat is taken up ( H is positive) are called endothermic.

36 Hess s law: If two or more chemical equations are added to give another chemical equation, the corresponding enthalpies of reaction must be added. The law is useful to find H even if the reaction of interest is difficult to study directly. For example, C s, gr O 2 g CO g H =?

37 Given that C s, gr + O 2 g CO 2 g H 1 = kj (1) CO 2 g CO g O 2 g H 2 = kj (2) Adding equations (1) and (2) gives the equation in question. Therefore, H = H 1 + H 2 = kj The corresponding internal energy change U is, U = H PV, PV PV = = nrt nrt = RT n = RT n g = 1 g = 1 2 mol 2 mol U = kj 1.24 kj = kj

38 <Standard-state enthalpies> Absolute values of the enthalpy of a substance cannot be measured or calculated. Only change in enthalpy can be measured. Just as altitudes are measured relative to a standard altitude (sea level), it is necessary to adopt a reference state for the enthalpies. Chemists define standard states as follows: For solids and liquids, the standard state is the thermodynamically stable state at a pressure of 1 atm and at a specified temperature. For gases, the standard sate is the gaseous phase at a pressure of 1 atm, at a specified temperature and exhibiting ideal gas behavior. For dissolved species, the standard state is a 1-M solution at a pressure of 1 atm, at a specified temperature and exhibiting ideal solution behavior. (Most common specified temperature is K.)

39 Once standard states have been defined, the zero of the enthalpy scale is defined by arbitrarily stetting the enthalpies of selected reference substances to zero in their standard states. Chemists agreed to the following: The chemical elements in their standard state at K have zero enthalpy. Chemists have agreed to assign zero enthalpy to the form that is most stable at 1 atm and K (for examples, O 2 (g) rather than O 3 (g) and graphite rather than diamond and fullerenes). The standard enthalpy change ( H ): The enthalpy change for a chemical reaction in which all reactants and products are in their standard states and at K. The standard enthalpy of formation ( H f ) of a compound: the enthalpy change for the reaction that produces 1 mol of the compound from its element in their stable states, all at 25 and 1 atm pressure.

40 For example, H f of liquid water is H 2 g O 2 H 2 O(l) H = kj H f H 2 O l = kj mol 1 Chemists have agreed that H f of H + aq is set to zero to establish a reference point for the enthalpies of formation of cations and anions. For a general reaction of the form aa + bb cc + dd The standard enthalpy change is H = c H f C + d H f D a H f C b H f C

41 6 Reversible processes in ideal gases Most thermodynamic processes conducted in laboratory work are irreversible. Because changes in the state functions are independent of the detailed path of the process, as long as the initial and final equilibrium states are known, the changes can be directly calculated along reversible paths. <Isothermal processes> An isothermal process is one conducted at constant temperature. In a reversible process, U = 0, w = q (isothermal process, ideal gas) P ext = P gas P = nrt V

[ F I G U R E 1 2. 1 9 ] Oxtoby, D. W.; Gillis, H. P.; Campion, A.

42 [ F I G U R E ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 552.

43 w = V 2 P dv V 1 (reversible process) [12.14] w = nrt V 2 1 V dv V 1 [12.15] w = nrt ln V 2 V 1 q = w = nrt ln V 2 V 1 U = 0 because T = 0 H = U + PV = U + nrt [12.16]

44 <Adiabatic process> An adiabatic process is one in which there is no transfer of heat into or out of the system. q = 0, U = w du = nc V dt nc V dt = P ext dv If the process is reversible, as well as adiabatic, so that P ext = P nc V dt = P dv = nrt V dv c V T dt = R T dv

45 Suppose now that the change is not infinitesimal but large. c V T 2 1 T 1 T dt = R V 2 1 V 1 V dv Evaluating integrals gives c V ln T 2 T 1 = R ln V 2 V 1 = R ln V 1 V 2 T 2 T 1 c V = V 1 V 2 R = V 1 V 2 c P c V

46 The last step used the factor that R = c P c V. Thus, T 2 T 1 = V 1 V 2 c P c V 1 = V 1 V 2 γ 1 Where γ = c P c V T 1 V 1 γ 1 = T 2 V 2 γ 1 [12.17] P 1 V 1 γ = P 2 V 2 γ [12.18] U = nc V T 2 T 1 = w (reversible adiabatic process for ideal gas) H = U + PV = U + P 2 V 2 P 1 V 1 or simply H = nc P T

[ F I G U R E 1 2. 2 0 ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 555.

47 [ F I G U R E ] Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7 th ed.; Cengage Learning: Boston, 2012; p 555. Because γ > 1, the adiabatic line falls more rapidly with increasing volume than the isothermal line. The adiabatic work ( q = 0, no heat transfer into the system) is 40% of the isothermal work.

Chapter 2 First Law Formalism

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