EQUILIBRIUM IN CHEMICAL REACTIONS

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EQUILIBRIUM IN CHEMICAL REACTIONS CHAPTER 12 Thermodynamic Processes and Thermochemistry CHAPTER 13 Spontaneous Processes and Thermodynamic Equilibrium CHAPTER 14 Chemical Equilibrium CHAPTER 15

1 EQUILIBRIUM IN CHEMICAL REACTIONS CHAPTER 12 Thermodynamic Processes and Thermochemistry CHAPTER 13 Spontaneous Processes and Thermodynamic Equilibrium CHAPTER 14 Chemical Equilibrium CHAPTER 15 Acid-Base Equilibrium CHAPTER 16 Solubility and Precipitation Equilibria CHAPTER 17 Electrochemistry Stalactites (top) and stalagmites (bottom) Ca 2+ (aq) + 2 HCO 3- (aq) CaCO 3 (s) + H 2 O + CO 2 (g)

4 The First Law and Ideal Gas Processes 12.5 Molecular Contributions to Internal Energy and Heat Capacity 12.

2 12 CHAPTER THERMODYNAMIC PROCESSES AND THERMOCHEMISTRY 12.1 Systems, States, and Processes 12.2 The First Law of Thermodynamics: Internal Energy, Work, and Heat 12.3 Heat Capacity, Calorimetry, and Enthalpy 12.4 The First Law and Ideal Gas Processes 12.5 Molecular Contributions to Internal Energy and Heat Capacity 12.6 Thermochemistry 12.7 Reversible Processes in Ideal Gases Steam locomotive thermal mechanical 519 Diesel locomotive chemical electrical mechanical

3 Thermodynamics Thermodynamics: Gr. therme, meaning heat, and dynamis, meaning power from one form to another Phenomenological (Macroscopic) Cannot be derived or proved but summary of observations and experimentation ~ operational Universal First law of thermodynamics: Energy conservation ~ Black, Davy, Rumford, Mayer(1842), Joule, Helmholtz Second law of thermodynamics: Irreversibility or Spontaneity ~ Carnot, Clausius, Thomson (Lord Kelvin), Boltzmann

temperature ~ Thermal equilibrium at contact (A,B,C ) 1

4 Third law of thermodynamics: Unavailability of 0 K ~ Nernst, Planck Zeroth law of thermodynamics: Concept of temperature ~ Thermal equilibrium at contact (A,B,C ) 1 Waterfall (1961) by Maurice C. Escher ( ) Dutch artist

else Universe = system + boundary + surroundings The system gains energy The system loses

5 SYSTEMS, STATES, AND PROCESSES System : Anything of our interest Surroundings: Everything else Universe = system + boundary + surroundings The system gains energy The system loses energy from the surroundings. to the surroundings. Open system : Exchange of both matter and heat with the surroundings Closed system: Exchange only heat Isolated system: Exchange nothing

6 A Identify the following systems as open, closed, or isolated: (a) Coffee in a very high quality thermos bottle (b) Coolant in a refrigerator coil (c) A bomb calorimeter in which benzene is burned (d) Gasoline burning in an automobile engine (e) Mercury in a thermometer (f) A living plant Thermodynamic state ~ A macroscopic condition of a system Properties uniquely determined at fixed values independent of time Equilibrium state 522 Thermodynamic process ~ leads to a change in the thermodynamic state along a path (physical and chemical processes) Isotherm: constant temperature Isochore: constant volume Fig P-V-T surface of 1 mol of ideal gas

Reversible process ~ infinitesimal change in external conditions ~ a path on the equation-of-state surface unique ~ a path along ideal equilibrium states ~ ideal, infinitesimally slow Irreversible

7 Reversible process ~ infinitesimal change in external conditions ~ a path on the equation-of-state surface unique ~ a path along ideal equilibrium states ~ ideal, infinitesimally slow Irreversible process ~ abrupt, finite, real changes in external conditions ~ many irreversible paths between thermodynamic states 523 Fig Stages in an irreversible expansion of a gas from an initial state (a) of volume V 1 to a final state (c) with volume V 2. In the intermediate stage (b) General the system Chemistry not in I equilibrium. Extensive property : m, V A property that does depend on the size (extent) of the sample. Additive property: m tot = m 1 + m 2 Intensive property : P, T A property that does not depend on the size of the sample. 523

8 State function : E, P, V, T, d, m, A property that depends only on the current state of the system and is independent of how that state was prepared. Path function : w, q, A property that depends on the paths leading to the current state Fig Differences in state properties are independent of the path followed.

12.2 THE FIRST LAW OF THERMODYNAMICS: INTERNAL ENERGY, WORK, AND HEAT Work Mechanical work 524 = ( ) (force along direction of path) = = + 2 = 2 2 = (Change in KE) w Mg( h h) Mg h E ( Change in PE) f

9 12.2 THE FIRST LAW OF THERMODYNAMICS: INTERNAL ENERGY, WORK, AND HEAT Work Mechanical work 524 = ( ) (force along direction of path) = = + 2 = 2 2 = (Change in KE) w Mg( h h) Mg h E ( Change in PE) f i pot Pressure-Volume Work (PV-work) w F h h P A h ext ( f i) ext ex w P V 525 Fig As the gas inside is heated, it expands, pushing the piston against the pressure P ext exerted by the gas outside. Expansion: V > 0 w < 0 (system does work) Compression: V < 0 w > 0 (work is done on the system)

7.3 Air in a bicycle pump is compressed by pushing in the handle. If the inner diameter of the pump is 3.0 cm and the pump is depressed 20 cm with a pressure of 2.

10 7.3 Air in a bicycle pump is compressed by pushing in the handle. If the inner diameter of the pump is 3.0 cm and the pump is depressed 20 cm with a pressure of 2.00 atm, (a) how much work is done in the compression? (b) Is the work positive or negative with respect to the air in the pump? A Internal energy, U ~ Sum of KE, PE, bond energies of molecules in a system Heat (or thermal energy), q ~ Amount of energy transferred between two substances at different temperature ~ Changes the internal energy of a system Fig Internal energy of a dropped ball increased. After the impact, the potential energy between the molecules is increased. As the ball bounces, the kinetic energy of the molecules increases.

Ice calorimeter Specific heat capacity, c s Amount of heat in raising temperature of 1 g of material by 1 o C q = Mc s T, c s = 1.

11 Measurement of amount of heat 527 Ice calorimeter ~ Amount of heat transfer vs. volume change of the bath (ice-water) System Bath decreases bath volume Bath System increases bath volume Fig Ice calorimeter Specific heat capacity, c s Amount of heat in raising temperature of 1 g of material by 1 o C q = Mc s T, c s = 1.00 cal K 1 g 1 for water at 15 o C Equivalence of heat and work 528 Thompson (later Count Rumford) ~ Cannon barrel Mayer and Joule A paddle driven by a falling weight 1 cal = J Fig The falling weight turns a paddle, doing work on the system, increasing T.

state function A247 The first law of thermodynamics (closed system) applicable to any process that begins

12 Work (or Heat) is a transient form of energy Work induces a concerted motion Heat induces a random motion 529 The First Law of Thermodynamics Principle of conservation of energy U = q + w q, w : path functions, U : state function A247 The first law of thermodynamics (closed system) applicable to any process that begins and ends in equilibrium states All the energies received turned into the energy of the system: Energy conservation

13 529 Change in internal energy in a process is the sum of the heat transfer and the work transfer. U univ = U sys + U surr = 0 =(q sys + w sys )+ (q surr + w surr ) = (q sys + w sys )+ ( q sys w sys ) = 0 A A gas sample in a cylinder is supplied with 524 kj of energy as heat. At the same time, a piston compresses the gas, doing 340 kj of work. What is the change in internal energy of the gas during this process?

K (Units of J K 1 ) q = C T Molar heat capacity at constant volume, c V q V = nc V T

14 12.3 HEAT CAPACITY, CALORIMETRY, AND ENTHALPY 530 Heat Capacity and Specific Heat Capacity Heat capacity, C Amount of energy to increase the temperature of the system by 1 K (Units of J K 1 ) q = C T Molar heat capacity at constant volume, c V q V = nc V T Molar heat capacity at constant pressure, c P q P = nc P T 531 Fig A styrofoam cup calorimeter.

15 531 -IfC V and C P do not change with temperature, q V = nc V,m T q P = nc P,m T q V < q P 531 Heat Transfer at Constant Volume: Internal Energy q V = U (constant V) Fig The combustion calorimeter, called a bomb calorimeter.

16 532 Heat Transfer at Constant Pressure: Enthalpy U (= q V ) = q P + w = q P P ext V Assume that P ext = P (internal pressure) U = q P P V q P = U + P V = (U + PV) H Enthalpy, HH= U + PV H = q P = U + P V (at constant P) H = U + (PV) (in general) 12.4 THE FIRST LAW AND IDEAL GAS PROCESSES 533 Heat Capacities of Ideal Gases Kinetic energy of an n mol of ideal gas E kin = (3/2) nrt U = (3/2)nR T (1) At constant volume, w = P V = 0. U = q V = nc V T (ideal gas) (2) Compare (1) and (2). c V = (3/2)R (monatomic ideal gas)

17 9.5 THE KINETIC THEORY OF GASES 412 mean-square speed = = = 1 3 = 1 3 = - Kinetic energy of N A molecules, = 1 2 = = average kinetic energy per molecule, = k B = R/N A - root-mean-square speed = = = M = molar mass = N A m 534 At constant pressure, U = q P + w [ U = nc V T, q P = nc P T, w = P V ] nc V T = nc P T P(V 2 V 1 ) nc V T = nc P T nr T (PV i = nrt i ) c P =c V + R U = nc V T H = nc P T (any ideal gas) (any ideal gas) (ideal gas)

18 Heat and Work for Ideal Gases 536 Along the path A C B, w AC =-P ext V =-P A (V B - V A ) w CB = 0 w ACB = w AC + w CB =-P A (V B - V A ) = L atm = J q AC = q p = nc p T = (5/2)nR(T C - T A ) = (5 / 2)(P C V C - P A V A ) q CB = q v = nc v T = (3/2)nR(T B - T C ) = (3 / 2)(P B V B - P C V C ) Fig Two different processes between the states A and B. q ACB = q AC + q CB = (5 / 2)(P C V C - P A V A ) + (3 / 2)(P B V B - P C V C ) = 5570 J 536 U = w ACB + q ACB = ( ) J = 1520 J State function U is independent of paths Similarly, along the path A D B, w ADB = J q ADB = 3550 J U = w ACB + q ACB = ( ) J = 1520 J Fig Two different processes between the states A and B. 1 L atm= J (exact)

12.5 MOLECULAR CONTRIBUTIONS TO INTERNAL ENERGY AND HEAT CAPACITY 537 Kinetic theory of matter Bridge between thermodynamics and mechanics of molecules Total kinetic energy in n moles of an ideal

19 12.5 MOLECULAR CONTRIBUTIONS TO INTERNAL ENERGY AND HEAT CAPACITY 537 Kinetic theory of matter Bridge between thermodynamics and mechanics of molecules Total kinetic energy in n moles of an ideal gas: 3 Ekin 2 nrt Internal energy of a monatomic gas Molar heat capacity of a monatomic ideal gas cp cv R 2 R R 2 R J mol K Good agreement with experiments! Diatomic molecules translational degrees of freedom: x-, y-, z-directions, 2 rotational degrees of freedom: z-y, z-x planes, I : moment of inertia, : angular velocity 1 vibrational degree of freedom: Along y-axis, ( PE) k( R R ) 1 vib 2 AB e trans 2 1 drab and ( KE) vib, R e : equilibrium bond length 2 dt E E 1 rot 2 2 I Mv 2

20 Polyatomic molecules 538 Translational degrees of freedom: 3 (motion of the center of mass) Rotational degrees of freedom: 3 (nonlinear-), 2 (linear-) molecule Vibrational degrees of freedom: 3N 6 (nonlinear) or 3N 5 (linear) Total degrees of freedom of N atoms of a molecule: 3N Subtract the degrees of freedom for translation (3) and rotation (3 or 2) 539 Equipartition theorem classical concept Each quadratic term that appears in the energy of a molecule contributes RT/2 to the average energy calculated from the Maxwell-Boltzmann distribution. Contributions to internal energy of a molecule: Each translational degree of freedom: RT/2 Each rotational degree of freedom: RT/2 Each vibrational degree of freedom: (only for high T) v 2 RT KE m PE kx Contribution of each mode to the heat capacities c V and c p (= c v + R) Table 12.3

Contributes only above room temp. Equipartition value for T+R+V, 9R/2 (= 37.41 J mol 1 K 1 ) reached at high T.

21 539 Temperature dependence of contributions of each modes to c p 540 Translation: 5R/2 at all temperatures above 0 K Rotation for H 2 : Begins at low temperature Reaches its equipartition value R at room temperature Translation + Rotation for H 2 : 7R/2 Vibration in H 2, N 2, O 2 : Contributes only above room temp. Equipartition value for T+R+V, 9R/2 (= J mol 1 K 1 ) reached at high T. Equipartition values do not agree with measured values at low temperature. General Quantum Chemistry mechanical I effect Fig Temperature dependence of c p for several gases.

c v Low values for c v at low temperatures QM effect!

22 Heat capacities for solids 541 Dulong-Petit s law (1820): c v = 3R (= 24.9 J K 1 ) for elemental solids at room temp Classical 3D spring model for atoms in solid 3 vibrational modes for each atom 6 quadratic terms in PE & KE 6R/2 = 3R to c v Low values for c v at low temperatures QM effect! Einstein (1907) ~ Planck s hypothesis for harmonic oscillators Predicted low values of c v at low temperature Debye (1912) ~ Modified Einstein s theory, better agreement with experiment, c v approaches 0 as a T 3 -power law 541 Fig Temperature dependence of c v for solids. (a) Measured values for elemental solids. (b) Debye and Einstein models for c v for Al.

23 A Which molecular substance do you expect to have the higher molar heat capacity, NO or NO 2? Why? 12.6 THERMOCHEMISTRY 542 Thermochemistry ~ Study effects of Heat given off or taken up during a chemical reaction ~ Usually at constant pressure (1 atm) Heat (or Enthalpy) of reaction, q P = H qp H Hf Hi Hproducts Hreactants Hreaction Exothermic: H reaction < 0 Endothermic: H reaction > 0

Exothermic Reaction 2 Al(s) + Fe 2 O 3 (s) 2 Fe(s) + Al 2 O 3 (s) 543 Endothermic

O(l) 545 Hess s Law When chemical equations are added, the corresponding enthalpies are

Calculate the heat of reaction that is difficult to measure.

24 Exothermic Reaction 2 Al(s) + Fe 2 O 3 (s) 2 Fe(s) + Al 2 O 3 (s) 543 Endothermic Reaction Ba(OH) 2 8H 2 O(s) + 2NH 4 NO 3 (s) Ba(NO 3 ) 2 (aq) + 2 NH 3 (aq) + 10 H 2 O(l) 545 Hess s Law When chemical equations are added, the corresponding enthalpies are also added. Enthalpy is an extensive quantity and a state function. Ex. Calculate the heat of reaction that is difficult to measure. C(s,gr) + O 2 (g) CO 2 (g) CO(g) + (1/2) O 2 (g) CO 2 (g) H = kj H = kj C(s,gr) + (1/2) O 2 (g) CO(g) H =? Fig Hess s law.

25 C(s,gr) + O 2 (g) CO 2 (g) CO(g) + (1/2) O 2 (g) CO 2 (g) H = kj H = kj C(s,gr) + (1/2) O 2 (g) CO(g) H =? C(s,gr) + O 2 (g) CO 2 (g) CO 2 (g) CO(g) + (1/2) O 2 (g) H 1 = kj H 2 = kj C(s,gr) + (1/2) O 2 (g) CO(g) H = H 1 + H 2 = kj A Calculate the reaction enthalpy for the synthesis of hydrogen chloride gas, H 2 (g) + Cl 2 (g) 2 HCl(g), from the following data: NH 3 (g) + HCl(g) NH 4 Cl(s) H o = kj N 2 (g) + 3 H 2 (g) 2 NH 3 (g) H o = kj N 2 (g) + 4 H 2 (g) + Cl 2 (g) 2 NH 4 Cl(s) H o = kj

Enthalpy of phase change at constant T & P 546 H 2 O(s) H 2 O(l) H fus = +6.007 kj mol 1 H 2 O(l) H 2 O(s) H freez = 6.

26 Enthalpy of phase change at constant T & P 546 H 2 O(s) H 2 O(l) H fus = kj mol 1 H 2 O(l) H 2 O(s) H freez = kj mol 1 H 2 O(l) H 2 O(g) H vap = kj mol 1 A How much heat is needed to convert 80.0 g of ice at 0.0 o C into liquid water at 20.0 o C?

27 547 Standard-State Enthalpies Standard states at a specified temperature (usually at 25 C) liquids, solids ~ thermodynamically stable states at 1 atm gases ~ at 1 atm, exhibiting ideal gas behavior dissolved species ~ 1 M at 1 atm, exhibiting ideal solution behavior Standard enthalpy of formation H f of a compound (Appendix D) ~ Enthalpy change of the formation reaction from its elements in their stable states at 25 C, 1 atm, per mole H 2 (g) + (1/2) O 2 (g) H 2 O(l), H f (H 2 O(l)) = kj mol 1 C(s, gr) C(s, dia), H f (C(s, dia)) = kj mol Standard Enthalpies of Formation at 25 o C (kj mol -1 ) (Appendix D)

28 Standard enthalpy change of reaction 548 aa bb cc dd, H H c H (C) d H (D) a H (A) b H (B) o o o o f f f f prod react o o o i i j j i 1 j 1 H n H n H Bond enthalpy ~ Enthalpy when a bond is broken in the gas phase Bond enthalpy of a C H bond in CH 4 (g) ~ measured CH 4 (g) CH 3 (g) + H(g), H = +438 kj 550

29 A277 EXAMPLE 7.14 Estimate the enthalpy of the reaction between gaseous iodoethane and water vapor: - Breaking the bonds H Bo (C-I) + H Bo (O-H) = - Forming the bonds H Bo (C-O) + H Bo (H-I) = - The overall enthalpy change: EXAMPLE 12.9 H fo (CCl 2 F 2 (g)) =? Freon C(s,gr) + Cl 2 (g) + F 2 (g) CCl 2 F 2 (g) H =? H 2 C(s,gr) + Cl 2 (g) + F 2 (g) C(g) + 2 Cl(g) + 2 F(g) H 1 H 1 = H fo (C(g)) + 2 H fo (Cl(g)) + 2 H fo (F(g)) = (121.7) + 2(79.0) = 1118 kj H 2 =-(2 H Bo (C-Cl) + 2 H Bo (C-F)) = - (2(328) + 2(441)) = kj H = H 1 + H 2 = = -420 kj

30 REVERSIBLE PROCESSES IN IDEAL GASES Isochoric process : constant volume Isobaric process : constant pressure Isothermal process : constant temperature Adiabatic process : q = 0 Reversible process : ideal, proceeds with infinitesimal speed Irreversible process : real, proceeds with finite speed Isothermal Processes 552 For an ideal gas, U =(3/2) nrt U = 0, w = q For a reversible process, P ext = P gas ( P) = nrt / V isothermal process P ext changes continuously as V increases. dw = P ext dv = = = T= 0, U = 0, q = w H = U + (PV) = U + (nrt) = 0 Fig Sum of the rectangles is approximated as the work

31 553 Calculate q and w along a process in which 5.00 mol of gas expands reversibly at constant T = 298 K From P = to 1.00 atm. EXAMPLE = = =10.0 w= nrtln V V = nrtln 10.0 = 28.5 kj q= w =+28.5kJ 553 Adiabatic Processes q = 0 U = w U w nc T V V H U ( PV) nc T nr T nc T P = = = For a reversible process, P ext = P. = = 1 = 1 = = Fig Comparison of reversible isothermal and adiabatic expansions.

553 = = U w nc T V H U ( PV) nc T nr T nc T V P = / = where = C P /C V TV TV 1 1 1 1 2 2 PV PV 1 1 2 2 Fig. 12.20. Comparison of reversible isothermal and adiabatic expansions.

32 553 = = U w nc T V H U ( PV) nc T nr T nc T V P = / = where = C P /C V TV TV PV PV Fig Comparison of reversible isothermal and adiabatic expansions. Calculate the final V and T, U, H, and w along a process in which 5.00 mol of monatomic gas at an initial T = 298 K and P = 10.0 atm expands adiabatically and reversibly until P = 1.00 atm. EXAMPLE = =12.2 = = = = = / =48.7 = =119 = = = = =

Thermodynamic Processes and Thermochemistry

General Chemistry Thermodynamic Processes and Thermochemistry 박준원교수 ( 포항공과대학교화학과 ) 이번시간에는! Systems, states, and processes The first law of thermodynamics: internal energy, work, and heat Heat capacity,