OCN 623: Thermodynamic Laws & Gibbs Free Energy. or: How to predict chemical reactions without doing experiments

Transcription

1 OCN 623: Thermodynamic Laws & Gibbs Free Energy or: How to predict chemical reactions without doing experiments

2 Outline Definitions Laws of Thermodynamics Enthalpy and entropy Gibbs free energy Predicting the feasibility of reactions

3 Definitions Extensive properties Depend on the amount of material e.g. # of moles, mass or volume of material Examples in chemical thermodynamics: G: Gibbs free energy H: enthalpy

4 Definitions Intensive properties Do not depend on quantity or mass Examples: Temperature Pressure Density Refractive index

5 Definitions Reversible and irreversible processes Reversible process occurs under equilibrium conditions e.g. gas expanding against a piston P p p = P + δp: reversible p = P + Δp: irreversible

6 No friction or other energy dissipation System can return to its original state Very few processes are really reversible in practice e.g. Daniell Cell Zn + CuSO 4 = ZnS0 4 + Cu with balancing external emf Compression of gases Vaporisation of liquids Is a concept used for comparison Definitions

7 Definitions Spontaneous processes Occur without external assistance Are irreversible by definition - occur at a finite rate Some examples: expansion of a gas from region of high pressure to low pressure diffusion of a solute in a solvent

8 Laws of Thermodynamics Zeroth Law of Thermodynamics Two systems that are in thermal equilibrium with a third system are in thermal equilibrium with each other

9 Laws of Thermodynamics First Law of Thermodynamics Energy cannot be created or destroyed when one kind of energy disappears, it is transformed into an equivalent quantity of another kind U = q - w du = dq - dw du = change in internal energy of the system dq = heat absorbed by the system (+) dw = work done by the system (+)

10 U is a thermodynamic function du depends only on the initial and final states of the system, not on the path taken q and w are NOT thermodynamic functions Internal energy of system is increased by gaining heat (q) Internal energy of system is decreased when work is done by the system du = dq - dw Laws of Thermodynamics

11 Laws of Thermodynamics Work Work of expansion: w exp = P V where P = pressure, V = change in volume At constant volume, w = 0: no work is done

12 Laws of Thermodynamics Work: Reversible vs. Irreversible Processes w rev > w irrev Work done by system during irreversible process is less than could be obtained if process was reversible e.g. if piston moved at finite rate, friction dissipates energy

13 Laws of Thermodynamics Electrical work Occurs in electrical cells e.g. Zn + Cu 2+ = Zn 2+ + Cu Electrical energy = I * E * t E = emf (voltage), t = time, I = current flowing It = zf (for 1 mol) z = # of electrons transferred F (Faraday) = 96,490 Coulombs/mol Electrical energy = zef

14 Laws of Thermodynamics System at constant volume (all non-gas reactions are at constant volume) P V = w = 0 U = q - w = q v q v = heat at constant volume System at constant pressure (all reactions open to atmosphere) U = q p - P V Ideal gas law: P V = nrt R is the gas constant = Joules mol -1 K -1 Therefore: U = q p - nrt Rearranging: q p = U + nrt

15 Laws of Thermodynamics Heat (q) is measured in terms of: amount of substance x molar heat capacity x temp rise For phase change Heat q = moles of substance x molar latent heat q is the heat of reaction

16 Laws of Thermodynamics Enthalpy q p is called the enthalpy H (constant pressure) Change in enthalpy: H = U + P V In absolute terms: H = U + PV H is a thermodynamic property, defined in terms of thermodynamic functions: U, P and V For an infinitesimal change at constant pressure: dh = du + PdV

17 Laws of Thermodynamics H f is the heat of formation of 1 mole of a compound from its elements at 298 o K H < 0 = exothermic reaction H > 0 = endothermic reaction (seen from system perspective) H is proportional to amount of material is an extensive property

18 H is equal in magnitude but opposite in sign for the reverse reaction, because it is a thermodynamic quantity H products - H reactants H for reaction is same regardless of number of steps between reactants and products H = U + nrt Laws of Thermodynamics

19 Calculate enthalpy change for unknown reaction Reaction Enthalpy (a) H O 2 = H 2 O H = kj mol -1 (b) C + O 2 = CO 2 H = kj mol -1 (c) C 2 H O 2 = 2 CO 2 + 3H 2 O H = kj mol -1 Calculate H for ethane formation 2*(b) + 3*(a) - (c) Laws of Thermodynamics 2C + 2O 2 + 3H O 2 - C 2 H 6-3.5O 2 = 2CO 2 + 3H 2 O - 2CO 2-3H 2 O Canceling yields: 2C + 3H 2 = C 2 H 6 H = 2*(-393.3) + 3*(-285.8) - ( ) = kj mol -1

20 Laws of Thermodynamics But enthalpy change alone is insufficient to allow prediction of likelihood of reaction Entropy change is also needed

21 Laws of Thermodynamics But enthalpy change alone is insufficient to allow prediction of likelihood of reaction Entropy change is also needed Second Law of Thermodynamics change in entropy (S) = amount of reversible heat absorbed by system divided by temperature

22 Laws of Thermodynamics Entropy is the degree of disorder of the system chance of finding something in a fixed volume- higher pressure, greater chance, liquid lower entropy than gas, solid lower than liquid Change in entropy measures capacity for spontaneous change diffusion of a solute from high concentration to low concentration, or a gas from high pressure to low pressure A system undergoing spontaneous change is moving to a greater degree of disorder

23 Laws of Thermodynamics Entropy is an extensive property Units heat/temperature = J(oules) K -1 mol -1 for solids: dq = moles x molar heat capacity x temperature rise dq = C m dt C m = molar heat capacity, dt = temperature change From T 1 to T 2 : where S m is molar entropy change

24 Laws of Thermodynamics For phase change S = L T where L is the latent heat of fusion e.g. for water L = 6 kj mol -1 S = 6000 = 22.0 J K -1 mol -1 for melting ice reversible reaction: S = 0 irreversible reaction: S > 0 where S is the net change in entropy

25 Laws of Thermodynamics Since nearly all reactions are irreversible, entropy is increasing -- called time s arrow Always increasing -- cannot run time backwards

26 Laws of Thermodynamics Since nearly all reactions are irreversible, entropy is increasing -- called time s arrow Always increasing -- cannot run time backwards Third Law of Thermodynamics The entropy of a perfectly crystalline material at the absolute zero ( C) is zero Entropy allows prediction of the feasibility of reactions

27 Gibbs free energy Gibbs free energy Gibbs function G = H - TS equals the enthalpy temperature (K) x entropy At constant volume, q = U Helmholtz function A = U - TS Gibbs function used most (constant pressure) for reactions of liquids or solids U = H (recall: H U + PV) No expansion, so A = G

28 Gibbs free energy Tendency of reaction to occur is combination of energy and entropy change Reactions proceed in direction that minimises the internal energy, i.e. H is lowered Reactions proceed to maximise degrees of freedom i.e. entropy increases G is negative for a spontaneous reaction

29 G = H - TS differentiating: dg = dh - TdS - SdT at constant temperature: dg = dh - TdS Gibbs free energy G is a thermodynamic function G for a reaction = G products - G reactants

30 Gibbs free energy Spontaneity of reactions Sign of H Sign of S Sign of G Comments (always) Spontaneous at all T; reverse never spontaneous (always) Never spontaneous at any T; reverse reaction occurs (high T) + (low T) (low T) + (high T) Spontaneous at high T; reverse reaction at low T Spontaneous at low T; reverse reaction at high T

31 Gibbs free energy For an electrical system G = -zef E = the emf of the cell (or half cell) F = Faraday (a positive number) z = number of electrons involved in the reaction Effect of pressure on G G = G 0 + nrtlnp can calculate Gibbs free energy for any material as long as know the standard state (G 0 ) value

32 Gibbs free energy Chemical potential Free energy per mole chemical potential µ = G/n µ is an intensive property Material flows from region of high chemical potential to region of low chemical potential Effect of pressure on µ µ = µ 0 + RT ln P

33 Gibbs free energy For an ideal solution: µ = µ 0 + RT ln C For non ideal solution: µ = µ 0 + RT ln a where a = activity and a i = γ i x i γ i is activity coefficient x i is mole fraction a < 1 ln a < 0 µ < µ 0 Chemical potential of a mixture < pure substance

34 Diffusion down a concentration gradient from a pure substance to a mixture is thus a result of thermodynamics Gibbs free energy and equilibrium Gibbs free energy Reaction aa + bb cc + dd Equilibrium constant K = [C] c [D] d [A] a [B] b K is ratio of products to reactants G = G 0 + RT ln K

35 Electrical Cell -zef = G = G 0 + RT ln K Nernst Equation: E = E 0 RT zf lnk More next time!

36 Gibbs free energy van t Hoff isotherm ΔG A,B G ΔG C,D,B 50% C,D A, B 50% Eq pos C, D Extent of reaction

37 At equilibrium G = 0 G 0 = -RT ln K Knowing G 0 for reaction, can calculate equilibrium constant e.g 0.5 N O 2 = NO H = kj mol -1 S: NO O 2 N S for rx = (0.5* 205.1) - (0.5*192.3) = 12.0 J K -1 mol -1 Gibbs free energy

38 Gibbs free energy G o = H - T S G o = (12) J mol -1 = kj mol -1 now as G = -RT lnk ln K = x 298 ln K = log K = K = 6.92 x i.e. predict the reaction is well to the left hand side (not surprising as G is large and positive)

39 Effect of temperature on equilibrium Gibbs free energy

40 Gibbs free energy For exothermic reactions ln K increases as 1/T increases, (T decreases), favouring product formation For endothermic reactions ln K increases as 1/T decreases (T increases) favouring product formation exothermic ln K endothermic 1/T

41 Summary Laws of Thermodynamics: Thermal equilibrium Energy is not created or destroyed (du = dq dw) Entropy increases for spontaneous reaction ( ) Entropy at 0 K is 0 Gibbs free energy: Allows prediction of feasibility of reaction G = H - T S = G 0 + RT ln K