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Thermodynamics and kinetics

Thermodynamics and kinetics. Heats of reaction Thermodynamic laws Electrochemistry Kinetics Acid-Base Equilibrium calculations. Heats of Reaction. 1 cal = 4.184 j Heat Capacity (C p ) Heat required to raise one gram of substance 1 °C Al; C p = 0.895 j/gK

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Thermodynamics and kinetics

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  1. Thermodynamics and kinetics • Heats of reaction • Thermodynamic laws • Electrochemistry • Kinetics • Acid-Base • Equilibrium calculations

  2. Heats of Reaction • 1 cal = 4.184 j • Heat Capacity (Cp) • Heat required to raise one gram of substance 1 °C • Al; Cp = 0.895 j/gK • What is the heat needed to 40 g Al 10 K • (0.895 j/gK)(40g)(10K)= 358 j • Exothermic • Reaction produces heat (at 25 °C) C(s) + O2(g) <--> CO2(g) + 393.76 kj

  3. Heats of Reaction • Endothermic • Reaction requires energy (at 25 °C) 2 HgO + 181.70 kj <--> 2 Hg + O2 Enthalpy (∆H) • Energy of a system (heat content) • ∆H = ∆Hproducts - ∆Hreactants • Exothermic reactions have negative ∆H • Negative ∆H tend to be spontaneous

  4. Enthalpy (∆H) • Bond energies • Can be used to estimate ∆H • N2 + 3 H2 <--> 2 NH3 • 6(351.5)-945.6-3(436.0) = -144.6 kj/2 mole =-72.3 kj/mole (actual -46.1 kj/mol) • Aqueous Ions (use ∆H values) • ∆Hproducts-∆Hreactants • 2 H+ + CO32- <--> CO2 + H2O • -393.5 + (-285.8)-(-677.1+2(0)) = -2.2 kj/mol H2O(l) CO32- H+ CO2(g)

  5. Bond Energies (kJ/mol) at 298 K Single Bonds Single Bonds CI 217.6 NN 133.9 NF 234.3 NCl 154.8 OO 138.1 OF 188.3 OSi 443.5 OCl 209.2 OS 518.8 FF 158.2 PCl 326.4 SS 205.0 ClCl 242.7 ClI 209.2 BrBr 192.5 II 150.6 HH 436.0 HC 418.4 HN 351.5 HO 464.4 HF 564.8 HS 338.9 HCl 431.8 HBr 368.2 HI 297.1 CC 343.1 CN 267.8 CO 347.3 CF 426.8 CS 255.2 CCl 330.5 CBr 276.1 Double Bond Triple Bond CC 610.9 836.8 CN 615.0 891.2 CO 740.6 1071.1 NN 418.4 945.6 Bond in O2 498.7

  6. Heat Capacities Elements (Jg-1K-1) Compounds (Jmol-1K-1-) Li 3.582 B 1.026 C 0.709 N 1.042 O 0.920 Al 0.900 Cr 0.449 Cu 0.385 Zr 0.278 Hf 0.140 W 0.130 Au 0.128 Hg 0.140 Pb 0.129 Th 0.113 U 0.120 Np 0.120 Pu 0.130 Am 0.110 H2 28.87 O2 29.50 N2 29.04 CO 29.16 CO2 37.49 CH4 35.98 C2H6 53.18 NH3 36.11 H2O(g) 24.77 HBr 27.53 SnO2 56.61 Al2O3 79.33 Fe2O3 104.35

  7. Pure Substance Standard ∆H (kJ/mol) Ag(g) 284.55 Ag+(g) 1021.73 AgCl(c,cerargyrite) -127.068 AgNO3(c) -124.39 Al3+(g) 5483.17 Al(OH)3 -1276 BaCO3(c,witherite) -1216.3 BaC2O4(c) -1368.6 BaCrO4(c) -1446 BaF2(c) -1207.1 BaSO4(c) -1473.2 BeO(c) -609.6 Bi2S3(c) -143.1 Br2(g) 30.907 Br(g) 111.88 Br-(g) -219.07 C(c,diamond) 1.895 C(g) 716.682 CO(g) -110.525 CO2(g) -393.509 COCl2(g,phosgene) -218.8 CH4(g,methane) -74.81 C2H2(g,ethyne) 226.73 C2H2(g,ethene) 52.25 C2H6(g,ethane) -84.68 CH3OCH3(g) -184.05 CH3OH(g,methanol) -200.66 CH3OH(l,methanol) -238.66 C2H5OH(g,ethanol) -235.1 C2H5OH(l,ethanol) -277.69 CH3COOH(l,acetic acid) -484.51 (CH3)2O(g) -184.05 CH3CHO(l) -192.3 CH3Cl(g) -80.83 CHCl3(g) -103.14 CCl4(l) -135.44 CaO(c) -635.09 Ca(OH)2(c) -986.09 CaCO3(c, calcite) -1206.92 CaCO3(c, aragonite) -1207.13

  8. Pure Substance Standard ∆H (kJ/mol) CaC2O4(c) -1360.6 CaF2(c) -1219.6 Ca3(PO4)2(c) -4109.9 CaSO4(c,anhydrite) -1434.1 Cd(g) 2623.54 Cd2+(g) 112.01 Cd(OH)2(c) -560.7 CdS(c) -161.9 Cl(g) 121.679 Cl-(g) -233.13 ClO2(g) 102.5 Cu(g) 338.32 Cu2O(c,cuprite) -168.6 CuO(c,tenorite) -157.3 Cu(OH)2(c) -449.8 Cu2S(c,chalcocite) -79.5 CuS(c,covellite) -53.1 F(g) 78.99 F-(g) -255.39 Fe(g) 416.3 Fe3+(g) 5712.8 Fe2O3(c,hematite) -824.2 H+(g) 1536.202 H2O(g) -241.818 H2O(l) -285.83 H2O2(g) -136.31 H2O2(l) -187.78 H2SO4(l) -813.989 HF(g) -271.1 HCl(g) -92.307 HBr(g) -36.4 HI(g) 26.48 HCN(g) 135.1 PbO(c,red) -218.99 PbO2(c) -277.4 Pb3O4(c) -718.4 PbS(c,galena) -100.4 PbSO4(c) -919.94 ThO2(c) -1226.4 UO2(c) -1084.9

  9. Solution Standard ∆H (kJ/mol) Ag+ 105.579 AgCl2- -245.2 Ag(NH3)2+ -111.29 Ag(S2O3)2- -1285.7 Al3+ -531 Br- -121.55 BrO3- -67.07 Ca2+ -542.83 Cd2+ -75.9 Cd(CN)42- 428 Cd(NH3)42+ -450.2 Ce3+ -696.2 Ce4+ -537.2 CH3COO- -486.01 CH3COOH -485.76 CN- 150.6 CNS- 76.44 Cl- -167.15 ClO4- -129.33 CO2 -413.8 CO2 -413.8 CO32- -677.14 H+ 0 H2O2 -191.17 I- -55.19 I3- -51.5 IO3- -221.3 K+ -252.38 NH3 -80.29 NH4+ -132.51 NO3- -205 Na+ -240.12 OH- -229.99 O2 -11.7 SO42- -909.27 Sn2+ -8.8 Sr2+ -545.8 Tl3+ 196.6 U4+ -591.2 UO22+ -1019.6

  10. ∆H determination from other data ∆HT2 Products at T2 Reactants at T2 ∆Hproducts=(SCp)(298-T2) ∆Hreactants=(SCp)(T2-298) ∆H298 Products at 298 K Reactants at 298 K SCp is the sum of the heat capacities

  11. Entropy (∆S) • Randomness of a system • increase in ∆S tends to be spontaneous • Enthalpy and Entropy can be used for evaluating the free energy of a system • Gibbs Free Energy • ∆G = ∆H -T∆S • ∆G=-RTlnK • K is equilibrium constant • Activity at unity

  12. Calculations Compound ∆G° (kJ/mol) at 298.15 K H2O -237.129 OH-(aq) -157.244 H+(aq) 0 H2OH++OH- • What is the constant for the reaction? • At 298.15 K ∆G(rxn) = 0 + -157.244 - (-273.129) = 79.9 kJ/mol lnK= (79.9E3/(-8.314*298.15))=-32.2 K=1E-14

  13. Thermodynamic Laws • 1st law of thermodynamics • If the state of a system is changed by applying work or heat or both, then the change in the energy of the system must equal the energy applied. • ∆E = q (heat absorbed) + w (work) • Conservation of energy • Energy can be transferred, but no direction is given

  14. Thermodynamic Laws • 2nd law of thermodynamics • Reactions tend towards equilibrium • Increase in entropy of a system • Spontaneous reaction for -∆G • ∆G = 0, system at equilibrium • 3rd law of thermodynamics • Entropies of pure crystalline solids are zero at 0K

  15. Faraday Laws • In 1834 Faraday demonstrated that the quantities of chemicals which react at electrodes are directly proportional to the quantity of charge passed through the cell • 96487 C is the charge on 1 mole of electrons = 1F (faraday)

  16. Faraday Laws • Cu(II) is electrolyzed by a current of 10A for 1 hr between Cu electrode • anode: Cu <--> Cu2+ + 2e- • cathode: Cu2+ + 2e- <--> Cu • Number of electrons • (10A)(3600 sec)/(96487 C/mol) = 0.373 F • 0.373 mole e- (1 mole Cu/2 mole e-) = 0.186 mole Cu

  17. Half-cell potentials • Standard potential • Defined as °=0.00V • H2(atm) <--> 2 H+ (1.000M) + 2e- • Cell reaction for • Zn and Fe3+/2+ at 1.0 M • Write as reduction potentials • Fe3+ + e- <--> Fe2+ °=0.77 V • Zn2+ + 2e- <-->Zn °=-0.76 V • Fe3+ is reduced, Zn is oxidized

  18. Half-Cell Potentials • Overall • 2Fe3+ +Zn <--> 2Fe2+ + Zn2+ °=0.77+0.76=1.53 V • Half cell potential values are not multiplied Application of Gibbs • If work is done by a system • ∆G = -°nF (n= e-) • Find ∆G for Zn/Cu cell at 1.0 M • Cu2+ + Zn <--> Cu + Zn2+ °=1.10 V • 2 moles of electrons (n=2) • ∆G =-2(96487C/mole e-)(1.10V) • ∆G = -212 kJ/mol

  19. Reduction Potentials Electrode Couple "E0, V" Na+ + e- --> Na -2.7144 Mg2+ + 2e- --> Mg -2.3568 Al3+ + 3e- --> Al -1.676 Zn2+ + 2e- --> Zn -0.7621 Fe2+ + 2e- --> Fe -0.4089 Cd2+ + 2e- --> Cd -0.4022 Tl+ + e- --> Tl -0.3358 Sn2+ + 2e- --> Sn -0.141 Pb2+ + 2e- --> Pb -0.1266 2H+ + 2e- --> H2(SHE) 0 S4O62- + 2e- --> 2S2O32- 0.0238 Sn4+ + 2e- --> Sn2+ 0.1539 SO42- + 4H+ + 2e- --> H2O + H2SO3(aq) 0.1576 Cu2+ + e- --> Cu+ 0.1607 S + 2H+ + 2e- --> H2S 0.1739 AgCl + e- --> Ag + Cl- 0.2221 Saturated Calomel (SCE) 0.2412 UO22+ + 4H+ + 2e- --> U4+ + 4H2O 0.2682

  20. Reduction Potentials Hg2Cl2 + 2e- --> 2Cl- + 2Hg 0.268 Bi3+ + 3e- --> Bi 0.286 Cu2+ + 2e- --> Cu 0.3394 Fe(CN)63- + e- --> Fe(CN)64- 0.3557 Cu+ + e- --> Cu 0.518 I2 + 2e- --> 2I- 0.5345 I3- + 2e- --> 3I- 0.5354 H3AsO4(aq) + 2H+ + 2e- -->H3AsO3(aq) + H2O 0.5748 2HgCl2 + 4H+ + 2e- -->Hg2Cl2 + 2Cl- 0.6011 Hg2SO4 + 2e- --> 2Hg + SO42- 0.6152 I2(aq) + 2e- --> 2I- 0.6195 O2 + 2H+ + 2e- --> H2O2(l) 0.6237 O2 + 2H+ + 2e- --> H2O2(aq) 0.6945 Fe3+ + e- --> Fe2+ 0.769 Hg22+ + 2e- --> Hg 0.7955 Ag+ + e- --> Ag 0.7991 Hg2+ + 2e- --> Hg 0.8519 2Hg2+ + 2e- --> Hg22+ 0.9083 NO3- + 3H+ + 2e- -->HNO2(aq) + H2O 0.9275

  21. Reduction Potentials VO2+ + 2H+ + e- --> VO2+ + H2O 1.0004 HNO2(aq) + H+ + e- --> NO + H2O 1.0362 Br2(l) + 2e- --> 2Br- 1.0775 Br2(aq) + 2e- --> 2Br- 1.0978 2IO3- + 12H+ + 10e- -->6H2O + I2 1.2093 O2 + 4H+ + 4e- --> 2H2O 1.2288 MnO2 + 4H+ + 2e- -->Mn2+ + 2H2O 1.1406 Cl2 + 2e- --> 2Cl- 1.3601 MnO4- + 8H+ + 5e- -->4H2O + Mn2+ 1.5119 2BrO3- + 12H+ + 10e- -->6H2O + Br2 1.5131

  22. Nernst Equation • Compensated for non unit activity (not 1 M) • Relationship between cell potential and activities • aA + bB +ne- <--> cC + dD • At 298K 2.3RT/F = 0.0592 • What is potential of an electrode of Zn(s) and 0.01 M Zn2+ • Zn2+ +2e- <--> Zn °= -0.763 V • activity of metal is 1

  23. Kinetics and Equilibrium • Kinetics and equilibrium are important concepts in examining and describing chemistry • Identify factors which determine rates of reactions • Temperature, pressure, reactants, mixing • Describe how to control reactions • Explain why reactions fail to go to completion • Identify conditions which prevail at equilibrium

  24. Kinetics • Rate of reaction • Can depend upon conditions • Paper reacts slowly with oxygen, but increases with temperature • Free energy does not dictate kinetics 16 H+ + 2 MnO4- + 5 Sn2+ <--> 5 Sn4+ + 2 Mn2+ + 8 H2O °= 1.39 V, ∆G = -1390 kcal/mol 8 H+ + MnO4- + 5 Fe2+ <--> 5 Fe3+ + Mn2+ + 4 H2O °= 0.78 V, ∆G = -376 kcal/mol • The reaction with Fe is much faster

  25. Kinetics • Rate can depend upon reaction path • C6H12O6(s) + 6 O2(g) <--> 6 CO2(g) + 6 H2O(l) • ∆G = -791 kcal/mol • Glucose can be stored indefinitely at room temperature, but is quickly metabolized in a cell • Thermodynamics is only concerned with difference between initial and final state • Kinetics account for reaction rates and describe the conditions and mechanisms of reactions

  26. Kinetics • Kinetics are very difficult to describe from first principles • structure, elements, behavior • General factors effecting kinetics • Nature of reactants • Effective concentrations • Temperature • Presence of catalysts • Number of steps

  27. Nature of Reactants • Ions react rapidly • Ag+ + Cl- <--> AgCl(s) Very fast • Reactions which involve bond breaking are slower • NH4+ + OCN- <-->OC(NH2)2 • Redox reactions in solutions are slow • Transfer of electrons are faster than those of atomic transfer • Reactions between covalently bonded molecules are slow • 2 HI(g) <--> H2(g) + I2(g)

  28. Nature of Reactants • Structure • P4 Same formula Concentration • Reaction can occur when molecules contact P P P P P P P P P P P P White Phosphorus Red Phosphorus

  29. Concentration • Surface area • larger surface area increases reaction • Mixing increases interaction • Need to minimized precipitation or colloid formation Rate Law • Concentration of reactant or product per unit time • Effect of initial concentration on rate can be examined

  30. Rate Law • rate = k[A]x[B]y • rate order = x + y • knowledge of order can help control reaction • rate must be experimentally determined Injection Flow meter mixing detector

  31. Rates Rate=k[A]n; A=conc. at time t, Ao=initial conc., X=product conc. Order rate equation k 0 [A0]-[A]=kt, [X]=kt mole/L sec 1 ln[A0]-ln[A]=kt, ln[A0]-ln([Ao]-[X])=kt 1/sec 2 L/mole sec 3 L2/mole2 sec

  32. Rate Law • Half-life • A =Aoe-t •  = ln2/t1/2 • If a rate half life is known, fraction reacted or remaining can be calculated (CH3)2N2(g) <--> N2(g) + C2H6(g) TimePressure (torr) 0 36.2 30 46.5

  33. Rate Law • Temperature • Reactions tend to double for every 10 °C • Catalysts • Accelerate reaction but are not used • Pt surface • Thermodynamically drive, catalysts drive kinetics • If not thermodynamically favored, catalysts will not drive reaction • Autocatalytic reactions form products which act as catalysts • Catalytic amount is moles of catalysts needed to cause reaction

  34. Complexation Kinetics Uranium and cobalt with pyridine based ligands 111Py12 111Py14 222Py14 Examine complexation by UV-Visible spectroscopy

  35. Complexation of U with 111Py12

  36. Absorbance Kinetics Absorbance sum from 250 nm to 325 nm for 111Py12 and uranium at pH 4

  37. Kinetic Data Evaluation Evaluation of change in absorbance Evaluation of absorbance and kinetic data for 111Py12 and 111Py14 with uranium at pH 4. The concentration of ligand and uranium is 50x10-6 mol/L. Ligand Abso∆Abseqk (min-1) 95% Equilibrium Time (min) 111Py12 7.86±0.82 5.66±1.28 4.65±0.47x10-5 6.44±0.65x104 111Py14 4.82±1.70 7.06±5.76 4.24±0.80x10-5 7.07±1.33x104

  38. Acid-Base Equilibria Water can act as solvent and reactant • Brønsted Theory of Acids and Bases • Acid • Substance which donates a proton • Base • Accepts proton from another substance NH3 + HCl <--> NH4+ + Cl- H2O + HCl <--> H3O+ + Cl- NH3 + H2O <--> NH4++ OH- • Remainder of acid is base • Complete reaction is proton exchange between sets • Extent of exchange based on strength

  39. Acid Strengths • Strong acids tend towards completion HCl + H2O <--> H3O+ + Cl- • Strong acids tend to have weak conjugate bases • Weak acid forms only slightly ionized species CH3COOH + H2O <--> CH3COO- + H3O+ • Stronger conjugate base • Relative strengths of acids can be compared • Can be rated relative to water • Some salts can have acid-base properties • NH4Cl

  40. Relative Strengths of Acids and Bases Conjugate Acid Conjugate Base HClO4 ClO4- H2SO4 SO42- HCl Cl- H3O+ H2O H2SO3 HSO3- HF F- HC2H3O2C2H3O2- HSO3- SO32- H2S HS- NH4+ NH3 HCO3CO32- H2O OH- HS- S2- OH O2- H2 H- Base Strength Acid Strength

  41. Dissociation Constants • Equilibrium expression for the behavior of acid HA + H2O <--> A- + H3O+ Water concentration is constant pKa=-logKa • Can also be measured for base Constants are characteristic of the particular acid or base

  42. Dissociation Constants for Acids at 25°C Acid Formula Ka Acetic HC2H3O2 1.8E-5 Hydrocyanic HCN 7.2E-10 Carbonic H2CO3 3.5E-7 HCO3- 5E-11 Nitrous HNO2 4.5E-4 Hydrosulfuric H2S 1E-7 HS- 1E-14 Phosphoric H3PO47.5E-3 H2PO4- 6.2E-8 HPO42- 4.8E-13 OxalicH2C2O45.9E-2 HC2O4- 6.4E-5

  43. Dissociation Constants for Bases at 25°C Base Formula Kb Ammonia NH3 1.8E-5 Pyridine C5H5N 2.3E-9 Methylamine CH3NH2 4.4E-4 Protonation of amine group

  44. Calculations • 1 L of 0.1 M acetic acid has pH = 2.87 What is the pKa for acetic acid CH3COOH + H2O <--> CH3COO- + H3O+ [CH3COO-] = [H3O+] =10-2.87 pKa=4.73

  45. Calculations • What is pH of 0.1 M NH3 Kb=1.8E-5 NH3 + H2O <-->NH4+ + OH- [NH4+] = [OH -] = x [NH3] = 0.1 - x x2+ 1.8E-5x -1.8E-6 = 0 • [OH-] = 1.33E-3 M, pOH = 2.87, pH ≈ 14-pOH ≈11.12

  46. Acid-Base Reactions For Water 2 H2O <--> H3O+ + OH- Water concentration remains constant, so for water: Kw = [H3O+][OH-]= 1E-14 at 25°C

  47. Common ion effect • Same products from different acids (hydronium ion) 0.2 M CH3COOH in 0.1 M HCl What is the free acetic acid concentration HCl is totally dissociated x=[CH3COO-], [CH3COOH]=0.2-x, [H3O+] = 0.1 + x • Ka = 1.8E-5 • Small Ka, x is much smaller than 0.1 x=3.6E-5 M

  48. Hydrolysis Constants • Reaction of water with metal ion • Common reaction • Environmentally important • Dependent upon metal ion oxidation state • Mz+ + H2O <--> MOHz-1+ + H+ • Constants are listed for many metal ion with different hydroxide amounts

  49. Buffers • Weak acid or weak base with conjugate salt • Acetate as example • Acetic acid, CH3COONa • CH3COOH + H2O <--> CH3COO- + H3O+ • If acid is added • hydronium reacts with acetate ion, forming undissociated acetic acid • If base is added • Hydroxide reacts with hydronium, acetic acid dissociates to removed hydronium ion large quantity huge quantity large quantity small quantity

  50. Buffer Solutions • Buffers can be made over a large pH range • Can be useful in controlling reactions and separations • Buffer range • Effective range of buffer • Determined by pKa of acid or pKb of base HA + H2O <--> A- + H3O- Write as pH

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