Second Year Chemistry 1st semester: Organic 1st semester: Physical (2008-2009) December exams 2nd: Analytical & Environmental 2nd: Inorganic Summer exams Physical: 4 lecturers 8 topics Dnal Leech: two topics Thermodynamics Gases, Laws 1

Introduction Energetics and Equilibria What makes reactions go! This area of science is called THERMODYNAMICS Thermodynamics is expressed in a mathematical language BUT Dont, initially anyway, get bogged down in the detail of the equations: try to picture the physical principle expressed in the equations We will develop ideas leading to one important Law, and explore 0 practical applications along the way rG RT ln K The Second Law of Thermodynamics 0 0 rG r H T r S 2

0 Thermodynamics: the 1st law The internal energy of an isolated system is constant Energy can neither be created nor destroyed only interEnergy: capacity to do work converted Work: motion against an opposing force System: part of the universe in which we are interested Surroundings: where we make our observations (the universe) Boundary: separates above two 3 System and Surroundings Systems Open: energy and matter exchanged

Closed: energy exchanged Isolated: no exchange Diathermic wall: heat transfer permitted Adiabatic wall: no heat transfer 4 Work and Heat

5 Work (w): transfer of energy that changes motions of atoms in the surroundings in a uniform manner Heat (q): transfer of energy that changes motions of atoms in the surroundings in a chaotic manner Endothermic: absorbs heat Exothermic: releases heat Work Mechanical work can generally be described by dw = -F.dz

Gravitational work (mg.dh) Electrical work (.dq) Extension work (f.dl) Surface expansion work (.d) As chemists we will concentrate on EXPANSION WORK (many chemical reactions produce gases) constant Expansion against external pressure 6 w = -F.z but pex = F/A therefore w = -pex.V Expansion Work Expansion against zero external pressure (free expansion)

w = -pex.V = 0 (external pressure = 0) Reversible isothermal expansion In thermodynamics reversible means a process that can be reversed by an infinitesimal change of a variable. A system does maximum expansion work when the external pressure is equal to that of the system at every stage of the expansion 7 Isothermal reversible expansion ome to the lecture to see what is on this slid 8 9 1st Law of Thermodynamics The internal energy of an isolated system is constant Energy can neither be created nor destroyed only interU = converted q+w

Exercise: A car battery is charged by supplying 250 kJ of energy to it as electrical work, but in the process it loses 25kJ of energy as heat to the surroundings. What is the change in internal energy of the battery? 10 INTERNAL ENERGY is a State Function Use calorimetry. If we enclose our How do we system in a constant volume container measure (no expansion), provided no other kind of heat? work can be done, then w = 0. U = qV Bomb calorimetry By measuring the change in Temperature of the water surrounding the bomb, and knowing the calorimeter heat capacity, C, we can determine the heat, and hence U.

Heat Capacity 11 U CV T V U CV T qV Amount of energy required to raise the temperature of a substance by 1C (extensive property) For 1 mol of substance: molar heat capacity (intensive property) For 1g of substance: specific heat capacity (intensive property) Calorimeter calibration Can calibrate the calorimeter, if its heat capacity is unknown, by passing a known electrical current for a given time to give rise to a measured temperature change. q IVt

Amperes.Volts.Sec = Coulombs.Volts = Joules Exercise: In an experiment to measure the heat released by the combustion of a fuel, the compound was burned in an oxygen atmosphere inside a calorimeter and the temperature rose by 2.78C. When a current of 1.12 A from an 11.5 V source was passed through a heater in the same calorimeter for 162 s, the temperature rose by 5.11C. What is the heat released by the combustion reaction? 12 Enthalpy Most reactions we investigate occur under conditions of constant PRESSURE (not Volume) ENTHALPY: Heat of reaction at constant pressure! H U pV H U pV but w - pV H q P Heat capacity Use a coffee-cup

calorimeter to measure it H C P T P H C P T qP Exercise: When 50mL of 1M HCl is mixed with 50mL of 1M NaOH in a coffeecup calorimeter, the temperature increases from 21C to 27.5C. What is the enthalpy change, if the density is 1g/mL and specific heat 4.18 J/g.K? 13 Perfect gas enthalpy Use intensive property of molar enthalpy and internal energy At 25C, RT = 2.5 kJ/mol H m U m pVm H m U m RT Thermicity-Revision

Endothermic reaction (q>0) results in an increase in enthalpy (H>0) Exothermic reaction (q<0) results in an increase in enthalpy (H<0) 14 NB: Internal energy and Enthalpy are STATE FUNCTIONS Temperature variation of enthalpy ome to the lecture to see what is on this slid 15 Relation between heat capacities H m U m RT H m U m RT H m U m RT H m U m R

T T C p ,m CV ,m R 16 Thermochemistry Chemists report data for a set of standard conditions: The standard state of a substance () is the pure substance at exactly 1 bar It is conventional (though not obligatory) to report data for a T of Standard enthalpies of phase transition 298.15K Energy that must be supplied (or is evolved) as heat, at constant pressure, per mole of molecules that undergo the phase transition under standard conditions (pure phases), denoted H Note: the enthalpy change

of a reverse transition is the negative of the enthalpy change of the forward transition 17 H 1 1 Substance Freezing point, Tf/K fusHo/(kJ mol ) Boiling point, Tb/K vapHo/(kJ mol ) Ammonia, NH3 195.3 5.65 239.7 23.4

83.8 1.2 87.3 6.5 Benzene, C6H6 278.7 9.87 353.3 30.8 Ethanol, C2H5OH 158.7 4.60 351.5

43.5 3.5 0.02 Argon, Ar Helium, He Mercury, Hg 4.22 0.08 234.3 2.292 629.7 59.30 90.7

0.94 111.7 8.2 175.5 3.16 337.2 35.3 Propanone, CH3COCH3 177.8 5.72 329.4 29.1 Water, H2O

6.01 373.2 40.7 Methane, CH4 Methanol, CH3OH 273.15 * For values at 298.15 K, use the information in the Data section. 18 Sublimation Direct conversion of a solid to a vapour The enthalpy change of an overall process is the sum of the enthalpy changes for the steps into which it may be divided

19 Enthalpies of ionisation (kJ/mol) 1 2 13 14 15 16 17 18 H He 1312

2370 5250 Li Be B C N O F Ne 519 900 799

1 090 1400 1310 1680 2080 7300 1760 2 420 2 350 2860 3390 3370 3950

14 800 3 660 P S Cl Ar 1060 1000 1260 1520 25 000 Na Mg

Al Si 494 738 577 4560 1451 1 820 7740 2 740 786 11 600 ionH(T)= Ionisation energy(0) + (5/2)RT (see Atkins & de Paula, Table

3.2) 20 Problems 21 Ethanol is brought to the boil at 1 atm. When the electric current of 0.682 A from a 12.0 V supply is passed for 500 s through a heating coil immersed in the boiling liquid, it is found that the temperature remains constant but 4.33 g of ethanol is vapourised. What is the enthalpy of vapourisation of ethanol at its boiling point at 1 atm? Calculate the standard enthalpy of sublimation of ice at 0C given that fusH is 6.01 kJ/mol and vapH is 45.07 kJ/mol, both at 0C. subH for Mg at 25C is 148 kJ/mol. How much energy as heat must be supplied to 1.00 g of solid magnesium metal to produce a gas composed of Mg2+ ions and electrons?

Bond enthalpies (kJ/mol) H H 436 C 412 C N O F Cl Br I

S P Si 348 (1) 612 (2) 838 (3) 518 (a) N O 388 463 305 (1) 163 (1) 613 (2)

409 (2) 890 (3) 945 (3) 360 (1) 157 743 (2) 146 (1) 497 (2) F 565 484 270 185

155 Cl 431 338 200 203 254 Br 366 276 219 193 I

299 238 210 178 S 338 259 250 212 P 322 Si

318 496 242 264 200 374 466 Values are for single bonds except where otherwise stated (in parentheses). (a) Denotes aromatic. 22 151 226 Problem

23 Estimate the standard reaction enthalpy for the formation of liquid methanol from its elements as 25C Enthalpies of combustion Enthalpies (heats) of combustion: complete reaction of compounds with oxygen. Measure using a bomb calorimeter. H U PV nRT RT V ng P P H U ng RT Most chemical reactions used for the production of heat are combustion reactions. The energy released when 1g of material is combusted is its Fuel Value. Since all heats of combustion are exothermic, fuel values are reported as positive.

Most of the energy our body needs comes from fats and carbohydrates. Carbohydrates are broken down in the intestines to glucose. Glucose is transported in the blood to cells where it is oxidized to produce CO 2, H2O and energy: C6H12O6(s) + 6O2(g) 6CO2(g) + 6H2O(l) cH=-2816 kJ The breakdown of fats also produces CO2 and H2O Any excess energy in the body is stored as fats 24 Heats of formation If one mole of the compound is formed under standard conditions from its elements in their reference state then the resulting enthalpy change is said to be the standard molar enthalpy (Heat) of formation, fH where the subscript indicates this. The reference state is the

most stable form under the prevailing conditions. 25 Hesss Law To evaluate unknown heats of reaction The standard enthalpy of a reaction is the sum of the standard enthalpies for the reactions into which the overall reaction may be divided rxnHo = fHom(products) - fHom(reactants) 26 Variation of rH with T rH(T2) = rH(T1) + rCp(T2-T1) Kirchoffs Law rCp = Cp,m(products) - Cp,m(reactants)

If heat capacity is temperature dependent, we need to integrate over the temperature range o o T2 o r H (T2 ) r H (T1 ) rC p dT T1 27 Thermodynamics: the 2 law nd Deals with the direction of spontaneous change (no work required to bring it about) Kelvin Statement No process is possible in which the sole result is the absorption

of heat from a reservoir and its complete conversion into work Impossible! 28 Entropy The apparent driving force for spontaneous change is the dispersal of energy A thermodynamic state function, Entropy, S, is a measure of the dispersal of energy (molecular disorder) of a system 2nd Law: The Entropy of an isolated system increases in the course of spontaneous change 29 Stot>0 Thermodynamic definition of S

Concentrates on the change in entropy: S = qrev/T Can use this equation to quantify entropy changes. We will see later (3rd & 4th year) a statistical description of entropy S = k lnW (Boltzmann formula) 30 Heat Engines ome to the lecture to see what is on this slid 31 Expansion entropy Intuitively can guess that entropy increases with gas expansion. Thermodynamic definition allows us to quantify this increase

Recall that: w = -nRT ln (Vf/Vi) BUT qrev = -w (U = 0 for isothermal processes) S = nR ln (Vf/Vi) 32 Note: independent of T Also: Because S is a state function, get the same value for an irreversible expansion Heating Entropy dq dS for infinitesimal change in T T q dq C or for infinitesimal change in T C T dT dqrev CdT Tf

S Ti CdT dS T T f dT Tf CdT C C ln Ti T T Ti for constant heat capacity 33 Entropy of phase transition Entropy of fusion fus S

Tf Entropy of vapourisation vap S 34 fus H (T f ) vap H (Tb ) Tb Troutons rule The entropy of vapourisation is approximately the same (85 J/K.mol) for all non-polar liquids Phase transitions To evaluate entropies of transition at T other than the transition temperature Entropy of vapourisation of water at 25C? Sum of S for heating from 25C to 100C, S for vapourisation at 100C, and S for

cooling vapour from 100C to 25C. Try it! (+118 J/K.mol). 35 Entropy changes in the surroundings Stot = Ssys + Ssur qsur ,rev S sur T qsur S sur T q S sur T Stot = Ssys q/T Example: Water freezing to ice. Entropy change of system is -22

J/K.mol, and heat evolved is -6.01 kJ/mol. Entropy change in surroundings must be positive for this process to occur spontaneously. Check this for different temperatures. 36 Note that Stot = 0 at equilibrium Spontaneity of water freezing ome to the lecture to see what is on this slid 37 Problem 38

Typical person heats the surroundings at a rate of 100W (=J/s). Estimate entropy change in one day at 20C. qsur = 86,400 s 100 J/s Ssur = qsur/T = (86,400 100 J)/293 K = 2.95 104 J/K 3 Law rd Entropy of sulfur phase transition is 1.09 J/K.mol. Consider plot at left. Subtract entropy for phase transition (to give plot at right) T=0 intercept is the same. Entropies of all perfectly

crystalline substances are the same at T=0. 39 Absolute and standard molar entropies (S and S0m) Absolute entropies can be determined by integration of areas under heat capacity/T as a function of T, and including entropies of phase transitions. Standard molar entropies are the molar entropies of substances at 1bar pressure (and usually 298 K) 40 Standard molar entropies 41 Standard reaction entropies

Difference in molar entropy between products and reactants in their standard states is called the standard reaction entropy and can be expressed (like enthalpy) as: rxnSo = Som(products) - Som(reactants) 42 Note: absolute entropies, S, and standard molar entropies, S0m, are discussed in section 4.7 of the textbook Spontaneity of reactions ome to the lecture to see what is on this slid 43 Gibbs Energy

Introduced by J.W. Gibbs to combine the calculations of 2 entropies, into one. Because Stot = S H/T (constant T and P) Introduce G = H TS (Gibbs free energy) Then G = H TS (constant T) So that G = TStot (constant T and P) G = H TS 44 In a spontaneous change at constant temperature and pressure, the Gibbs energy decreases Maximum non-expansion work

Can derive (see box 4.5 in textbook) that G = wmax Example: formation of water: enthalpy -286kJ, free energy -237kJ Example: suppose a small bird has a mass of 30 g. What is the minimum mass of glucose that it must consume to fly to a branch 10 m above the ground? (G for oxidation of glucose to carbon dioxide and water is -2828 kJ at 25C) Exercise: A human brain operates at about 25 W (J/s). What mass of glucose must be consumed to sustain that power for 1 hour? 45 Problem solved ome to the lecture to see what is on this slid 46 Summary Thermodynamics tells which way a process will go

Internal energy of an isolated system is constant (work and heat). We looked at expansion work (reversible and irreversible). Thermochemistry usually deals with heat at constant pressure, which is the enthalpy. Spontaneous processes are accompanied by an increase in the entropy (disorder?) of the universe 47 Gibbs free energy decreases in a spontaneous process