First Year Physical Chemistry Tutorials Michaelmas Term Week 3 Thermodynamics I : Entropy, Enthalpy & Internal energy There are three tasks for this week; (1) Reading – minimum required reading is the two chapters of Atkins listed below (supplement this as necessary from the other references, and your lecture notes so far) (2) Questions for discussion in tutorial; please think about these questions and make notes on your answers as necessary - you should come to the tutorial prepared to discuss these (no need to hand in your answers) (3) Numerical problems – please attempt as many of these as possible. Hand in your answers to my pigeon hole in Merton by 5.00 on Tuesday 28th. Reading -Physical Chemistry, Chapters 2 - 3, P.W. Atkins and J. De Paula, 8th ed., OUP -Thermodynamics of Chemical Processes, Chapters 1-3, G. Price, Oxford Chemistry Primer #56, OUP, 1998. -Basic Chemical Thermodynamics, Chapters 1-3, E.B. Smith, OUP. Questions for discussion at tutorial (1) What is the definition of enthalpy, H, and why is this quantity more commonly used in chemistry than the internal energy U? (2) What is meant by the following: (a) adiabatic change (b) isothermal change (c) reversible change (d) state function? (3) (a) How is entropy defined (i) thermodynamically, (ii) in statistical terms? (b) What role does S play in determining the direction of spontaneous change? (c) On cold nights, water spontaneously freezes to form ice, yet the entropy of ice is lower than that of water. How is this change consistent with your answer to (b)? (d) In a certain sense both the following statements (i) and (ii) are true - think about how one or both of these could be rewritten to clarify their meaning. (i) “In a reversible process the entropy change is dq/T ” (ii) “In a reversible process there is no change in entropy.” (4) Would you expect the entropy changes of the following systems to be positive or negative? Give qualitative explanations for your answers. (i) A sample of water is heated from 300K to 325K at constant pressure. (ii) Nitrogen gas is compressed at constant temperature. (iii) A sample of argon gas at 1 atm pressure is allowed to mix with a sample of krypton at the same pressure, such that the total pressure remains at 1 atm. (iv) One mole of water forms one mole of ice at 273K. (v) The following reactions occur at constant pressure; (i) 2AgCl(s) + Br2(l) 2AgBr(s) + Cl2(g) (ii) N2(g) + 3H2(g) 2NH3(g) (vi) Crystalline sodium chloride dissolves in water. (5) How do the entropy and enthalpy of a substance vary with temperature? (You should be able to derive relationships for these starting with definitions of the heat capacity and the 2nd law of thermodynamics) Numerical Problems 1. (a) Calculate the work done when 1 mole of an ideal gas (initial volume V1 ) expands isothermally and reversibly to a final volume V2 = 3V1 at 298K. (b) Calculate the work done when 1 mole of an ideal gas (initial volume V1) expands isothermally into an evacuated space to a final volume V2 = 3V1 at 298K. (c) The initial and final states of the gas are the same in parts (a) and (b) so that the change in internal energy is the same in the two cases. How can the different results for (a) and (b) be reconciled with the First Law. (d) One mole of CaCO3 was heated in an open vessel at 1 atm pressure to 700C when it decomposed into CaO(s) and CO2(g). Calculate the work done during the decomposition assuming that CO2(g) can be regarded as an ideal gas. 2. A 0.825g sample of benzoic acid was ignited in a bomb calorimeter in the presence of excess oxygen. The temperature of the calorimeter rose by 1.940 K from 298 K. In two separate experiments in the same apparatus, 0.498 g of fumaric acid and 0.509 g of maleic acid were ignited and gave temperature rises of 0.507 K and 0.528 K respectively. In all experiments a drop of water was added to the calorimeter. Using the data given below: (i) Determine the heat capacity of the calorimeter. (ii) For both fumaric and maleic acids, calculate (a) the molar internal energy of combustion; (b) the molar enthalpy of combustion (c) the molar enthalpy of formation Comment on the difference between the enthalpies of formation of the two isomers. (iii) Why would it have been necessary to add a drop of water to the calorimeter? The standard enthalpy of formation of water is 285.8 kJ mol1 and of CO2 393.5 kJ mol1. The internal energy of combustion of benzoic acid is 3251 kJ mol1. The relative molecular masses of benzoic, fumaric and maleic acids are 122, 116 and 116 respectively. 3. At 298K, the standard enthalpy of formation (Hf) of NH3(g) is 46.11 kJ mol1. Assuming that the molar heat capacities can be represented by expressions of the form: Cp,m = a + bT with the coefficients given below, calculate Hf at 1000K. N2 H2 NH3 1 1 a / J K mol 28.58 27.28 29.75 103 b / J K2 mol1 3.77 3.26 25.1 (Hint: you need to perform an integration) 4. The following table gives the molar heat capacity of lead over a range if temperatures. What is the standard molar Third Law entropy of lead at 25C? T/K 10 15 20 25 30 50 70 100 150 200 250 298 Cp,m / J K1 mol1 2.8 7.0 10.8 14.1 16.5 21.4 23.3 24.5 25.3 25.8 26.2 26.6 (Hint: You need to estimate this from the area under a suitable graph) 5. (a) Calculate the change in entropy of a system comprising one mole of water at 10C that is cooled to 0C and then freezes to form ice at 0C. Cp(H2O(liq)) =75.3 J K1 mol1; Hfus(H2O) = 6.0 kJ mol1. (b) Comment on the sign of S you obtained in (a) in the light of the microscopic changes occurring in the system. 6. (a) Calculate the entropy change of 3 moles of CH4 that is heated from 298K to 1098K at 1 atm pressure. Cp(CH4) / J K1 mol1 = 23.64 + 4.79102T 1.93105T2 over the temperature range 298 2000 K. (Hint: Again, a mathematical integration is required) (b) The entropy change of 2 moles of an ideal gas when it was expanded isothermally from V1 to V2 was found to be 5.595 J K1. Calculate the ratio V2/V1. If this isothermal expansion takes place with the gas doing no work, what is the total entropy change of the system plus surroundings? Show that your result is consistent with the second law of thermodynamics. 7. Calculate the entropy changes when: (a) 0.5 moles of H2O(l) at 0C is added to 0.5 moles of H2O(l) at 100C in an insulated vessel. (b) the water is then heated to 100C at 1 atm pressure, (c) and then evaporated at 100C at 1 atm pressure, (d) the water vapour so formed is compressed isothermally to half its volume. (e) and then heated at constant volume to twice its absolute temperature. Cp(H2O(liq)) = 75.48 J K1 mol1; Cv(H2O(g)) = 25.3 J K1 mol1 and Hvap(H2O) = 40.7 kJ mol1 (all of which may be assumed to be independent of temperature). 8. (a) Calculate the difference in molar entropy (i) between water at 5C and ice at 5C and (ii) between water at 95C and steam at 95C and 1 atm pressure. (b) Calculate the entropy change of the surroundings and hence (c) the total entropy change of the universe for the two cases. Discuss the spontaneity of transitions between phases at these temperatures. The difference in molar heat capacities on melting is 37.3 J K1 mol1 and on vaporisation is 41.9 J K1 mol1. Further Hmelt(273) = 6.01 kJ mol1 and Hvap(373) = 40.7 kJ mol1. 9. A sample of ideal gas initially at 1 atm pressure and 273K is expanded to a volume greater by 36.6% in four different ways: (a) reversibly and isothermally; (b) reversibly and adiabatically; (c) adiabatically, doing no external work (expansion into vacuum); (d) by contact with steam at 100C (assuming negligible thermal capacity of the container. Note that 373/273 = 1.366, so that the volume and temperature both increase by the same fraction i.e. the change occurs at constant pressure). Note for (a) that the internal energy of an ideal gas U only depends on its temperature. In each case express, in terms of Cv and/or the gas constant, (i) the change of entropy of the gas sample, and (ii) that of the general surroundings.