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Chapter 4 Thermochemistry Physical Chemistry 2nd Edition Thomas Engel, Philip Reid Objectives • Discussion of Hess’s Law. • Derive property that allows ∆H and ∆U to be calculated without experiments. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Outline 1. Energy Stored in Chemical Bonds Is Released or Taken Up in Chemical Reactions 2. Internal Energy and Enthalpy Changes Associated with Chemical Reactions 3. Hess’s Law Is Based on Enthalpy Being a State Function 4. The Temperature Dependence of Reaction Enthalpies 5. The Experimental Determination of ∆U and ∆H for Chemical Reactions 6. Differential Scanning Calorimetry Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.1 Energy Stored in Chemical Bonds Is Released or Taken Up in Chemical Chemical Reactions • The change in enthalpy or internal energy due to temperature result in heat flow and/or in the form of expansion or non-expansion work. • The focus is on using measurements of heat flow to determine changes in U and H due to chemical reactions. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.2 Internal Energy and Enthalpy Changes Associated with Chemical Chemical Reactions • The enthalpy of reaction, ∆H°reaction, is the heat withdrawn from the surroundings as the reactants are transformed into products at constant T and P. • The standard enthalpy of formation, ∆Hf°, is the enthalpy associated with the reaction of 1 mol of the species under standard state conditions. • The enthalpy change associated with reaction Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.2 Internal Energy and Enthalpy Changes Associated with Chemical Chemical Reactions • The enthalpy change associated with a chemical reaction is ∆ H °reaction = ∑ vi ∆H ° f , i i Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.3 Hess’s Law Is Based on Enthalpy Being a State Function • Hess’s law states that the enthalpy change for any sequence of reactions that sum to the same overall reaction is identical. • It is useful to have tabulated values of ∆Hf° for chemical compounds at one fixed combination of P and T. • ∆H°reaction can then be calculated for all reactions among these compounds at the tabulated values of P and T. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Example 4.1 The average bond enthalpy of the O-H bond in water is defined as one-half of the enthalpy change for the reaction H2O(g) → 2H(g) O(g). The formation enthalpies, ∆H °f , for H(g) and O(g) are 218.0 and 249.2 kJ mol-1, respectively, ° ∆ H at 298.15 K, and f for H2O(g) is 241.8 kJ mol-1 at the same temperature. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Example 4.1 a. Use this information to determine the average bond enthalpy of the O-H bond in water at 298.15 K. b. Determine the average bond energy, ∆U, of the O-H bond in water at 298.15 K. Assume ideal gas behavior. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Solution a. We consider the sequence H 2O( g ) → H(g) + 1 2 O 2 ( g ) ∆H ° = 241.8kJmol −1 H 2 ( g ) → 2H(g) ∆H ° = 2 × 218.0kJmol−1 1 2 O 2 ( g ) → O(g) ∆H ° = 249.2 kJmol−1 ________________________________________________ H 2 )( g ) → 2H(g) + O (g) Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd ∆H ° = 927.0kJmol−1 Solution a. This is the enthalpy change associated with breaking both O-H bonds under standard conditions. We conclude that the average bond enthalpy of the O-H bond in water is 1 × 927.0 = 463. 5kJmol−1 2 We emphasize that this is the average value because the values of for the transformations H2O(g) → H(g) OH(g ) and OH(g ) → O(g) H(g) differ. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Solution b. ∆U ° = ∆H ° − ∆(PV ) = ∆H ° − ∆nRT = 927.0 − 2 × 8.314 × 298.15 = 922.0kJmol −1 The average value for ∆U ° for the O-H bond in 1 water is 2 × 922.0 = 461.0kJmol . The bond energy and the bond enthalpy are nearly identical. −1 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.3 Hess’s Law Is Based on Enthalpy Being a State Function • Values of bond energies tabulated in the format of the periodic table together with the electro- negativities are shown. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.4 The Temperature Dependence of Reaction Enthalpies • ∆H°T at elevated temperature is used to determine a reaction to be endothermic or exothermic. • The enthalpy for each reactant and product at temperature T relating to the value at 298.15 K is T ∆H °T = ∆H ° 298 .15 K + ∫ ∆C (T ')dT ' p 298.15K where ∆C p (T ') = ∑ vi C p ,i Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd i Example 4.2 Calculate the enthalpy of formation of HCl(g) at 1450 K and 1 bar pressure given that ∆H ° f ( HCl, g ) = −92.3kJmol−1 at 298.15 K and that over this temperature range. The ratios T/K and T2/K2 appear in these equations in order to have the right units for the heat capacity. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Solution By definition, the formation reaction is written as 1 2 H 2(g) + 1 2 Cl 2(g) → HCl( g ) and 1450 ∆H °1450 K = ∆H ° 298.15 K + ∫ ∆C° (T )dT P 298 .15 28.165 + 1.809 × 10 −3 + 15.464 × 10− 7 1 ∆C° P (T ) = − 29.064 − 0.8363 × 10 −3 + 20.111 ×10 − 7 2 1 − 31.695 + 10.143 ×10 −3 + 40.73 × 10− 7 2 ( ( ( ) ) = − 2.215 − 2.844 × 10 −3 + 25.595 × 10− 7 JK −1mol −1 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd ) Solution Solution: ∫ (− 2.215 − 2.844 ×10 1450 ∆H °1450 K = −92.3 + 298. 15 = −92.3 − 2 .836 = −95 .1kJmol −1 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd −3 + 25.595 ×10 −7 ) T × d K 4.5 The Experimental Determination of ΔU and ΔH for Chemical Reactions • ∆U°reaction can be determined through experiment in a bomb calorimeter, which carried out in constant volume. m ∆ U ° = s ∆ U ° reaction Ms ,m + mH20 M Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd H20 ∆ T + C calorimete r ∆ T = 0 Example 4.3 When 0.972 g of cyclohexane undergoes complete combustion in a bomb calorimeter, ∆T of the inner water bath is 2.98°C. For cyclohexane,∆U ° reaction, m is -3913 kJ mol-1. Given this result, what is the value for ∆U reavction ,m for the combustion of benzene if ∆T is 2.36°C when 0.857 g of benzene undergoes complete combustion in the same calorimeter? The mass of the water in the inner bath is 1.812 × 103 g, and the CP,m of water is 75.291 J K-1 mol-1 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Solution To calculate the calorimeter constant through the combustion of cyclohexane, Ccalorimeter = mH 2 O ms − ∆U °reaction − C H 2 O ∆T Ms M H 2O ∆T 3 0.972 1 . 812 × 10 × 3919 ×103 − × 75.291 × 2.98°C 18.02 = 84.16 2.98°C = 7.59 ×10 3 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd −1 ( ) J °C Solution In calculating ∆U ° reaction for benzene, mH 2 O ∆U °reaction C H 2O ∆T + C calorimeter ∆T MH O 2 78.12 1.812 ×10 3 =− × × 75.291× 2.36 0.857 18.02 M =− s ms = − 3.26 × 106 Jmol −1 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.5 The Experimental Determination of ΔU and ΔH for Chemical Reactions • When ∆U°reaction is obtained, we can get ∆H °reaction = ∆U °reaction + ∆nRT ∆n = number of moles of gas change in reaction • For constant pressure calorimetry involving the solution of a salt in water: ∆H ° reaction mH 2 0 ms = ∆H ° solution ,m + C H 2 O ,m ∆T + Ccalorimete r ∆T = 0 Ms M H20 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.5 The Experimental Determination of ΔU and ΔH for Chemical Reactions • For constant pressure calorimetry involving the solution of a salt in water: ∆H ° reaction mH 2 0 ms = ∆H ° solution ,m + C H 2 O ,m ∆T + Ccalorimete r ∆T = 0 Ms M H20 Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Example 4.4 The enthalpy of solution for the reaction is determined in a constant pressure calorimeter. The calorimeter constant was determined to be 342.5 J K-1. When 1.423 g of Na2SO4 is dissolved in 100.34 g of H2O(l), ∆T = 0.037 K. Calculate ∆H m for Na2SO4 from these data. Compare your result with that calculated using the standard enthalpies of formation in Table 4.1 (Appendix B, Data Tables) and in Chapter 10 in Table 10.1. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Solution mH 2O ∆H ° solution, m C H 2O ∆T + C calorimeter ∆T MH O 2 142.04 100.34 = × × 75.3 × 0.037 + 342.5 × 0.037 1.423 18.02 = −2.8 × 103 Jmol −1 M =− s ms ( ) ( ) ∆H ° solution,m = 2∆H ° f Na + , aq + ∆H ° f SO42− , aq − ∆H ° f (Na2 SO4 , s ) = 2 × (− 240 .1) − 909.3 + 1387 .1 = −2.4kJmol −1 The agreement between the calculated and experimental results is satisfactory. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.6 Differential Scanning Calorimetry • Enthalpy of fusion ∆Hfusion of a dozen related solid materials is determined by differential scanning calorimetry. • The temperatures of each of the samples and the reference are measured with a thermocouple. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 4.6 Differential Scanning Calorimetry • ∆Hfusion can be ascertained by determining the area under the curve from the output data. Chapter 4: Thermochemistry Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd