* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 10
Survey
Document related concepts
Stoichiometry wikipedia , lookup
Spinodal decomposition wikipedia , lookup
Electrolysis of water wikipedia , lookup
Solar air conditioning wikipedia , lookup
Chemical equilibrium wikipedia , lookup
Internal energy wikipedia , lookup
Heat transfer wikipedia , lookup
Bioorthogonal chemistry wikipedia , lookup
Thermodynamics wikipedia , lookup
Transition state theory wikipedia , lookup
Chemical thermodynamics wikipedia , lookup
Transcript
1/7/2013 Chemistry: Atoms First Julia Burdge & Jason Overby 10 Chapter 10 Energy Changes in Chemical Reactions Kent L. McCorkle Cosumnes River College Sacramento, CA Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 10.1 Energy and Energy Changes Thermochemistry 10.1 Energy and Energy Changes 10.2 Introduction to Thermodynamics States and State Functions The First Law of Thermodynamics Work and Heat 10.3 Enthalpy Reactions Carried Out at Constant Volume or at Constant Pressure Enthalpy and Enthalpy Changes Thermochemical Equations 10.4 Calorimetry Specific Heat and Heat Capacity Constant-Pressure Calorimetry Constant-Volume Calorimetry 10.5 Hess’s Law 10.6 Standard Enthalpies of Formation 10.7 Bond Enthalpy and the Stability of Covalent Molecules 10.8 Lattice Energy and the Stability of Ionic Compounds The Born-Haber Cycle Comparison of Ionic and Covalent Compounds Energy and Energy Changes The system is a part of the universe that is of specific interest. The surroundings constitute the rest of the universe outside the system. Thermochemistry is the study of heat (the transfer of thermal energy) in chemical reactions. Heat is the transfer of thermal energy. Heat is either absorbed or released during a process. System heat Surroundings Surroundings Universe = System + Surroundings The system is usually defined as the substances involved in chemical and physical changes. Energy and Energy Changes Energy and Energy Changes An exothermic process occurs when heat is transferred from the system to the surroundings. An endothermic process occurs when heat is transferred from the surroundings to the system. “Feels hot!” 2H2(g) + O2(g) System 2H2O(l) + energy heat “Feels cold” energy + 2HgO(s) System 2Hg(l) + O2(g) heat Surroundings Surroundings Universe = System + Surroundings Universe = System + Surroundings 1 1/7/2013 10.2 Introduction to Thermodynamics Introduction to Thermodynamics Thermodynamics is the study of the interconversion of heat and other kinds of energy. State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. In thermodynamics, there are three types of systems: The magnitude of change depends only on the initial and final states of the system. An open system can exchange mass and energy with the surroundings. Energy Pressure A closed system allows the transfer of energy but not mass. Volume An isolated system does not exchange either mass or energy with its surroundings. Temperature The First Law of Thermodynamics Work and Heat The first law of thermodynamics states that energy can be converted from one form to another, but cannot be created or destroyed. The overall change in the system’s internal energy is given by: ΔU = q + w ΔUsys + ΔUsurr = 0 ΔU is the change in the internal energy. “sys” and “surr” denote system and surroundings, respectively. ΔU = Uf – Ui; the difference in the energies of the initial and final states. ΔUsys = –ΔUsurr q is heat q is positive for an endothermic process (heat absorbed by the system) q is negative for an exothermic process (heat released by the system) w is work w is positive for work done on the system w is negative for work done by the system Work and Heat Worked Example 10.1 Calculate the overall change in internal energy, ΔU, (in joules) for a system that absorbs 188 J of heat and does 141 J of work on its surroundings. ΔU = q + w Strategy Combine the two contributions to internal energy using ΔU = q + w and the sign conventions for q and w. Solution The system absorbs heat, so q is positive. The system does work on the surroundings, so w is negative. ΔU = q + w = 188 J + (-141 J) = 47 J Think About It Consult Table 10.1 to make sure you have used the proper sign conventions for q and w. 2 1/7/2013 10.3 Enthalpy Enthalpy Sodium azide detonates to give a large quantity of nitrogen gas. 2NaN3(s) 2Na(s) + 3N2(g) Under constant volume conditions, pressure increases: Enthalpy 2NaN3(s) 2Na(s) + 3N2(g) Under constant volume conditions, pressure increases: Worked Example 10.2 Pressure-volume, or PV work, is done when there is a volume change under constant pressure. w = −PΔV ΔV is the change in the volume of the container. Worked Example 10.2 (cont.) 1L 1000 mL Determine the work done (in joules) when a sample of gas extends from 552 mL to 891 mL at constant temperature (a) against a constant pressure of 1.25 atm, (b) against a constant pressure of 1.00 atm, and (c) against a vacuum (1 L∙atm = 101.3 J). Strategy Determine change in volume (ΔV), identify the external pressure (P), and use w = −PΔV to calculate w. The result will be in L∙atm; use the equality 1 L∙atm = 101.3 J to convert to joules. P is the external opposing pressure. Solution (c) w = -(0 atm)(339 mL) Sodium azide detonates to give a large quantity of nitrogen gas. 101.3 J =0J 1 L∙atm Think About It Remember that the negative sign in the answers to part (a) and (b) indicate that the system does work on the surroundings. When an expansion happens against a vacuum, no work is done. This example illustrates that work is not a state function. For an equivalent change in volume, the work varies depending on external pressure against which the expansion must occur. Solution ΔV = (891 – 552)mL = 339 mL. (a) P = 1.25 atm, (b) P = 1.00 atm, (c) P = 0 atm. (a) w = -(1.25 atm)(339 mL) 1L 1000 mL 101.3 J = -42.9 J 1 L∙atm (b) w = -(1.00 atm)(339 mL) 1L 1000 mL 101.3 J = -34.3 J 1 L∙atm Enthalpy Pressure-volume, or PV work, is done when there is a volume change under constant pressure. w = −PΔV substitute ΔU = q + w ΔU = q − PΔV When a change occurs at constant volume, ΔV = 0 and no work is done. qV = ΔU 3 1/7/2013 Enthalpy Enthalpy Under conditions of constant pressure: The thermodynamic function of a system called enthalpy (H) is defined by the equation: ΔU = q + w H = U + PV ΔU = q − PΔV A note about SI units: Pressure: pascal; 1Pa = 1 kg/(m . s2) qP = ΔU + PΔV Volume: cubic meters; m3 PV: 1kg/(m . s2) x m3 = 1(kg . m2)/s2 = 1 J Enthalpy: joules U, P, V, and H are all state functions. Enthalpy and Enthalpy Changes Enthalpy and Enthalpy Changes For any process, the change in enthalpy is: ΔH = ΔU + Δ(PV) (1) The enthalpy of reaction (ΔH) is the difference between the enthalpies of the products and the enthalpies of the reactants: If pressure is constant: ΔH = ΔU + PΔV Rearrange to solve for ΔU: (2) ΔU = ΔH + PΔV (3) qp = ΔU + ΔV (4) ΔH = H(products) – H(reactants) Assumes reactions in the lab occur at constant pressure Remember, qp: Substitute equation (3) into equation (4) and solve: qp = (ΔH − PΔV) + PΔV (5) ΔH > 0 (positive) endothermic process ΔH < 0 (negative) exothermic process qp = ΔH for a constant-pressure process Thermochemical Equations H2O(s) Thermochemical Equations H2O(l) ΔH = +6.01 kJ/mol Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔH = −890.4 kJ/mol Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? ΔH < 0 exothermic ΔH > 0 endothermic 4 1/7/2013 Thermochemical Equations Thermochemical Equations Enthalpy is an extensive property. The following guidelines are useful when considering thermochemical equations: Extensive properties are dependent on the amount of matter involved. H2O(l) → H2O(g) Double the amount of matter ΔH = +44 kJ/mol Double the enthalpy 2H2O(l) → 2H2O(g) 1) Always specify the physical states of reactants and products because they help determine the actual enthapy changes. CH4(g) + 2O2(g) CO2(g) + 2H2O(g) ΔH = +88 kJ/mol Units refer to mole of reaction as written Thermochemical Equations different states CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔH = −802.4 kJ/mol different enthalpies ΔH = +890.4 kJ/mol Worked Example 10.3 The following guidelines are useful when considering thermochemical equations: 2) When multiplying an equation by a factor (n), multiply the ΔH value by same factor. CH4(g) + 2O2(g) CO2(g) + 2H2O(g) ΔH = − 802.4 kJ/mol 2CH4(g) + 4O2(g) 2CO2(g) + 4H2O(g) ΔH = − 1604.8 kJ/mol Given the thermochemical equation for photosynthesis, 6H2O(l) + 6CO2(g) → C6H12O6(s) + 6O2(g) ΔH = +2803 kJ/mol calculate the solar energy required to produce 75.0 g of C6H12O6. Strategy The thermochemical equation shows that for every mole of C6H12O6 produced, 2803 kJ is absorbed. We need to find out how much energy is absorbed for the production of 75.0 g of C6H12O6. We must first find out how many moles there are in 75.0 g of C6H12O6. The molar mass of C6H12O6 is 180.2 g/mol, so 75.0 g of C6H12O6 is 3) Reversing an equation changes the sign but not the magnitude of ΔH. CH4(g) + 2O2(g) CO2(g) + 2H2O(g) ΔH = − 802.4 kJ/mol CO2(g) + 2H2O(g) CH4(g) + 2O2(g) ΔH = +802.4 kJ/mol 1 mol C6H12O6 = 0.416 mol C6H12O6 180.2 g C6H12O6 We will multiply the thermochemical equation, including the enthalpy change, by 0.416, in order to write the equation in terms of the appropriate amount of C6H12O6. 10.4 Calorimetry Worked Example 10.3 (cont.) Solution (0.416 mol)[6H2O(l) + 6CO2(g) → C6H12O6(s) + 6O2(g)] and (0.416 mol)(ΔH) = (0.416 mol)(2803 kJ/mol) gives 2.50H2O(l) + 2.50CO2(g) → 0.416C6H12O6(s) + 2.50O2(g) 75.0 g C6H12O6 × ΔH = +1.17×103 kJ 1.17×103 Therefore, kJ of energy in the form of sunlight is consumed in the production of 75.0 g of C6H12O6. Note that the “per mole” units in ΔH are canceled when we multiply the thermochemical equation by the number of moles of C6H12O6. Calorimetry is the measurement of heat changes. Heat changes are measured in a device called a calorimeter. The specific heat (s) of a substance is the amount of heat required to raise the temperature of 1 g of the substance by 1°C. Think About It The specified amount of C6H12O6 is less than half a mole. Therefore, we should expect the associated enthalpy change to be less than half that specified in the thermochemical equation for the production of 1 mole of C6H12O6. 5 1/7/2013 Specific Heat and Heat Capacity Specific Heat and Heat Capacity The heat capacity (C) is the amount of heat required to raise the temperature of an object by 1°C. The heat associated with a temperature change may be calculated: q = msΔT The “object” may be a given quantity of a particular substance. heat capacity of 1 kg of water = 4.184 J 1000 g = 4184 J/C 1 g C Specific heat capacity of water heat capacity of 1 kg water q = CΔT m is the mass. s is the specific heat. Specific heat capacity has units of J/(g • °C) ΔT is the change in temperature (ΔT = Tfinal – Tinitial). Heat capacity has units of J/°C C is the heat capacity. Worked Example 10.4 Calculate the amount of heat (in kJ) required to heat 255 g of water from 25.2°C to 90.5°C. Strategy Use q = msΔT to calculate q. s = 4.184 J/g∙°C, m = 255 g, ΔT = 90.5°C – 25.2°C = 65.3°C. Solution 4.184 J 4 q= g∙°C × 255 g × 65.3°C = 6.97×10 J or 69.7 kJ Think About It Look carefully at the cancellation of units and make sure that the number of kilojoules is smaller than the number of joules. It is a common error to multiply by 1000 instead of dividing in conversions of this kind. Calorimetry Calculate the amount of heat required to heat 1.01 kg of water from 0.05°C to 35.81°C. Solution: Step 1:Use the equation q = msΔT to calculate q. q 1.01 kg 1000 g 4.184 J [35.81C 0.05C] = 151000 J = 151 kJ 1 kg g C Calorimetry Calorimetry A coffee-cup calorimeter may be used to measure the heat exchange for a variety of reactions at constant pressure: Concepts to consider for coffee-cup calorimetry: Heat of neutralization: HCl(aq) + NaOH(aq) → H2O(l) + NaCl(aq) Heat of ionization: H2O(l) → H+(aq) + OH‒(aq) Heat of fusion: H2O(s) → H2O(l) qP = ΔH System: reactants and products (the reaction) Surroundings: water in the calorimeter For an exothermic reaction: the system loses heat the surroundings gain (absorb) heat qsys = −msΔT qsurr = msΔT qsys = −qsurr Heat of vaporization: H2O(l) → H2O(g) The minus sign is used to keep sign conventions consistent. 6 1/7/2013 Worked Example 10.5 Worked Example 10.5 (cont.) A metal pellet with a mass of 100.0 g, originally at 88.4°C, is dropped into 125 g of water originally at 25.1°C. The final temperature of both pellet and the water is 31.3°C. Calculate the heat capacity C (in J/°C) of the pellet. Strategy Water constitutes the surroundings; the pellet is the system. Use qsurr = msΔT to determine the heat absorbed by the water; then use q = CΔT to determine the heat capacity of the metal pellet. mwater = 125 g, swater = 4.184 J/g∙°C, and ΔTwater = 31.3°C – 25.1°C = 6.2°C. The heat absorbed by the water must be released by the pellet: qwater = -qpellet, mpellet = 100.0 g, and ΔTpellet = 31.3°C – 88.4°C = -57.1°C. Solution 4.184 J qwater = g∙°C × 125 g × 6.2°C = 3242.6 J Thus, qpellet = -3242.6 J From q = CΔT we have -3242.6 J = Cpellet × (-57.1°C) Thus, Cpellet = 57 J/°C Think About It The units cancel properly to give appropriate units for heat capacity. Moreover, ΔTpellet is a negative number because the temperature of the pellet decreases. Constant-Volume Calorimetry Constant-Volume Calorimetry Constant volume calorimetry is carried out in a device known as a constant-volume bomb. To calculate qcal, the heat capacity of the calorimeter must be known. A constant-volume calorimeter is an isolated system. qcal = CcalΔT Bomb calorimeters are typically used to determine heats of combustion. qrxn = −qcal qrxn = −CcalΔT qcal = −qrxn 10.5 Hess’s Law A Famous Amos bite-sized chocolate chip cookie weighing 7.25 g is burned in a bomb calorimeter to determine its energy content. The heat capacity of the calorimeter is 39.97 kJ/°C. During the combustion, the temperature of the water in the calorimeter increases by 3.90°C. Calculate the energy content (in kJ/g) of the cookie. Think About It According to the label on the cookie package, a service size or 29 g, the andheat eachreleased serving by contains 150 Strategy Use qrxnis =four -Ccalcookies, ΔT to calculate the combustion of Cal. Convert the heat energy per gram to Calories per cookie servingtotodetermine verify its the cookie. Divide the released by the mass of the the result. energy content per gram Ccal = 39.97 kJ/°C and ΔT = 3.90°C. 21.5 kJ 1 Cal 29 g × = 1.5×102 Cal/serving × g 4.184 kJ serving Solution qrxn = -CcalΔT = -(39.97 kJ/°C)(3.90°C) = -1.559×102 kJ Because energy content is a positive quantity, we write energy content per gram = 1.559×102 7.25 g kJ = 21.5 kJ/g Hess’s law states that the change in enthalpy for a stepwise process is the sum of the enthalpy changes for each of the steps. CH4(g) + 2O2(g) 2H2O(l) CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔH = −890.4 kJ/mol 2H2O(g) ΔH = +88.0 kJ/mol CO2(g) + 2H2O(g) ΔH = −802.4 kJ/mol CH4(g) + 2O2(g) Enthalpy Worked Example 10.6 ΔH = −802.4 kJ ΔH = −890.4 kJ CO2(g) + 2H2O(g) CO2(g) + 2H2O(l) ΔH = +88.0 kJ 7 1/7/2013 Hess’s Law Worked Example 10.7 When applying Hess’s Law: 1) Manipulate thermochemical equations in a manner that gives the overall desired equation. 2) Remember the rules for manipulating thermochemical equations: Always specify the physical states of reactants and products because they help determine the actual enthalpy changes. When multiplying an equation by a factor (n), multiply the ΔH value by same factor. Reversing an equation changes the sign but not the magnitude of ΔH. Given the following thermochemical equations, NO(g) + O3(g) → NO2(g) + O2(g) 3 O3(g) → O2(g) 2 O2(g) → 2O(g) ΔH = –198.9 kJ/mol ΔH = –142.3 kJ/mol ΔH = +495 kJ/mol determine the enthalpy change for the reaction NO(g) + O(g) → NO2(g) Strategy Arrange the given thermochemical equations so that they sum to the desired equation. Make the corresponding changes to the enthalpy changes, and add them to get the desired enthalpy change. 3) Add the ΔH for each step after proper manipulation. 4) Process is useful for calculating enthalpies that cannot be found directly. Worked Example 10.7 (cont.) Worked Example 10.7 (cont.) Solution The first equation has NO as a reactant with the correct coefficients, so we will use it as is. NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol The second equation must be reversed so that the O3 introduced by the first equation will cancel (O3 is not part of the overall chemical equation). We also must change the sign on the corresponding ΔH value. 3 ΔH = +142.3 kJ/mol O (g) → O3(g) 2 2 These two steps sum to give: NO(g) + O3(g) → NO2(g) + O2(g) 1 3 + O2(g) O2(g) → O3(g) 2 2 1 NO(g) + O2(g) → NO2(g) 2 10.6 ΔH = –198.9 kJ/mol ΔH = +142.3 kJ/mol ΔH = –56.6 kJ/mol Standard Enthalpies of Formation The standard enthalpy of formation (ΔH °) f is defined as the heat change that results when 1 mole of a compound is formed from its constituent elements in their standard states. C(graphite) + O2(g) Elements in standard states CO2(g) 1 mole of product ΔH f° = −393.5 kJ/mol 1 Solution We then replace 2 O2 on the left with O by incorporating the last equation. To do so, we divide the third equation by 2 and reverse its direction. As a result, we must also divide ΔH value by 2 and change its sign. 1 O(g) → O2(g) ΔH = –247.5 kJ/mol 2 Finally, we sum all the steps and add their enthalpy changes. NO(g) + O3(g) → NO2(g) + O2(g) 3 O (g) → O3(g) 2 2 1 + O(g) → O2(g) 2 NO(g) + O(g) → NO2(g) ΔH = –198.9 kJ/mol ΔH = +142.3 kJ/mol ΔH = –247.5 kJ/mol ΔH = –304 kJ/mol Think About It Double-check the cancellation of identical items–especially where fractions are involved. Standard Enthalpies of Formation The standard enthalpy of formation (ΔH f°) is defined as the heat change that results when 1 mole of a compound is formed from its constituent elements in their standard states. The superscripted degree sign denotes standard conditions. 1 atm pressure for gases 1 M concentration for solutions “f” stands for formation. ΔH f° for an element in its most stable form is zero. ΔH f° for many substances are tabulated in Appendix 2 of the textbook. 8 1/7/2013 Standard Enthalpies of Formation Worked Example 10.8 The standard enthalpy of reaction (ΔH °rxn) is defined as the enthalpy of a reaction carried out under standard conditions. aA + bB → cC + dD ΔH °rxn = [cΔH f°(C) + dΔH f°(D) ] – [aΔH f°(A) + bΔH f°(B)] Using data from Appendix 2, calculate ΔH °rxn for Ag+(aq) + Cl-(aq) → AgCl(s). Strategy Use ΔH °rxn = ΣnΔH f°(products) – ΣmΔH f°(reactants) and ΔH f° values from Appendix 2 to calculate ΔH °rxn. The ΔH °f values for Ag+(aq), Cl-(aq), and AgCl(s) are +105.9, –167.2, and –127.0 kJ/mol, respectively. Solution ΔH °rxn = ΔH f°(AgCl) – [ΔH f°(Ag+) + ΔH f°(Cl-)] = –127.0 kJ/mol – [(+105.9 kJ/mol) + (–167.2 kJ/mol)] ΔH °rxn = ΣnΔH f°(products) – ΣmΔH f°(reactants) n and m are the stoichiometric coefficients for the reactants and products. Worked Example 10.9 Think About It Watch out for misplaced or missing minus signs. This is an easy place to lose track of them. Worked Example 10.9 (cont.) Given the following information, calculate the standard enthalpy of formation of acetylene (C2H2) from its constituent elements: C(graphite) + O2(g) → CO2(g) 1 H2(g) + O2(g) → H2O(l) 2 2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l) = –127.0 kJ/mol – (–61.3 kJ/mol) = –65.7 kJ/mol ΔH °rxn = –393.5 kJ/mol (1) ΔH °rxn = –285.5 kJ/mol (2) ΔH °rxn = –2598.8 kJ/mol (3) Strategy Arrange the equations that are provided so that they will sum to the desired equation. This may require reversing or multiplying one or more of the equations. For any such change, the corresponding change must also be made to the ΔH rxn ° value. The desired equation, corresponding to the standard enthalpy of formation of acetylene, is 2C(graphite) + H2(g) → C2H2(g) Solution We multiply Equation (1) and its ΔH °rxn value by 2: 2C(graphite) + 2O2(g) → 2CO2(g) We reverse Equation (3) and divide it by 2 (i.e., multiply through by 1/2): 5 Think About It Remember °rxn isΔH only °f whenkJ/mol there is °rxn a=ΔH +1299.4 2CO2(g) + H2O(l) → C2H2(g)that + 2aOΔH 2(g) just one product, just one mole produced, and all the reactants are elements in their standard states. Summing the resulting equations and the corresponding ΔH ° values: rxn 2C(graphite) + 2O2(g) → 2CO2(g) Bond Enthalpy and the Stability of Covalent Molecules The bond enthalpy is the enthalpy change associated with breaking a bond in 1 mole of gaseous molecule. ΔH °rxn = –787.0 kJ/mol ΔH °rxn = –285.5 kJ/mol 1 H2(g) + 2 O2(g) → H2O(l) 5 2CO2(g) + H2O(l) → C2H2(g) + 2 O2(g) 2C(graphite) + H2(g) → C2H2(g) 10.7 ΔH °rxn = –787.0 kJ/mol We include Equation (2) and its ΔH °rxn value as is: 1 ΔH °rxn = –285.5 kJ/mol H2(g) + 2 O2(g) → H2O(l) ΔH °rxn = +1299.4 kJ/mol ΔH °f = +226.6 kJ/mol Bond Enthalpy and the Stability of Covalent Molecules Bond enthalpy change in an exothermic reaction.: H2(g) → H(g) + H(g) ΔH° = 436.4 kJ/mol The enthalpy for a gas phase reaction is given by: ΔH° = ΣBE(reactants) – ΣBE(products) ΔH° = total energy input – total energy released bonds broken bonds formed 9 1/7/2013 Bond Enthalpy and the Stability of Covalent Molecules Bond enthalpy change in an endothermic reaction: Worked Example 10.10 Use bond enthalpies from Table 10.4 to estimate the enthalpy of reaction for the combustion of methane: CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) Think About It structures Use equation ΔH °rxn = ΣnΔH Strategy Draw Lewis to determine what f°(products) bonds are to–be broken and ΣmΔHare and data from Appendix 2 to calculate this what bonds to be formed. f°(reactants) enthalpy of reaction again; then compare your results using the two approaches. The difference in this case is due to two things: most tabulated bond enthalpies are averages and, by convention, we show the product of combustion as liquid water–but average bond Bonds enthalpies to break: 4apply C–H to andspecies 2 O=Oin the gas phase, where there is little or influence exerted neighboring molecules. Bonds no to form: 2 C=O and 4byH–O Bond enthalpies from Table 10.4: 414 kJ/mol (C–H), 498.7 kJ/mol (O=O), 799 kJ/mol (C=O in CO2), and 460 kJ/mol (H–O). Solution [4(414 kJ/mol) + 2(498.7 kJ/mol)] – [2(799 kJ/mol) + 4(460 kJ/mol)] = –785 kJ/mol 10.8 Lattice Energy and the Stability of Ionic Compounds A Born-Haber cycle is a cycle that relates the lattice energy of an ionic compound to quantities that can be measured. Na(s) + Lattice Energy and the Stability of Ionic Compounds A Born-Haber cycle is a cycle that relates the lattice energy of an ionic compound to quantities that can be measured. 1 Cl (g) → Na+(g) + Cl-(g) 2 2 Lattice Energy and the Stability of Ionic Compounds Na(s) + 1 Cl (g) → Na+(g) + Cl-(g) 2 2 Worked Example 10.11 Using data from Figure 4.8 and 4.10 and Appendix 2, calculate the lattice energy of cesium chloride (CsCl). Strategy Using the Born-Haber Cycle Figure as a guide, combine pertinent thermodynamic data and Hess’s law to calculate the lattice energy. Think4.8, About It Compare this value that for NaCl Figure From Figure IE1(Cs) = 376 kJ/mol. FromtoFigure 4.10, EAin1(Cl) = 349.0 -) kJ/mol). Both compounds contain theΔH same anion =(Cl kJ/mol.10.14 From(787 Appendix 2, ΔH °f [Cs(g)] = 76.50 kJ/mol, °f [Cl(g)] 121.7 have cations withkJ/mol. the same chargewe (+1), the relative kJ/mol,and ΔHboth °f [CsCl(s)] = – 422.8 Because areso interested in magnitudes sizes thethe cations willvalues determine thethermodynamic relative strengths ofAnd, their because lattic only, we canofuse absolute of the data. + is larger than Na+, the lattice energy of CsCl energies. only the standardBecause heat of Cs formation of CsCl(s) is a negative number, it is only one is smaller the lattice energy of NaCl. for which the signthan changes. Solution {ΔH °f [Cs(g)] + ΔH °f [Cl(g)] + IE1(Cs) + ΔH °f [CsCl(s)]} – EA1(Cl) = lattice energy = (76.50 kJ/mol + 121.7 kJ/mol + 376 kJ/mol + 422.8 kJ/mol) – 349.0 kJ/mol = 648 kJ/mol 10 1/7/2013 10 Chapter Summary: Key Points Group Quiz #21 Energy and Energy Changes Forms of Energy Energy Changes in Chemical Reactions Units of Energy Introduction to Thermodynamics States and State Functions The First Law of Thermodynamics Work and Heat Enthalpy Reactions Carried Out at Constant Volume or at Constant Pressure Enthalpy and Enthalpy Changes Thermochemical Equations Calorimetry Specific Heat and Heat Capacity Constant-Pressure Calorimetry Constant-Volume Calorimetry Hess’s Law Standard Enthalpies of Formation • A hot piece of copper (at 98.7oC, specific heat = 0.385 J/g•oC) weighs 34.6486 g. When placed in room temperature water, it is calculated that 915.1 J of heat are released by the metal. • What gains heat? • What loses heat? • What is the final temperature of the metal? • Watch signs!!!! System Surroundings Universe = System + Surroundings Group Quiz #23 Group Quiz #22 • Given the following equations: • 2CO2 (g) O2 (g) + 2CO (g) DH = 566.0 kJ • ½ N2 (g) + ½ O2 (g) NO (g) DH = 90.3 kJ • Use Standard Heat of Formation values to calculate the enthalpy of reaction for: • C6H12O6(s) C2H5OH(l) + CO2(g) • Hint: Is the equation balanced? • Calculate the enthalpy change for: • 2CO (g) + 2NO (g) 2CO2 (g) + N2 (g) DH = ? • DHof (C6H12O6(s)) = -1260.0 kJ/mol • DHof (C2H5OH(l)) = -277.7 kJ/mol • DHof (CO2(g)) = -393.5 kJ/mol 63 11