Chemistry: Atoms First Julia Burdge & Jason Overby 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.

Energy is the capacity to do work Radiant energy comes from the sun and is earth’s primary energy source Thermal energy is the energy associated with the random motion of atoms and molecules Chemical energy is the energy stored within the bonds of chemical substances Nuclear energy is the energy stored within the collection of neutrons and protons in the atom Potential energy is the energy available by virtue of an object’s position 6.1

Energy Changes in Chemical Reactions Heat is the transfer of thermal energy between two bodies that are at different temperatures. Temperature is a measure of the thermal energy. 400C Temperature = Thermal Energy 900C greater thermal energy

Energy and Energy Changes 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. heat Surroundings

Energy and Energy Changes 10.1 The system is a part of the universe that is of specific interest. The surroundings constitute the rest of the universe outside the system. The system is usually defined as the substances involved in chemical and physical changes. System Surroundings Universe = System + Surroundings

Energy and Energy Changes An exothermic process occurs when heat is transferred from the system to the surroundings. “Feels hot!” System 2H2(g) + O2(g) 2H2O(l) + energy heat Surroundings Universe = System + Surroundings

Energy and Energy Changes An endothermic process occurs when heat is transferred from the surroundings to the system. “Feels cold” System energy + 2HgO(s) 2Hg(l) + O2(g) heat Surroundings Universe = System + Surroundings

Introduction to Thermodynamics 10.2 Thermodynamics is the study of the interconversion of heat and other kinds of energy. In thermodynamics, there are three types of systems: An open system can exchange mass and energy with the surroundings. A closed system allows the transfer of energy but not mass. An isolated system does not exchange either mass or energy with its surroundings.

Introduction to Thermodynamics State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. The magnitude of change depends only on the initial and final states of the system. Energy Pressure Volume Temperature

The First Law of Thermodynamics The first law of thermodynamics states that energy can be converted from one form to another, but cannot be created or destroyed. 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 = 0 ΔUsys = –ΔUsurr

Work and Heat The overall change in the system’s internal energy is given by: 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 ΔU = q + w

Work and Heat ΔU = q + w

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. 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.

10.4 Calorimetry 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.

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 “object” may be a given quantity of a particular substance. Specific heat capacity has units of J/(g • °C) Heat capacity has units of J/°C Specific heat capacity of water heat capacity of 1 kg water

Specific Heat and Heat Capacity The heat associated with a temperature change may be calculated: m is the mass. S (c) is the specific heat. ΔT is the change in temperature (ΔT = Tfinal – Tinitial). C is the heat capacity. q = msΔT q = CΔT

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 q = 4.184 J g∙°C × 255 g × 65.3°C = 6.97×104 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.

Heat of neutralization: Calorimetry A coffee-cup calorimeter may be used to measure the heat exchange for a variety of reactions at constant pressure: 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) Heat of vaporization: H2O(l) → H2O(g)

The minus sign is used to keep sign conventions consistent. Calorimetry Concepts to consider for coffee-cup calorimetry: qP = nΔH 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 The minus sign is used to keep sign conventions consistent.

Worked Example 10.5 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.

Worked Example 10.5 (cont.) Solution qwater = Thus, qpellet = -3242.6 J From q = CΔT we have -3242.6 J = Cpellet × (-57.1°C) Cpellet = 57 J/°C 4.184 J g∙°C × 125 g × 6.2°C = 3242.6 J 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 is carried out in a device known as a constant-volume bomb. A constant-volume calorimeter is an isolated system. Bomb calorimeters are typically used to determine heats of combustion. qcal = −qrxn

Constant-Volume Calorimetry To calculate qcal, the heat capacity of the calorimeter must be known. qcal = CcalΔT qrxn = −qcal qrxn = −CcalΔT

Qsystem = - Qsurroundings If the system (reaction) gives off heat it is said to be exothermic this means the surroundings get warmer If the system (reaction) takes in heat it is said to be endothermic this means the surroundings get colder

Bomb Calorimetry A device that enables us to measure the heat transfer Between the system and the surroundings When finding the specific heat of a metal Q of the surroundings is equal to the specific heat of the the water X the mass of the water X the change in temperature of the water Q of the metal is equal to –Q of the surroundings Then, the specific heat (c) of the metal is equal to –Q of the surroundings (mass of the metal) X (the change in temp of the metal)

A piece of stainless steel of mass 25. 0 g at 88 A piece of stainless steel of mass 25.0 g at 88.0 °C was placed in a calorimeter that contained 150.0 g of water at 20.0 °C. If the temperature of the water rose to 21.4 °C, what is the specific heat capacity of the stainless steel? The specific heat capacity of water is 4.184 J/ g·°C Ans: 0.53 J/ g ·°C

A piece of graphite of mass 75. 0 g at 92 A piece of graphite of mass 75.0 g at 92.0 °C was placed in a calorimeter that contained 200.0 g of water at 12.0 °C. If the temperature of the water rose to 16.8 °C, what is the specific heat capacity of graphite? The specific heat capacity of water is 4.184 J/ g·°C Ans: 0.71 J/ g·°C

Calculate the heat required to raise the temperature of 50 Calculate the heat required to raise the temperature of 50.0 g of water from 25.0 °C to 39.0 °C. The specific heat capacity of water is 4.184 J/ g·°C Ans: 2.93 kJ

How much heat is absorbed by a 25. 0-g sample of gold at 25 How much heat is absorbed by a 25.0-g sample of gold at 25.0 °C when it is immersed in boiling water? The specific heat capacity of gold is 0.128 J/ g·°C and the specific heat capacity of water is 4.184 J/ g·°C. Ans: 0.240 kJ

A reaction occurs in a calorimeter that contains 120 A reaction occurs in a calorimeter that contains 120.0 g of water at 25.00 °C, and 3.60 kJ of heat is evolved. If the specific heat capacity of water is 4.184 J/ g·°C, what is the final temperature of the water? Ans: 32.17 °C

Bomb Calorimetry and DH Bomb calorimetry can be used to determine the Heat of Reaction (DHrxn) the Heat of formation (DHf) and the Heat of solution (DHsoln) Q of the surroundings is equal to the total mass of the solution X specific heat of the solution X the change in temp of the solution Q of the reaction is equal to – Q of the surroundings Q of the reaction is equal to n DH. Where n is equal to the moles of reaction Therefore DH equals - (mass of soln X D temp of soln X spec. heat of soln) n of reaction

When 5. 00 g of ammonium nitrate are dissolved in 1 When 5.00 g of ammonium nitrate are dissolved in 1.00 L of water in a calorimeter with a heat capacity of 2.30 kJ/ C, the temperature drops 0.760 C. What is the heat of solution of ammonium nitrate? Ans: +28.0 kJ/ mol

If 100 mL of 1. 00 M barium chloride are added to 100 mL of 1 If 100 mL of 1.00 M barium chloride are added to 100 mL of 1.00 M potassium sulfate in a calorimeter with a heat capacity of 1.52 kJ/ C, the temperature rises by 1.73 C. Calculate the heat of reaction for Ba2+(aq) + SO42–(aq)  BaSO4(s) Ans: –26.3 kJ

The standard enthalpy of formation (heat of formation) of H2O2(l) is –187.8 kJ/ mol and of H2O(l) is –285.8 kJ/ mol. (Oxygen is in it’s standard state) Calculate the reaction enthalpy for 2H2O2(l)  2H2O(l) + O2(g) Ans: –196.0 kJ

Chemistry in Action: Fuel Values of Foods and Other Substances C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l) DH = -2801 kJ/mol 1 cal = 4.184 J 1 Cal = 1000 cal = 4184 J

Worked Example 10.6 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 is four cookies, or 29 g, and each serving contains 150 Cal. Convert the energy per gram to Calories per serving to verify the result. 21.5 kJ g × 1 Cal 4.184 kJ 29 g serving = 1.5×102 Cal/serving Strategy Use qrxn = -CcalΔT to calculate the heat released by the combustion of the cookie. Divide the heat released by the mass of the cookie to determine its energy content per gram Ccal = 39.97 kJ/°C and ΔT = 3.90°C. 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 kJ 7.25 g = 21.5 kJ/g

Enthalpy and Enthalpy Changes The enthalpy of reaction (ΔH) is the difference between the enthalpies of the products and the enthalpies of the reactants: Assumes reactions in the lab occur at constant pressure ΔH > 0 (positive) endothermic process ΔH < 0 (negative) exothermic process ΔH = H(products) – H(reactants)

Without looking up the values, What is the standard heat of reaction for 2HN3(g)  H2(g) + 3N2(g) Ans –2 DHf°[HN3(g)]

Thermochemical Equations H2O(s) H2O(l) ΔH = +6.01 kJ/mol Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? ΔH > 0 endothermic

Thermochemical Equations 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

Thermochemical Equations Enthalpy is an extensive property. Extensive properties are dependent on the amount of matter involved. H2O(l) → H2O(g) ΔH = +44 kJ/mol 2H2O(l) → 2H2O(g) ΔH = +88 kJ/mol Double the amount of matter Double the enthalpy Units refer to mole of reaction as written

Thermochemical Equations The following guidelines are useful when considering thermochemical equations: 1) Always specify the physical states of reactants and products because they help determine the actual enthapy changes. CH4(g) + 2O2(g) ΔH = −802.4 kJ/mol CO2(g) + 2H2O(g) different states different enthalpies CH4(g) + 2O2(g) ΔH = +890.4 kJ/mol CO2(g) + 2H2O(l)

Thermochemical Equations 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) ΔH = − 802.4 kJ/mol CO2(g) + 2H2O(g) 2CH4(g) + 4O2(g) ΔH = − 1604.8 kJ/mol 2CO2(g) + 4H2O(g) 3) Reversing an equation changes the sign but not the magnitude of ΔH. CH4(g) + 2O2(g) ΔH = − 802.4 kJ/mol CO2(g) + 2H2O(g) CO2(g) + 2H2O(g) ΔH = +802.4 kJ/mol CH4(g) + 2O2(g)

6H2O(l) + 6CO2(g) → C6H12O6(s) + 6O2(g) ΔH = +2803 kJ/mol Worked Example 10.3 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 75.0 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. 1 mol C6H12O6 180.2 g C6H12O6 = 0.416 mol C6H12O6

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) ΔH = +1.17×103 kJ Therefore, 1.17×103 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. 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.

Hess’s Law 10.5 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) ΔH = −890.4 kJ/mol CO2(g) + 2H2O(l) 2H2O(l) ΔH = +88.0 kJ/mol 2H2O(g) CH4(g) + 2O2(g) ΔH = −802.4 kJ/mol CO2(g) + 2H2O(g) CH4(g) + 2O2(g) Enthalpy ΔH = −802.4 kJ ΔH = −890.4 kJ CO2(g) + 2H2O(g) ΔH = +88.0 kJ CO2(g) + 2H2O(l)

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: 3) Add the ΔH for each step after proper manipulation. 4) Process is useful for calculating enthalpies that cannot be found directly. 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.

Worked Example 10.7 Given the following thermochemical equations, determine the enthalpy change for the reaction NO(g) + O(g) → NO2(g) NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol 3 2 O3(g) → O2(g) ΔH = –142.3 kJ/mol O2(g) → 2O(g) ΔH = +495 kJ/mol 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.

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. 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. These two steps sum to give: NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol 3 2 O2(g) → O3(g) ΔH = +142.3 kJ/mol NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol 1 2 3 2 + O2(g) O2(g) → O3(g) ΔH = +142.3 kJ/mol 1 2 NO(g) + O2(g) → NO2(g) ΔH = –56.6 kJ/mol

Worked Example 10.7 (cont.) 1 2 Solution We then replace 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. Finally, we sum all the steps and add their enthalpy changes. 1 2 O(g) → O2(g) ΔH = –247.5 kJ/mol NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol 3 2 O2(g) → O3(g) ΔH = +142.3 kJ/mol 1 2 + O(g) → O2(g) ΔH = –247.5 kJ/mol NO(g) + O(g) → NO2(g) ΔH = –304 kJ/mol Think About It Double-check the cancellation of identical items–especially where fractions are involved.

The standard enthalpy of formation of NO(g) is +90 The standard enthalpy of formation of NO(g) is +90.3 kJ/ mol and of NO2(g) is +33.2 kJ/ mol. (Oxygen is in It’s standard state) Calculate the reaction enthalpy (heat of reaction) for 2NO(g) + O2(g)  2NO2(g) Ans: –114.2 kJ

The heat of reaction for 3PbO2(s)  Pb3O4(s) + O2(g) is +22.8 kJ/ mol. The standard heat of formation of Pb3O4(s) is –175.6 kJ/ mol. What is the standard heat of formation of PbO2(s)? Ans: –66.1 kJ/mol

The heat of reaction for 2SO3(g)  2SO2(g) + O2(g ) is +198.4 kJ The standard heat of formation of SO2(g) is –296.8 kJ/ mol. What is the standard heat of formation of SO3(g)? Ans: –396.0 kJ/ mol

Calculate the heat of reaction for H2O(l)  H2(g) + ½ O2(g) from the data 2H2(g) + O2(g)  2H2O(l) DH° = –571.6 kJ Ans: +285.8 kJ

For the combustion of methane, DHr = -890 kJ/mol For the combustion of methane, DHr = -890 kJ/mol. What is the heat of reaction for the following reaction? 4H2O(l) + 2CO2(g)  2CH4(g) + 4O2(g) Ans: +1780 kJ

Calculate the heat of reaction for CH4(g) + 4S(s)  CS2(l) + 2H2S(g) from the data C(s) + 2H2(g)  CH4(g) DH° = –74.8 kJ C(s) + 2S(s)  CS2(l) DH° = +87.9 kJ S(s) + H2(g)  H2S(g) DH° = –20.6 kJ Ans: +121.5 kJ

Calculate the heat of reaction for 2PbO(s) + O2(g)  2PbO2(s) from the data 2Pb(s) + O2(g)  2PbO(s) DH° = –435.8 kJ Pb(s) + O2(g)  PbO2(s) DH° = –276.6 kJ Ans: –117.4 kJ

Calculate the heat of reaction for C6H6(l)  3C2H2(g) from the data 2C2H2(g) + 5O2(g)  4CO2(g) + 2H2O(l) DH° = –2600 kJ 2C6H6(l) + 15O2(g)  12CO2(g) + 6H2O(l) DH° = –6536 kJ Ans: +632 kJ

Calculate the heat of reaction for the combustion of methane, CH4(g), CH4(g) + 2O2(g)  CO2(g) + 2H2O(l) from the data C(s) + O2(g)  CO2(g) DH° = –393.5 kJ H2(g) + ½ O2(g)  H2O(l) DH° = –285.8 kJ C(s) + 2H2(g)  CH4(g) DH° = –74.8 kJ Ans: –890.3 kJ

Standard Enthalpies of Formation 10.6 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) CO2(g) ΔH f° = −393.5 kJ/mol Elements in standard states 1 mole of product

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.

Standard Enthalpies of Formation The standard enthalpy of reaction (ΔH °rxn) is defined as the enthalpy of a reaction carried out under standard conditions. aA + bB → cC + dD n and m are the stoichiometric coefficients for the reactants and products. ΔH °rxn = [cΔH f°(C) + dΔH f°(D) ] – [aΔH f°(A) + bΔH f°(B)] ΔH °rxn = ΣnΔH f°(products) – ΣmΔH f°(reactants)

Worked Example 10.8 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)] = –127.0 kJ/mol – (–61.3 kJ/mol) = –65.7 kJ/mol 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 Given the following information, calculate the standard enthalpy of formation of acetylene (C2H2) from its constituent elements: C(graphite) + O2(g) → CO2(g) ΔH °rxn = –393.5 kJ/mol (1) 1 2 H2(g) + O2(g) → H2O(l) ΔH °rxn = –285.5 kJ/mol (2) 2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l) 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)

Worked Example 10.9 (cont.) Solution We multiply Equation (1) and its ΔH °rxn value by 2: We include Equation (2) and its ΔH °rxn value as is: We reverse Equation (3) and divide it by 2 (i.e., multiply through by 1/2): Summing the resulting equations and the corresponding ΔH °rxn values: 2C(graphite) + 2O2(g) → 2CO2(g) ΔH °rxn = –787.0 kJ/mol Think About It Remember that a ΔH °rxn is only a ΔH °f when there is just one product, just one mole produced, and all the reactants are elements in their standard states. 1 2 H2(g) + O2(g) → H2O(l) ΔH °rxn = –285.5 kJ/mol 5 2 2CO2(g) + H2O(l) → C2H2(g) + O2(g) ΔH °rxn = +1299.4 kJ/mol 2C(graphite) + 2O2(g) → 2CO2(g) ΔH °rxn = –787.0 kJ/mol 1 2 H2(g) + O2(g) → H2O(l) ΔH °rxn = –285.5 kJ/mol 5 2 2CO2(g) + H2O(l) → C2H2(g) + O2(g) ΔH °rxn = +1299.4 kJ/mol 2C(graphite) + H2(g) → C2H2(g) ΔH °f = +226.6 kJ/mol

Bond Enthalpy and the Stability of Covalent Molecules 10.7 The bond enthalpy is the enthalpy change associated with breaking a bond in 1 mole of gaseous molecule. The enthalpy for a gas phase reaction is given by: H2(g) → H(g) + H(g) ΔH° = 436.4 kJ/mol ΔH° = ΣBE(reactants) – ΣBE(products) ΔH° = total energy input – total energy released bonds broken bonds formed 67

Bond Enthalpy and the Stability of Covalent Molecules Bond enthalpy change in an exothermic reaction.: 68

Bond Enthalpy and the Stability of Covalent Molecules Bond enthalpy change in an endothermic reaction: 69

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) 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 Use equation ΔH °rxn = ΣnΔH f°(products) – ΣmΔH f°(reactants) and data from Appendix 2 to calculate this 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 enthalpies apply to species in the gas phase, where there is little or no influence exerted by neighboring molecules. Strategy Draw Lewis structures to determine what bonds are to be broken and what bonds are to be formed. Bonds to break: 4 C–H and 2 O=O Bonds to form: 2 C=O and 4 H–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