Chapter 5 Thermochemistry Definitions • Thermochemistry - the study of how energy in the form of heat is consumed and produced by chemical reactions. • Thermochemical Reaction: Example H2(g) + O2(g) 2 H2O (l) + heat • Energy is anything having the capacity to do work or to transfer heat. • Work is Force X Distance • Thermodynamics The study of energy and its transformation from one form to another. Energy Examples Definition-Energy is anything with the capacity to do work, or create heat. • Food • Gasoline • Electricity • An apple on a tree • A baseball moving Energy Units Units of Energy Joules = kg(m/s)2 Calories, an older unit; the energy to increase one gram of water one deg. C Calories, unit of food energy = kcal Definitions Continued • Heat is energy transferred between objects because of a difference in their temperatures. • Thermodynamics is the study of relationship between chemical reactions and changes in heat energy. • Heat transfer is the process of heat energy flowing from one object into another Two Types of Energy Potential: due to position or composition - can be converted to work PE = mgh (m = mass, kg, g = force of gravity(9.8m/s2), and h = vertical distance in meters) • These units multiplied together = joule • (chemical energy is a form of potential energy) • Kinetic: due to motion of the object KE = 1/2 mv 2 (m = mass(kg), v = velocity(m/s)) • These units multiplied together also equal a joule • Joule = kg(m/s)2 Kinetic vs. Potential Energy Potential Energy: A State Function • Depends only on the present state of the system - not how it arrived there. • It is independent of pathway. Other State Functions? Heat (a form of energy)? Work? Altitude? Altitude? Other State Functions? Heat (a form of energy)? Yes, not path dependent Work? Altitude? Other State Functions? Heat (a form of energy)? Yes, not path dependent Work? No, work depends on path Altitude? Other State Functions? Heat (a form of energy)? Yes, not path dependent Work? No, work depends on path Altitude? Yes, does not depend on path Enthalpy ΔH,? Other State Functions? Heat (a form of energy)? Yes, not path dependent Work? No, work depends on path Altitude? Yes, does not depend on path Enthalpy ΔH,? Yes, does not depend on path The Nature of Energy • Energy is conserved: Law of Conservation of Energy states that energy cannot be created nor destroyed, but converted from one form to another Energy at the Molecular Level Kinetic energy at the molecular level depends on the mass and velocity of the particle but because its velocity depends on temperature KE does too. • As temperature increases then the KE of the same will increase. One of the most important forms of potential energy at the atomic-molecular level arises from electrostatic interactions. Potential can be converted into kinetic • Example: an apple falling from a tree Electrostatic Potential Energy Coulombic attraction, not gravitational force, determines the potential energy of matter at the atomic level. Q1 x Q2 Eel d is the electrostatic potential energy • Eel • Q is the charge in coulombs • d is the distance between particles Electrostatic Potential Energy Bond length Energy of an ionic bond Bonds contain potential energy Energy required to break bonds Energy released when bonds are created Crystal Lattice of NaCl Ionic compounds do not exist as discrete molecules. Instead they exist as crystals where ions of opposite charges occupy positions known as lattice sites. In an ionic compound the ions organize in such a way as to minimize repulsive and maximize attractive forces. - + + - The arrangement of charged particles in a covalent bond organized in such a way as to minimize repulsive and maximize attractive forces to give the lowest potential energy. Terms Describing Energy Transfer • System: the part of the universe that is the focus of a thermodynamic study. Example a beaker or test tube in the lab • Surroundings: everything in the universe that is not part of the system. • Universe = System + Surroundings • An isolated system exchanges neither energy nor matter with the surroundings. Examples Heat Flow • In an exothermic process, heat flows from a system into its surroundings. • In an endothermic process, heat flows from the surroundings into the system Phase Changes Internal Energy • The internal energy of a system is the sum of all the KE and PE of all of the components of the system. First Law of Thermodynamics • The first law of thermodynamics states that the energy gained or lost by a system must equal the energy lost or gained by surroundings. ΔE = q + w (mathematical statement) • The calorie (cal) is the amount of heat necessary to raise the temperature of 1 g of water 1oC. • The joule (J) is the SI unit of energy; 4.184 J = 1 cal. Energy Flow Diagrams Change in Internal Energy E = q + w E = change in system’s internal energy q = heat Endothermic +q Exothermic -q Expansion –w (since system is losing energy to do work) Compression +w First Law Problem Find the change in energy of a system when 12 j of energy flows into the system while the system is doing 8 j of work on the surroundings. First Law Problem Find the change in energy of a system when 12 j of energy flows into the system while the system is doing 8 j of work on the surroundings. ΔE = q + w ↔ ΔE = + 12 – 8 = 4 j PV Work Expansion Atm = 14 Facts lb/in2 A A h W=Fxd P = F/A F = PA W = PA x d ΔV = A x d W = P ΔV ΔV = Vfinal – Vinitial PV Work Facts Expansion A ΔV = Vfinal – Vinitial h ΔV = A x d W=Fxd P = F/A Since expansion is defined as negative work and ΔV is positive for expansion, then we change the sign of PΔV to –PΔV, ΔE = q - PΔV F = PA Substituting W = PxAxd W = PΔV PV Work Facts Expansion A h ΔV = Vfinal – Vinitial ΔV = A x d W=Fxd P = F/A Since expansion is defined as negative work and ΔV is positive for expansion, then we change the sign of PΔV to – PΔV, ΔE = q - PΔV (L-atm = 101.3 j) F = PA Substituting W = PxAxd W = PΔV Calculation of Work Calculate the work in L•atm and joules associated with the expansion of a gas in a cylinder from 54 L to 72 L at a constant external pressure of 18 atm (Note that as the gas expands, it does work on its surroundings. Energy flows out of the gas, so it is a negative quantity) Calculation of Work Calculate the work in L•atm and joules associated with the expansion of a gas in a cylinder from 54 L to 72 L at a constant external pressure of 18 atm (Note that as the gas expands, it does work on its surroundings. Energy flows out of the gas, so it is a negative quantity) W = -pΔV W = -18atm(72-54)L = -320L-atm -320L-atm j 101.3 L-atm = -3.2 j Calculation of Work Calculate the work in L•atm and joules associated with the expansion of a gas in a cylinder from 54 L to 72 L at a constant external pressure of 18 atm (Note that as the gas expands, it does work on its surroundings. Energy flows out of the gas, so it is a negative quantity) Note: The result is W = -pΔV W = -18atm(72-54)L = -320L-atm -320L-atm j 101.3 L-atm = -3.2 j negative, which we would predict relative to expansion. This is the reason that work is pΔV, to give the correct sign for expansion. Enthalpy and Change in Enthalpy • • • • • Enthalpy (H) = E + PV ( mathematical definition) Change in Enthalpy (H) = E + PV At constant P, qP = E + PV, therefore qP = H H = change in enthalpy: an energy flow as heat (at constant pressure) H > 0, Endothermic; H < 0, Exothermic Heating Curves Heat Capacities • Molar heat capacity (cp) is the heat required to raise the temperature of 1 mole of a substance by 1oC at constant pressure. • q = ncpT • Specific heat (cs) is the heat required to raise the temperature of 1 gram of a substance by 1oC at constant pressure. • Heat capacity (Cp) is the quantity of heat needed to raise the temperature of some specific object by 1oC at constant pressure. Phase Change and Energy • Molar heat of fusion (Hfus) - the heat required to convert 1 mole of a solid substance at its melting point to 1 mole of liquid. • q = nHfus • Molar heat of vaporization (Hvap) - the heat required to convert 1 mole of a substance at its boiling point to 1 mole of vapor. • q = nHvap WATER THERMO VALUES • • • • • Ice H2O (s) 2.06 j/g-°C Water H2O (l) 4.184 j/g-°C Steam H2O (g) 1.86 j/g-°C Heat of Fusion (melting) 334.0 j/g Heat of vaporization (evaporation) 2257 j/g Practice During a strenuous workout, a student generates 2000 kJ of heat energy. What mass of water would have to evaporate from the student’s skin to dissipate this much heat? Practice During a strenuous workout, a student generates 2000 kJ of heat energy. What mass of water would have to evaporate from the student’s skin to dissipate this much heat? g 2257 j Practice During a strenuous workout, a student generates 2000 kJ of heat energy. What mass of water would have to evaporate from the student’s skin to dissipate this much heat? g 2257 j 10 3 j kj Practice During a strenuous workout, a student generates 2000 kJ of heat energy. What mass of water would have to evaporate from the student’s skin to dissipate this much heat? g 2257 j 10 3 j kj 2000 kj Practice During a strenuous workout, a student generates 2000 kJ of heat energy. What mass of water would have to evaporate from the student’s skin to dissipate this much heat? g 2257 j 10 3 j kj 2000 kj = 886 g water Practice 5.53 From Text Exactly 10 mL of water at 25oC was added to a hot iron skillet. All of the water was converted into steam at 100oC. If the mass of the pan was 1.20 kg and the molar heat capacity of iron is 25.19 J/mol•oC, what was the temperature change of the skillet? Sample Problem Solution mole-°C 25.19 j Sample Problem Solution mole-°C 55.85 g 25.19 j mole Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j g-°C Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g g-°C Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g 75 °C g-°C Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g 75 °C = 3138 j g-°C Evaporating 10.0 mL of water Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g 75 °C = 3138 j g-°C Evaporating 10.0 mL of water 2257 j g Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g 75 °C = 3138 j g-°C Evaporating 10.0 mL of water 2257 j 10.0 g g Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g 75 °C = 3138 j g-°C Evaporating 10.0 mL of water 2257 j 10.0 g =22570 j g Sample Problem Solution mole-°C 55.85 g kg 25.19 j mole 103 g 1.20 kg Now the energy required to heat 10mL of water from 25°C to 100°C and then to vaporize the water is outlined below. Heating from 25°C to 100°C 4.184 j 10.0g 75 °C = 3138 j g-°C Now Combine Evaporating 10.0 mL of water 3138 j + 22570 j = 25708j 2257 j 10.0 g =22570 j g Sample Problem Solution mole-°C 55.85 g kg 25708 j 25.19 j mole 103 g 1.20 kg = 47.5 °C Heat of Reaction Heat of reaction is also known as enthalpy of reaction (Hrxn) is the heat absorbed or released by a chemical reaction. A Specific Enthalpy • The standard enthalpy of formation (Hfo) is also called the standard heat of formation and is the enthalpy change of the a formation reaction. • A formation reaction is the process of forming 1 mole of a substance in its standard state from its component elements in their standard states. • H2(g) + 1/2 O2(g) ---> H2O(l) Hfo for water • The standard state of a substance is its most stable form under 1 bar pressure and 25oC. Methods of Determining Hrxn 1. from calorimetry experiments 2. from enthalpies of formation 3. using Hess’s Law Calorimetry • Calorimetry is the measurement of the change in heat that occurs during a physical change or chemical process. • A calorimeter is the device used to measure the absorption or release of heat by a physical or chemical process. Measuring Heat Capacity -qaluminum = qwater; qwater = ncpT and -qaluminum = ncsT Calorimetry: Bomb Calorimeter • H = -qcal = -CcalT • A bomb calorimeter is a constant-volume device used to measure the heat of a combustion reaction. Practice Write the standard enthalpy of formation reaction for nitric acid. Practice Write the standard enthalpy of formation reaction for nitric acid. Standard enthalpy, ΔH°, is the change in energy when elements, in their standard state (25°C and 1 atm) combine to make 1 mole of products at their standard state. Calculating Hrxn° • Hrxn° = npHf(products) nrHf(reactants) Calculating Hrxn° • Hrxn° = npHf(products) nrHf(reactants) ½ N2 (g) + ½ H2 (g) + 3/2 O2 (g) HNO3 (l) Calculating Hrxn° • Hrxn° = npHf(products) nrHf(reactants) 1/2(0.00) ½(0.00) 3/2(0.0) ½ N2 (g) + ½ H2 (g) + 3/2 O2 (g) 1(-135.1 kj) HNO3 (l) Calculating Hrxn° • Hrxn° = npHf(products) nrHf(reactants) 1/2(0.00) ½(0.00) 3/2(0.0) ½ N2 (g) + ½ H2 (g) + 3/2 O2 (g) 1(-135.1 kj) HNO3 (l) ΔH°rxn = [1(-135.1 kj)] – [1/2(0.00) + 1/2(0.00) + 3/2(0.0)] ΔH°rxn = - 135.1 kj Example Use Table 5.2 to calculate an approximate enthalpy of reaction for CH4(g) + 2O2(g) ---> CO2(g) + 2H2O(l) Practice One step in the production of nitric acid is the combustion of ammonia. Using the data in the appendix to calculate the enthalpy of this reaction. 4NH3(g) + 5O2(g) ---> 4NO(g) + 6H2O(g) Fuel Values Molecular Formula Fuel Value (kJ/g)* Methane CH4 50.0 Ethane C2H6 47.6 Propane C3H8 46.3 Butane C4H10 45.8 Compound * Based on the formation of H2O (g) Hess’s Law • Hess’s law states that the enthalpy change of a reaction that is the sum of two or more reactions is equal to the sum of the enthalpy changes of the constituent reactions. Calculations via Hess’s Law 1. If a reaction is reversed, H sign changes. N2(g) + O2(g) 2NO(g) H = 180 kJ 2NO(g) N2(g) + O2(g) H = 180 kJ 2. If the coefficients of a reaction are multiplied by an integer, H is multiplied by that same integer. 6NO(g) 3N2(g) + 3O2(g) H = 540 kJ Example Calculate the enthalpy change for C2H4(g) + H2(g) C2H6(g) using the following data. H2(g) + 1/2O2(g) C2H4(g) + 3O2(g) C2H6(g) + 7/2O2(g) H2O(l) -285.8 kJ 2H2O(l) + 2CO2(g) -1411 kJ 3H2O(l) + 2CO2(g) -1560 kJ Example Calculate the enthalpy change for C2H4(g) + H2(g) C2H6(g) using the following data. H2(g) + 1/2O2(g) C2H4(g) + 3O2(g) 3H2O(l) + 2CO2(g) H2O(l) -285.8 kJ 2H2O(l) + 2CO2(g) -1411 kJ C2H6(g) + 7/2O2(g) +1560 kJ H2(g) +1/2O2(g)+C2H4(g)+3O2(g)+3H2O(l)+2CO2(g) H2O(l)+ 2H2O(l) + 2CO2(g)+ C2H6(g) + 7/2O2(g) -136.8 simplify C2H4(g) + H2(g) C2H6(g) -136.8 kj Review ChemTour: State Functions and Path Functions Click to launch animation PC | Mac This ChemTour defines and explores the difference between state and path functions using a travel analogy that leads into a discussion of energy, enthalpy, heat, and work. ChemTour: Internal Energy Click to launch animation PC | Mac This ChemTour explores how energy is exchanged between a system and its surroundings as heat and/or work, and how this transfer in turn affects the internal energy (E) of a system. ChemTour: Pressure-Volume Work Click to launch animation PC | Mac An animated ChemTour of an internal combustion engine shows how a system undergoing an exothermic reaction can do work on its surroundings; students can explore the relationship among pressure, volume, and work. ChemTour: Heating Curves Click to launch animation PC | Mac In this ChemTour, students use interactive heating curve diagrams to explore phase changes, heat of fusion, and heat of vaporization. Macroscopic views of ice melting and water boiling are shown in sync with the appropriate sections of the heating curve. ChemTour: Calorimetry Click to launch animation PC | Mac This ChemTour demonstrates how a bomb calorimeter works, and walks students through the equations used to solve calorimetry problems. Includes an interactive experiment. ChemTour: Hess’s Law Click to launch animation PC | Mac This ChemTour explains Hess’s law of constant heat of summation using animated sample problems and step-bystep descriptions. An ideal gas in a sealed piston is allowed to expand isothermally (at a constant temperature) against a pressure of 1 atm. In what direction, if at all, does heat flow for this process? A) into the system B) out of the system Isothermal Expansion of Ideal Gas C) heat does not flow Consider the following arguments for each answer and vote again: A. When the gas expands isothermally, it does work without a decrease in its energy, so heat must flow into the system. B. During the expansion, the gas pressure decreases, thereby releasing heat to the surroundings. C. The fact that the process is isothermal means that heat does not flow. Isothermal Expansion of Ideal Gas When air is released from a tire does it get warmer or cooler? When air is released from a tire does it get warmer or cooler? Cooler Isothermal means that the temperature is unchanged, so what must happen for the temperature to remain the same? When air is released from a tire does it get warmer or cooler? Cooler Isothermal means that the temperature is unchanged, so what must happen for the temperature to remain the same? Heat must flow into the tire An ideal gas in an insulated piston is compressed adiabatically (q = 0) by its surroundings. What can be said of the change in the temperature (ΔT) of the gas for this process? A) ΔT > 0 Adiabatic Compression of an Ideal Gas B) ΔT = 0 C) ΔT < 0 Consider the following arguments for each answer and vote again: A. The surroundings are doing work on the system, and no heat is flowing. Therefore, ΔE > 0 and so ΔT > 0. B. The volume of the gas decreases, but the pressure increases to keep the product of the pressure and volume constant. Therefore, the temperature is also constant. C. The gas is being compressed to a more ordered state, which corresponds to a lower temperature. Adiabatic Compression of an Ideal Gas Consider a stretched rubber band that is suddenly released. What can be said of the change in the temperature (ΔT) of the rubber band for this process? A) ΔT > 0 ΔT of a Released Rubber Band B) ΔT = 0 C) ΔT < 0 Consider the following arguments for each answer and vote again: A. The stretched rubber band is at a higher energy state than the unstretched rubber band. Releasing the stretched rubber band causes the energy to be released. B. Because the recoil of the rubber band is rapid, this process is essentially adiabatic. Therefore, the temperature of the rubber band will not change. C. As the rubber band contracts, it does work and its energy decreases, resulting in a decrease in its temperature. ΔT of a Released Rubber Band A 1.0 gram block of Al (cs = 0.9 J/·°C1·g) at 100 °C and a 1.0 gram block of Fe (cs = 0.4 J/·°C-1·g) at 0 °C are added to 10 mL of water (cs = 4.2 J·/°C-1·g) at 50 °C. What will be the final temperature of the water? A) < 50 °C Specific Heat Capacity of Al and Fe B) 50 °C C) > 50 °C Consider the following arguments for each answer and vote again: A. The specific heat capacity of Fe(s) is smaller than that of Al(s), so heat from both the Al(s) and the water will be required to warm the Fe(s). B. The average initial temperature of the three components is 50 °C. Therefore, the final temperature of the water will be 50 °C. C. The specific heat capacity of Al(s) is greater than that of Fe(s), so the Al block at 100 °C will heat the water more than the Fe block will cool it. Specific Heat Capacity of Al and Fe This is called a first law problem (energy cannot be created nor destroyed), and a mathematical statement would be – q = q. Remember q is measured in joules, so – j = + j This is called a first law problem (energy cannot be created nor destroyed), and a mathematical statement would be – q = q. Remember q is measured in joules, so – j = + j Since the heat capacity of aluminum is twice that of carbon, then it will lose more heat than iron will gain. This means more heat is lost by the aluminum than gained by the iron. Therefore, the water will increase in temperature and the resultant temperature will be greater than 50°C. Cyclooctatetraene, C8H8, can undergo a transformation between two possible states, A and B, by rearranging its 4 double bonds. Which of the following graphs depicts the dependence of the equilibrium constant (K) on temperature for the conversion from state A to state B? A) B) Equilibium Constant of Cyclooctatetraene C) Consider the following arguments for each answer and vote again: A. The intermediate is at a higher energy state than either states A or B, so at high temperatures, the reaction will favor the intermediate and K will decrease. B. The enthalpies of formation for states A and B are equal, so ΔH° = 0 and K is not temperature dependent. C. At high temperatures, the conversion from state A to state B will occur at a much faster rate, thus increasing the value of K. Equilibium Constant of Cyclooctatetraene The reaction of N2(g) and O2(g) to form N2O(g) is an endothermic process. The reaction of N2(g) and H2(g) to form NH3(g) is an exothermic process. Given this information, which of the following species has the lowest enthalpy of formation, ? A) N2(g) Enthalpies of N , NH , and N O B) NH3(g) C) N2O(g) Consider the following arguments for each answer and vote again: A. N2(g) is the elemental form of nitrogen, which by definition will have H f= 0, the lowest possible enthalpy of formation. B. N2O(g) has a higher H f than N2(g), O2(g), and H2(g), whereas NH3(g) has a lower H f than N2(g), O2(g), and H2(g). C. The formation of an N−N double bond and a N−O double bond, as found in N2O, releases more energy than does the creation of 3 N−H bonds to form NH3(g). Enthalpies of N , NH , and N 0 Which of the following is true of ΔH° for the polymerization of ethylene to form polyethylene? Note: the C-C single bond enthalpy is ~350 kJ/mole and the C-C double bond enthalpy is ~600 kJ/mole. A) ΔH° > 0 Polymerization of Ethylene B) ΔH° = 0 C) ΔH° < 0 Consider the following arguments for each answer and vote again: A. The energy required to break double bonds is more than the energy released by forming new single bonds. B. The total number of C-C bonds (if we count double bonds twice) does not change with polymerization. Therefore, there can be no change in ΔH°. C. For each C-C double bond that breaks (~600 kJ/mole), two single bonds form, (2×~350 = ~700 kJ/mole). Polymerization of Ethylene THE END