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General Chemistry: An Integrated Approach Hill, Petrucci, 4th Edition Chapter 6 Thermochemistry Mark P. Heitz State University of New York at Brockport © 2005, Prentice Hall, Inc. Energy Literally means “work within,” however no object contains work Energy refers to the capacity to do work – that is, to move or displace matter 2 basic types of energy: – Potential (possibility of doing work because of composition or position) – Kinetic (moving objects doing work) Chapter 6: Thermochemistry EOS 2 Energy Potential Energy – in a gravitational field (= position) Kinetic Energy – energy of motion PE = mgh m = mass (kg) g = gravity constant (m s–2) h = height (m) KE = 1/2mv2 m = mass (kg) v = velocity (m s–1) v2 = (m2 s–2) units are kg m2 s–2 J units are kg m2 s–2 J EOS Chapter 6: Thermochemistry 3 Work Work is the product of the force in the direction of motion and the distance the object is moved Work = force × distance energy (J) Collisions in the real world are not perfectly elastic Energy transfer occurs as a result of inelastic collisions e.g., the ball loses height EOS Chapter 6: Thermochemistry 4 Thermochemistry System Surroundings Universe Surroundings Thermochemistry is the study of energy changes that occur during chemical reactions Surroundings Focus is on heat and matter transfer between the system ... and the surroundings EOS Chapter 6: Thermochemistry 5 Thermochemistry Types of systems one can study: Matter Matter Energy OPEN Energy Matter Matter Energy Matter Matter Energy CLOSED Energy Energy ISOLATED EOS Chapter 6: Thermochemistry 6 Internal Energy Internal Energy (U) is the total energy contained within the system, partly as kinetic energy and partly as potential energy Kinetic involves three types of molecular motion ... EOS Chapter 6: Thermochemistry 7 Internal Energy Internal Energy (U) is the total energy contained within the system, partly as kinetic energy and partly as potential energy Potential energy involves intramolecular interactions ... and intermolecular interactions ... EOS Chapter 6: Thermochemistry 8 Heat (q) Heat is energy transfer resulting from thermal differences between the system and surroundings “flows” spontaneously from higher T lower T “flow” ceases at thermal equilibrium EOS Chapter 6: Thermochemistry 9 Heat Transfer Mechanism Illustrated Inelastic molecular collisions are responsible for heat transfer EOS Chapter 6: Thermochemistry 10 Heat Transfer Illustrated Chapter 6: Thermochemistry 11 Work (w) Work is an energy transfer between a system and its surroundings Recall from gas laws … the product PV = energy Pressure–volume work is the work of compression (or expansion) of a gas EOS Chapter 6: Thermochemistry 12 Calculating Work (w) PV work is calculated as follows: w = –PDV Sign conventions: think SYSTEM WORK from the perspective of the system If work is done by the system, the system loses energy equal to –w EOS Chapter 6: Thermochemistry 13 Calculating Work (w) SYSTEM WORK Expansion is an example of work done by the system—the weight above the gas is lifted compression (or expansion) of a gas ExpansionWork EOS Chapter 6: Thermochemistry 14 Calculating Work (w) SYSTEM WORK If work is done on the system, the system gains energy equal to +w compression (or expansion) of a gas EOS Chapter 6: Thermochemistry 15 States of a System The state of a system refers to its exact condition, determined by the kinds and amounts of matter present, the structure of this matter at the molecular level, and the prevailing pressure and temperature Example: internal energy (U) is a function of the state of the system ... EOS Chapter 6: Thermochemistry 16 State Functions A state function is a property that has a unique value that depends only on the present state of a system and not on how the state was reached, nor on the history of the system DU = Uf – Ui EOS Chapter 6: Thermochemistry 17 First Law of Thermodynamics The Law of Conservation of Energy states that in a physical or chemical change, energy can be exchanged between a system and its surroundings, but no energy can be created or destroyed The change in U is related to the energy exchanges that occur as heat (q) and work (w) The First Law: DU = q + w EOS Chapter 6: Thermochemistry 18 First Law – Sign Conventions Energy entering a system carries a positive sign: if heat is absorbed by the system, q > 0. If work is done on a system, w > 0 Energy leaving a system carries a negative sign: if heat is given off by the system, q < 0. If work is done by a system, w < 0 EOS Chapter 6: Thermochemistry 19 Heats of Reaction The heat of reaction (qrxn) is the quantity of heat exchanged between the system and its surroundings Examples – for exothermic reactions, in isolated systems, system T in non-isolated systems, heat is given off to the surroundings, i.e., q < 0 – endothermic reactions, in isolated systems, system T in non-isolated systems, heat is absorbed from the surroundings, i.e., q > 0 EOS Chapter 6: Thermochemistry 20 Conceptualizing an Exothermic Reaction Surroundings are at 25 °C 25 °C Typical situation: some heat is released to the surroundings, some heat is absorbed by the solution. Hypothetical situation: all heat is instantly released to the surroundings. Heat = qrxn 32.2 °C 35.4 °C In an isolated system, all heat is absorbed by the solution. Maximum temperature rise. Chapter 6: Thermochemistry 21 Internal Energy Changes w = –PDV and DU = q + w For systems where the reaction is carried out at constant volume, DV = 0 and DU = qV All the thermal energy produced by conversion from chemical energy is released as heat Because the reaction is exothermic, both qV and DU are negative EOS Chapter 6: Thermochemistry 22 Internal Energy Changes w = –PDV and DU = q + w For systems where the reaction is carried out at constant pressure, DU = qP – PDV or qP = DU + PDV Most of the thermal energy is released as heat, but some is work used to expand the system against the surroundings The quantity of heat liberated is somewhat less than in the constantvolume case EOS Chapter 6: Thermochemistry 23 Example 6.2 The internal energy of a fixed quantity of an ideal gas depends only on its temperature. If a sample of an ideal gas is allowed to expand against a constant pressure at a constant temperature, (a) what is ∆U for the gas? (b) Does the gas do work? (c) Is any heat exchanged with the surroundings? Analysis and Conclusions (a) Because the expansion occurs at a constant temperature, the expanded gas (state 2) is at a lower pressure than the compressed gas (state 1) but the temperature is unchanged. Because the internal energy of the ideal gas depends only on the temperature, U2 = U1 and ∆U = U2 – U1 = 0. (b) The gas does work in expanding against the confining pressure, P. The pressure– volume work is w = –P∆V, as was illustrated in Figure 6.8. The work is negative because it is done by the system. (c) The work done by the gas represents energy leaving the system. If this were the only energy exchange between the system and its surroundings, the internal energy of the system would decrease, and so would the temperature. However, because the temperature remains constant, the internal energy does not change. This means that the gas must absorb enough heat from the surroundings to compensate for the work that it does in expanding: q = –w. And, according to the first law of thermodynamics, ∆U = q + w = –w + w = 0. Chapter 6: Thermochemistry 24 Example 6.2 continued Exercise 6.2A In an adiabatic process, a system is thermally insulated from its surroundings so that there is no exchange of heat (q = 0). If an ideal gas undergoes an adiabatic expansion against a constant pressure, (a) does the gas do work? (b) Does the internal energy of the gas increase, decrease, or remain unchanged? (c) What happens to the temperature? a) yes w = - PΔV b) ΔU = q + w = 0 + w = w = - PΔV since ΔV >0, ΔU< 0 c) For an ideal gas U ~ T so if U decreases, T decreases Chapter 6: Thermochemistry 25 Enthalpy Most heats of reaction are measured at constant pressure … it is useful to have a function equal to qP Enthalpy (H) is the sum of the internal energy and the pressure–volume product of a system qP = DH = DU + PDV Enthalpy is an extensive property (depends on how much of the substance is present) Enthalpy is a state function. U, P, and V are all state functions, therefore H must be a state function also EOS Chapter 6: Thermochemistry 26 Enthalpy Diagrams EOS Chapter 6: Thermochemistry 27 Reversing a Reaction • DH changes sign when a process is reversed. • Therefore, a cyclic process has the value DH = 0. Same magnitude; different signs. Chapter 6: Thermochemistry 28 Using DH Values are measured experimentally Negative values indicate exothermic reactions Positive values indicate endothermic reactions Changes sign when a process is reversed. Therefore, a cyclic process has the value DH = 0 For problem-solving, one can view heat being absorbed in an endothermic reaction as being like a reactant and heat being evolved in an exothermic reaction as being like a product EOS Chapter 6: Thermochemistry 29 Calorimetry • We measure heat flow using calorimetry. • A calorimeter is a device used to make this measurement. • A “coffee cup” calorimeter may be used for measuring heat involving solutions. A “bomb” calorimeter is used to find heat of combustion; the “bomb” contains oxygen and a sample of the material to be burned. Chapter 6: Thermochemistry 30 Calorimetry Relationships The heat capacity (C) of a system is the quantity of heat required to change the temperature of the system by 1 oC calculated from C = q/DT units of J oC–1 or J K–1 Specific heat is the heat capacity of a one-gram sample Specific heat = C/m = q/mDT units of J g–1 oC–1 or J g–1 K–1 EOS Chapter 6: Thermochemistry 31 Specific Heats Molar heat capacity is the product of specific heat times the molar mass of a substance units are J mol–1 K–1 A useful form of the specific heat equation is: q = m CDT If DT > 0, then q > 0 and heat is gained by the system If DT < 0, then q < 0 and heat is lost by the system EOS Chapter 6: Thermochemistry 32 Specific Heats EOS Chapter 6: Thermochemistry 33 Hess’s Law of Constant Heat Summation The heat of a reaction is constant, regardless of the number of steps in the process DHoverall = S DH’s of individual reactions When it is necessary to reverse a chemical equation, change the sign of DH for that reaction When multiplying equation coefficients, multiply values of DH for that reaction EOS Chapter 6: Thermochemistry 34 An Enthalpy Diagram EOS Chapter 6: Thermochemistry 35 Standard State Conditions The standard state of a solid or liquid substance is the pure element or compound at 1 atm pressure and the temperature of interest Gaseous standard state is the “ideal gas” at 1 atm pressure and the temperature of interest e.g., at 1 atm, 25 oC standard state for Hg is liquid, C is solid, water is liquid, He is gas EOS Chapter 6: Thermochemistry 36 Standard Enthalpies The standard enthalpy of reaction (DHo) is the enthalpy change for a reaction in which the reactants in their standard states yield products in their standard states The standard enthalpy of formation (DHof) of a substance is the enthalpy change that occurs in the formation of 1 mol of the substance from its elements when both products and reactants are in their standard states EOS Chapter 6: Thermochemistry 37 Standard Enthalpies o of Formation at 25 C EOS Chapter 6: Thermochemistry 38 Calculations Based on Standard Enthalpies of Formation General Expression: DHo = Snp × DHof (products) – Snr × DHof (reactants) Each coefficient is multiplied by the standard enthalpy of formation for that substance The sum of numbers for the reactants is subtracted from the sum of numbers for the products With organic compounds, the measured DHof is often the standard enthalpy of combustion DHocomb EOS Chapter 6: Thermochemistry 39 Standard Enthalpies of Formation of Ions in Aqueous Solution Chapter 6: Thermochemistry 40 Combustion Fuels Fossil Fuels: Coal, Natural Gas, and Petroleum A fuel is a substance that burns with the release of heat These fossil fuels were formed over a period of millions of years from organic matter that became buried and compressed under mud and water EOS Chapter 6: Thermochemistry 41 Respiration Foods Foods: Fuels for the Body The three principal classes of foods are fats, proteins, and carbohydrates 1 Food Calorie (Cal) is equal to 1000 cal (or 1 kcal) EOS Chapter 6: Thermochemistry 42 Summary of Concepts • Thermochemistry concerns energy changes in physical processes or chemical reactions • Thermochemical ideas include the notion of a system and its surroundings; the concepts of kinetic energy, potential energy, and internal energy; and the distinction between two types of energy exchanges: heat (q) and work (w) • Internal energy (U) is a function of state EOS Chapter 6: Thermochemistry 43 Summary of Concepts • Enthalpy (H) is a function based on internal energy, but modified for use with constantpressure processes • The first law of thermodynamics relates the heat and work exchanged between a system and its surroundings to changes in the internal energy of a system • A calorimeter is used to measure quantities of heat EOS Chapter 6: Thermochemistry 44 Summary of Concepts • The concepts of standard state, a standard enthalpy change, and a standard enthalpy of formation are important in thermochemical calculations • Some practical applications of thermochemistry deal with the heats of combustion of fossil fuels and the energy content of foods EOS Chapter 6: Thermochemistry 45