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Chapter 6 Energy Thermodynamics Energy is... • • • • • The ability to do work. Conserved. made of heat and work. a state function. independent of the path, or how you get from point A to B. • Work is a force acting over a distance. • Heat is energy transferred between objects because of temperature difference. 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 3 Energy Potential Energy – in a gravitational field (= position) PE = mgh m = mass (kg) g = gravity constant (m s2) h = height (m) units are kg m2 s–2 J Kinetic Energy – energy of motion KE = 1/2mv2 m = mass (kg) v = velocity (m s– 1) v2 = (m2 s–2) units are kg m2 s–2 =J Chapter 6: Thermochemistry EOS 4 Potential Energy Potential energy is energy an object possesses by virtue of its position or chemical composition. © 2009, Prentice-Hall, Inc. Kinetic Energy Kinetic energy is energy an object possesses by virtue of its motion. 1 KE = mv2 2 © 2009, Prentice-Hall, Inc. Conversion of Energy • Energy can be converted from one type to another. • For example, the cyclist above has potential energy as she sits on top of the hill. © 2009, Prentice-Hall, Inc. Conversion of Energy • As she coasts down the hill, her potential energy is converted to kinetic energy. • At the bottom, all the potential energy she had at the top of the hill is now kinetic energy. © 2009, Prentice-Hall, Inc. Units of Energy • The SI unit of energy is the joule (J). kg m2 1 J = 1 s2 • An older, non-SI unit is still in widespread use: the calorie (cal). 1 cal = 4.184 J © 2009, Prentice-Hall, Inc. The universe • • • • • is divided into two halves. the system and the surroundings. The system is the part you are concerned with. The surroundings are the rest. Exothermic reactions release energy to the surroundings. • Endo thermic reactions absorb energy from the surroundings. Thermochemistry System Surroundings Universe Surroundings Thermochemistry is the study of energy changes that occur during chemical reactions Surroundings Chapter 6: Thermochemistry Focus is on heat and matter transfer between the system ... and the surrounding EOS s 11 Definitions: System and Surroundings • The system includes the molecules we want to study (here, the hydrogen and oxygen molecules). • The surroundings are everything else (here, the cylinder and piston). © 2009, Prentice-Hall, Inc. Thermochemistry Types of systems one can study: Matter Matter Energy OPEN Energy Matter Matter Energy Energy CLOSED Matter Matter Energy Energy ISOLATED EOS Chapter 6: Thermochemistry 13 Definitions: Work • Energy used to move an object over some distance is work. • w=Fd where w is work, F is the force, and d is the distance over which the force is exerted. © 2009, Prentice-Hall, Inc. 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 15 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 16 Heat • Energy can also be transferred as heat. • Heat flows from warmer objects to cooler objects. © 2009, Prentice-Hall, Inc. 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 18 Potential energy CH 4 + 2O 2 CO 2 + 2H 2 O + Heat CH 4 + 2O 2 Heat CO 2 + 2 H 2 O N 2 + O 2 + heat 2NO Potential energy 2NO Heat N2 + O2 Same rules for heat and work • Heat given off is negative. • Heat absorbed is positive. • Work done by system on surroundings is positive. • Work done on system by surroundings is negative. • Thermodynamics- The study of energy and the changes it undergoes. 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 Chapter 6: Thermochemistry EOS 22 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 23 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 24 What is work? • • • • • • Work is a force acting over a distance. w= F x Dd P = F/ area d = V/area w= (P x area) x D (V/area)= PDV Work can be calculated by multiplying pressure by the change in volume at constant pressure. • units of liter - atm L-atm Work needs a sign • If the volume of a gas increases, the system has done work on the surroundings. • work is negative • w = - PDV • Expanding work is negative. • Contracting, surroundings do work on the system w is positive. • 1 L atm = 101.3 J Examples • What amount of work is done when 15 L of gas is expanded to 25 L at 2.4 atm pressure? • If 2.36 J of heat are absorbed by the gas above. what is the change in energy? • How much heat would it take to change the gas without changing the internal energy of the gas? Surroundings System Energy DE <0 Surroundings System Energy DE >0 Direction • 1. 2. 3. • • Every energy measurement has three parts. A unit ( Joules of calories). A number how many. and a sign to tell direction. negative - exothermic positive- endothermic First Law of Thermodynamics • Energy is neither created nor destroyed. • In other words, the total energy of the universe is a constant; if the system loses energy, it must be gained by the surroundings, and vice versa. © 2009, Prentice-Hall, Inc. First Law of Thermodynamics • • • • • • The energy of the universe is constant. Law of conservation of energy. q = heat w = work DE = q + w Take the systems point of view to decide signs. Internal Energy The internal energy of a system is the sum of all kinetic and potential energies of all components of the system; we call it E. © 2009, Prentice-Hall, Inc. Internal Energy By definition, the change in internal energy, DE, is the final energy of the system minus the initial energy of the system: DE = Efinal − Einitial © 2009, Prentice-Hall, Inc. Changes in Internal Energy • When energy is exchanged between the system and the surroundings, it is exchanged as either heat (q) or work (w). • That is, DE = q + w. © 2009, Prentice-Hall, Inc. DE, q, w, and Their Signs © 2009, Prentice-Hall, Inc. Exchange of Heat between System and Surroundings • When heat is absorbed by the system from the surroundings, the process is endothermic. © 2009, Prentice-Hall, Inc. Exchange of Heat between System and Surroundings • When heat is absorbed by the system from the surroundings, the process is endothermic. • When heat is released by the system into the surroundings, the process is exothermic. © 2009, Prentice-Hall, Inc. 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 39 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 40 State Functions • However, we do know that the internal energy of a system is independent of the path by which the system achieved that state. – In the system below, the water could have reached room temperature from either direction. © 2009, Prentice-Hall, Inc. State Functions • Therefore, internal energy is a state function. • It depends only on the present state of the system, not on the path by which the system arrived at that state. • And so, DE depends only on Einitial and Efinal. © 2009, Prentice-Hall, Inc. State Functions • However, q and w are not state functions. • Whether the battery is shorted out or is discharged by running the fan, its DE is the same. – But q and w are different in the two cases. © 2009, Prentice-Hall, Inc. • • • • Enthalpy Symbol is H Change in enthalpy is DH delta H If heat is released the heat content of the products is lower • DH is negative (exothermic) • If heat is absorbed the heat content of the products is higher • DH is positive (endothermic) 44 Enthalpy • If a process takes place at constant pressure (as the majority of processes we study do) and the only work done is this pressurevolume work, we can account for heat flow during the process by measuring the enthalpy of the system. • Enthalpy is the internal energy plus the product of pressure and volume: H = E + PV © 2009, Prentice-Hall, Inc. Enthalpy • • • • abbreviated H H = E + PV (that’s the definition) at constant pressure. DH = DE + PDV • the heat at constant pressure qp can be calculated from • DE = qp + w = qp - PDV • qp = DE + P DV = DH Enthalpy • Since DE = q + w and w = -PDV, we can substitute these into the enthalpy expression: DH = DE + PDV DH = (q+w) − w DH = q • So, at constant pressure, the change in enthalpy is the heat gained or lost. © 2009, Prentice-Hall, Inc. Endothermicity and Exothermicity • A process is endothermic when DH is positive. © 2009, Prentice-Hall, Inc. Endothermicity and Exothermicity • A process is endothermic when DH is positive. • A process is exothermic when DH is negative. © 2009, Prentice-Hall, Inc. Enthalpy of Reaction The change in enthalpy, DH, is the enthalpy of the products minus the enthalpy of the reactants: DH = Hproducts − Hreactants © 2009, Prentice-Hall, Inc. Enthalpy of Reaction This quantity, DH, is called the enthalpy of reaction, or the heat of reaction. © 2009, Prentice-Hall, Inc. The Truth about Enthalpy 1. Enthalpy is an extensive property. 2. DH for a reaction in the forward direction is equal in size, but opposite in sign, to DH for the reverse reaction. 3. DH for a reaction depends on the state of the products and the state of the reactants. © 2009, Prentice-Hall, Inc. Calorimetry Calorimetry is a technique used to measure heat exchange in chemical reactions A calorimeter is the device used to make heat measurements Calorimetry is based on the law of conservation of energy EOS Chapter 6: Thermochemistry 53 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 54 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 55 Calorimetry • • • • Measuring heat. Use a calorimeter. Two kinds Constant pressure calorimeter (called a coffee cup calorimeter) • heat capacity for a material, C is calculated • C= heat absorbed/ DT = DH/ DT • specific heat capacity = C/mass Calorimetry • • • • • • • • molar heat capacity = C/moles heat = specific heat x m x DT heat = molar heat x moles x DT Make the units work and you’ve done the problem right. A coffee cup calorimeter measures DH. An insulated cup, full of water. The specific heat of water is 1 cal/gºC Heat of reaction= DH = sh x mass x DT Heat Capacity and Specific Heat The amount of energy required to raise the temperature of a substance by 1 K (1C) is its heat capacity. © 2009, Prentice-Hall, Inc. Heat Capacity and Specific Heat We define specific heat capacity (or simply specific heat) as the amount of energy required to raise the temperature of 1 g of a substance by 1 K. © 2009, Prentice-Hall, Inc. Heat Capacity and Specific Heat Specific heat, then, is Specific heat = s= heat transferred mass temperature change q m DT © 2009, Prentice-Hall, Inc. Examples • The specific heat of graphite is 0.71 J/gºC. Calculate the energy needed to raise the temperature of 75 kg of graphite from 294 K to 348 K. • A 46.2 g sample of copper is heated to 95.4ºC and then placed in a calorimeter containing 75.0 g of water at 19.6ºC. The final temperature of both the water and the copper is 21.8ºC. What is the specific heat of copper? Calorimetry • Constant volume calorimeter is called a bomb calorimeter. • Material is put in a container with pure oxygen. Wires are used to start the combustion. The container is put into a container of water. • The heat capacity of the calorimeter is known and tested. • Since DV = 0, PDV = 0, DE = q Constant Pressure Calorimetry By carrying out a reaction in aqueous solution in a simple calorimeter such as this one, one can indirectly measure the heat change for the system by measuring the heat change for the water in the calorimeter. © 2009, Prentice-Hall, Inc. Constant Pressure Calorimetry Because the specific heat for water is well known (4.184 J/g-K), we can measure DH for the reaction with this equation: q = m s DT © 2009, Prentice-Hall, Inc. Bomb Calorimeter • thermometer • stirrer • full of water • ignition wire • Steel bomb • sample Properties • intensive properties not related to the amount of substance. • density, specific heat, temperature. • Extensive property - does depend on the amount of stuff. • Heat capacity, mass, heat from a reaction. Hess’s Law • Enthalpy is a state function. • It is independent of the path. • We can add equations to to come up with the desired final product, and add the DH • Two rules • If the reaction is reversed the sign of DH is changed • If the reaction is multiplied, so is DH Hess’s Law Hess’s law states that “[i]f a reaction is carried out in a series of steps, DH for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps.” © 2009, Prentice-Hall, Inc. Hess’s Law Because DH is a state function, the total enthalpy change depends only on the initial state of the reactants and the final state of the products. © 2009, Prentice-Hall, Inc. H (kJ) O2 NO2 -112 kJ 180 kJ N2 2O2 NO2 68 kJ 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 71 Standard Enthalpy • The enthalpy change for a reaction at standard conditions (25ºC, 1 atm , 1 M solutions) • Symbol DHº • When using Hess’s Law, work by adding the equations up to make it look like the answer. • The other parts will cancel out. Standard Enthalpies of Formation Standard enthalpies of formation, DHf°, are measured under standard conditions (25 °C and 1.00 atm pressure). © 2009, Prentice-Hall, Inc. Calculation of DH C3H8 (g) + 5 O2 (g) 3 CO2 (g) + 4 H2O (l) DH = [3(-393.5 kJ) + 4(-285.8 kJ)] – [1(-103.85 kJ) + 5(0 kJ)] = [(-1180.5 kJ) + (-1143.2 kJ)] – [(-103.85 kJ) + (0 kJ)] = (-2323.7 kJ) – (-103.85 kJ) = -2219.9 kJ © 2009, Prentice-Hall, Inc. Example 5 • Given C 2 H 2 (g) + O 2 (g) 2CO 2 (g) + H 2 O( l) 2 DHº= -1300. kJ C(s) + O 2 (g) CO 2 (g) DHº= -394 kJ 1 H 2 (g) + O 2 (g) H 2 O(l) 2 DHº= -286 kJ calculate DHº for this reaction 2C(s) + H (g) C H (g) 2 2 2 Example Given O 2 (g) + H 2 (g) 2OH(g) DHº= +77.9kJ O 2 (g) 2O(g) DHº= +495 kJ H 2 (g) 2H(g) DHº= +435.9kJ Calculate DHº for this reaction O(g) + H(g) OH(g) Standard Enthalpies of Formation • Hess’s Law is much more useful if you know lots of reactions. • Made a table of standard heats of formation. The amount of heat needed to for 1 mole of a compound from its elements in their standard states. • Standard states are 1 atm, 1M and 25ºC • For an element it is 0 • There is a table in Appendix 4 (pg A22) Standard Enthalpies of Formation • Need to be able to write the equations. • What is the equation for the formation of NO2 ? • ½N2 (g) + O2 (g) NO2 (g) • Have to make one mole to meet the definition. • Write the equation for the formation of methanol CH3OH. Since we can manipulate the equations • We can use heats of formation to figure out the heat of reaction. • Lets do it with this equation. • C2H5OH +3O2(g) 2CO2 + 3H2O • which leads us to this rule. Since we can manipulate the equations • We can use heats of formation to figure out the heat of reaction. • Lets do it with this equation. • C2H5OH +3O2(g) 2CO2 + 3H2O • which leads us to this rule. ( DH of products) - ( DH of reactants) = DH o 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 DHo f is often the standard enthalpy of combustion DHocomb Chapter 6: Thermochemistry EOS 81