Thermodynamics and Thermochemistry Thermodynamics concerns itself with energy and its relationship to the large scale bulk properties of a system that are measurable: Volume, Temperature, Pressure, Heat Capacity, Density etc. Thermodynamics describes the behaviour of matter and the transformation between different forms of energy on a macroscopic scale (i.e. large collections of molecules, not individual molecules). Thermochemistry is a branch of thermodynamics that investigates the flow of energy into or out of a reaction system. From this, we can deduce the energy stored in chemical bonds. *The products of a chemical reaction aren t only the new molecules that are formed. Energy can also be released or consumed - the most important/salient feature of many reactions. Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, it doesn't bother you any more. Arnold Sommerfeld A theory is the more impressive the greater the simplicity of its premises, the more varied the kinds of things that it relates and the more extended the area of its applicability. Therefore thermodynamics has made a deep impression upon me. It is the only physical theory of universal content which I am convinced, within the areas of the applicability of its basic concepts, will never be overthrown. Ch. 7: Thermochemistry 7-1 Getting Started: Some Terminology 7-2 Heat 7-3 Heats of Reaction and Calorimetry 7-4 Work 7-5 The First Law of Thermodynamics 7-6 Heats of Reaction: U and H 7-7 The Indirect Determination of H: Hess s Law 7-8 Standard Enthalpies of Formation A. Einstein, 1949 7-1 Terminology of Thermodynamics System: All the materials involved in the process under study Surroundings: The rest of the universe or at least those materials outside of the system with which the system interacts. The interface between a system and its surroundings is called a boundary Different types of systems Open System: Free to exchange both matter and energy with its surrounding (e.g. an open beaker) Closed System: Free to exchange only energy with its surrounding (e.g. a sealed flask) Isolated system: Exchanges neither matter nor energy with its surrounding (e.g. a thermos.. at least for a short time) * It is the nature of the boundary that determines whether a system is open, closed or isolated!
More Terminology Energy (from Greek: work within ) Energy is the capacity to do work. Work Work is done when a force acts through a distance. Forms of Energy Kinetic Energy ( kinetic means motion in Greek) Energy associated with the motion of a body, or the particles within it. Potential Energy Energy due to condition, position, or composition. Associated with forces of attraction or repulsion between objects. Energy can change form from potential to kinetic. Relationship Between Work and Energy Kinetic Energy e k = Work 1 2 mv 2 [e k ] = w = F d [w ] = 2 kg m s = J kg m s 2 m = J 7.2 Heat: q Heat is the quantity of energy, q, transferred between a system and its surroundings (i.e. across a boundary) as a result of a temperature difference. Heat is energy in transit, and flows from the warmer to the colder body. Heat flow can occur by different means: conduction, convection or radiation. Temperature Objects do not contain Heat! Heat is transitory/temporary: It flows due to a temperature difference, so: No temperature difference, No Heat flow. We will see that the net effect of heat is to change the internal energy of the system and surroundings Related to the average energy per particle of the microscopic motions in the system (intensive quantity). From the Kinetic theory of gases we found that: e 3 k RT N 2 A For a solid, the microscopic motions are principally the vibrations of the constituent atoms about their lattice sites In a liquid there are even more degrees of freedom for motion, i.e. Translational motion, rotations, intra and intermolecular vibrations
Computer model of a crystal forming Heat and Temperature Heat will flow between 2 bodies, A & B, in thermal contact until the average energy per particle of the microscopic motions is equal, i.e. until T A = T B Why? For heat transfer by conduction or convection: collisions between atoms at the surface/boundary. Consider two billiard/pool balls traveling at quite different speeds. If these two balls collide, is it usually the case that the slower of the two is going even slower after the collision? Zeroth Law of Thermodynamics If two systems, A & B, are separately in thermal equilibrium with a third system, C, (i.e. no Heat flow between A C or B C) then they are in thermal equilibrium with each other. Heat Capacity, C The quantity of heat required to change the temperature of a system by one degree. Depends on the system/material This means that it is possible to define a Temperature, and to construct a thermometer (i.e. measure the temperature of A or B using a third system, C): A gas thermometer might measure the pressure of a fixed volume of gas to indirectly determine T, since: T P V nr Molar heat capacity. System is one mole of substance. Specific heat capacity, c. System is one gram of substance Heat capacity, C Mass specific heat. q = mc T q = C T Units of Heat Heat has units of Energy Calorie (cal) The quantity of heat required to change the temperature of one gram of water by one degree Celsius. Joule (J) SI unit for heat 1 cal = 4.184 J Microscopic interpretation of Heat Capacities Note: c ice = 1.96 J/K g c water = 4.18 J/K g In general, the more ways there are to distribute energy throughout the system (i.e. the more microscopic degrees of freedom ) the higher the heat capacity. No translation or rotation in ice!
Conservation of Energy In interactions between a system and its surroundings the total energy remains constant energy is neither created nor destroyed. q system + q surroundings = 0 q system = -q surroundings There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law it is exact so far we know. The law is called conservation of energy. It states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same. The Feynman Lectures on Physics, Vol. 1. R. P. Feynman Determination of Specific Heat 7-3 Heats of Reaction and Calorimetry Chemical energy. Contributes to the internal energy of a system. Associated with chemical bonds and intermolecular interactions. Heat of reaction, q rxn. The quantity of heat exchanged between a system and its surroundings when a chemical reaction occurs within the system, at constant temperature. Heats of Reaction Bomb Calorimeter Exothermic reactions. Produces heat, q rxn < 0. Endothermic reactions. Consumes heat, q rxn > 0. Calorimeter A device for measuring quantities of heat. q rxn = -q cal q cal = q bomb + q water + q wires + Define the heat capacity of the calorimeter: q cal = m i c i T= C T all i heat
Coffee Cup Calorimeter A simple calorimeter. Well insulated and therefore isolated. Measure temperature change. q rxn = -q cal 7-4 Work In addition to heat effects chemical reactions may also do work. Gas formed pushes against the atmosphere. Volume changes. See example 7-4 for a sample calculation. Pressure-volume work. Pressure Volume Work Calculating Pressure-Volume Work. Suppose the gas in the previous figure is 0.100 mol He at 298 K and the each mass in the figure corresponds to an external pressure of 1.20 atm. How much work, in Joules, is associated with its expansion at constant pressure. Internal Energy, U Viewed at a microscopic level many things contribute to the total energy content of a system Translational kinetic energy of the molecules. Molecular rotations. Intra and Intermolecular vibrations. Intermolecular attractions. Chemical bonds. The sum of all energy contributions is called the internal energy, U, of the system. 7.5 First Law of Thermodynamics The relationship between Heat (q), Work (w) and the Internal Energy (U) of a system is dictated by the conservation of energy: U = q + w The internal energy of an isolated system is constant
First Law of Thermodynamics Functions of State Any property that has a unique value for a specified state of a system is said to be a State Function. Water at 293.15 K and 1.00 atm is in a specified state. d = 0.99820 g/ml This density is a unique function of the state. It does not matter how the state was established. Functions of State U is a function of state. But cannot be measured in most cases. U has a unique value between two states. Is easily measured. Path Dependent Functions Changes in heat and work are not functions of state. Remember previous example: w = -1.24 10 2 J in a one step expansion of 0.1mol of He gas at 298K from 1.02L to 2.04L: Consider a 2 step expansion. First 2.40 atm to 1.80 atm and finally to 1.20 atm. Path Dependent Functions Thermochem. (Ch. 7) Problems From Petrucci (9 th ed.) Ch.7 9,10,15,23,25,33,41,49,57,63,77,81,91,96, 98 w = (-1.80 atm)(1.36-1.02)l (1.30 atm)(2.04-1.36)l = -0.61 L atm 0.82 L atm = -1.43 L atm = -1.44 10 2 J Compared -1.24 10 2 J for the two stage process
7-6 Heats of Reaction: U Heats of Reaction, U Reactants Products U i U f U = U f -U i U = q rxn + w In a system at constant volume: U = q rxn + 0 = q rxn = q v But we live in a constant pressure world! How does q p relate to q v? Heats of Reaction: H q V = q P + w We know that w = - P V and q V = U, therefore: U = q P -P V q P = U + P V Comparing H and U 2CO(g) + O 2 (g) 2CO 2 (g) H = H f H i = -566.0 kj (at T = 298K) These are all state functions, so define a new function. Let H = U + PV (H = Enthalpy) Then H = H f H i = U + PV At constant pressure and temperature: H = U + P V = q P Changes of State of Matter Molar enthalpy of vaporization: H 2 O (l) H 2 O(g) H = 44.0 kj at 298 K Molar enthalpy of fusion: H 2 O (s) H 2 O(l) H = 6.01 kj at 273.15 K Standard States and Standard Enthalpy Changes Define a particular state as a standard state. Standard enthalpy of reaction, H The enthalpy change of a reaction in which all reactants and products are in their standard states. Standard State The pure element or compound at a pressure of 1 bar and at the temperature of interest.
Enthalpy Diagrams H as a function of Temp. 7-7 Indirect Determination of H: Hess s Law H is an extensive property. Enthalpy change is directly proportional to the amount of substance in a system. N 2 (g) + O 2 (g) 2 NO(g) ½N 2 (g) + ½O 2 (g) NO(g) H = +180.50 kj H = +90.25 kj H changes sign when a process is reversed NO(g) ½N 2 (g) + ½O 2 (g) H = -90.25 kj Hess s Law Hess s law of constant heat summation If a process occurs in stages or steps (even hypothetically), the enthalpy change for the overall process is the sum of the enthalpy changes for the individual steps. ½N 2 (g) + ½O 2 (g) NO(g) NO(g) + ½O 2 (g) NO 2 (g) ½N 2 (g) + O 2 (g) NO 2 (g) H = +90.25 kj H = -57.07 kj H = +33.18 kj A consequence of H being a function of state. Hess s Law Schematically 7-8 Standard Enthalpies of Formation: H f The enthalpy change that occurs in the formation of one mole of a substance in the standard state from the reference forms of the elements in their standard states. The standard enthalpy of formation of a pure element in its reference state is 0.
Standard Enthalpy of Formation Standard Enthalpies of Reaction 2NaHCO 3 (s) Na 2 CO 3 (s) +CO 2 (g) + H 2 O(l) H o = H f Na2 CO 3 + H f CO2 + H f H2 O -2 H f NaHCO3 Enthalpy of Reaction H rxn = v p H f products - v r H f reactants Thermochem. (Ch. 7) Problems From Petrucci (9 th ed.) Ch.7 9,10,15,23,25,33,41,49,57,63,77,81,91,96, 98