Thermochemistry Thermochemistry is an important subset of thermodynamics. Thermodynamics is the study of energy conversion between heat and mechanical work. Thermochemistry is the study of heat involved in chemical reactions and its utilization in performing mechanical work. Forms of Energy – Energy is defined as the ability to do work or transfer heat. Some forms of energy that are of interest in this course are: 1. Kinetic energy results from motion. We have learned in the previous chapter on gases that molecules can have kinetic energy. Kinetic energy (EK) is calculated from the formula 1 𝐾𝑒 = 𝑚𝑢2 (1) 2 Where m is the mass of an object and 𝑢 is the velocity of the object. Thermal energy, as defined in the section on gases, is a form of kinetic energy and can be expressed in terms of the molecular properties of molecules or their macroscopic temperature T as shown below. 1 3 𝐾 = 𝑀𝑢̅2 = RT (2) 2 2 2. Potential energy is the energy of an object based upon its position. 3. Chemical Energy is the energy in molecules atoms and ions due to the attraction and repulsions of the electrons and nuclei in these species. Kinetic and potential energy are interchangeable with the sum of these two quantities being constant because of the law of conservation of energy. Energy Changes in Chemical Reactions – In our society chemical reactions are employed to generate heat (for example in space heating) and to generate motion by doing mechanical work ( for example in automobiles and electrical generators) Most of the time we employ combustion reactions for this purpose. In addition, in the biosphere chemical reactions are used to sustain life (for example in the combustion of glucose which provides heat and energy). For any discussion of thermodynamics we define a system and its surroundings. In thermochemistry the system is the reaction and its container (beaker, flask, or test tube etc.) and the surrounds is everything else (the rest of the universe) In thermochemistry we define an endothermic reaction as a reaction that absorbs heat and an exothermic reaction as one that liberates or give off heat. As shown in Figure 5.2 in the textbook if we plot energy for an exothermic reaction the products are at a lower energy than the reactants and for an endothermic reaction the products are at a higher energy than the reactants. In this course we will use two different units for energy. These are the joule and the calorie. The joule is the S.I. unit of energy. The calorie is a commonly used unit especially in biology. There are 4.184 Joules in a calorie. The food industry commonly employs a unit called the Calorie (upper case) which is 1000 times greater than the scientific calorie. In the scientific nomenclature this unit is referred to as a kilocalorie. The First Law of Thermodynamics The first law of thermodynamics is a simple application of the law of conservation of energy. Simply stated when heat is converted to work no energy is created or destroyed. The first quantity that we define is internal energy , U. In the molecular world molecules can have several types of energy: 1. Intermolecular energy or the attraction or repulsion of the atoms between different molecules. 2. Intramolecular energy or the attraction or repulsion of the atoms in the same molecule. For any molecule, this intramolecular energy can manifest itself in the following ways. a. The movement of the molecule. This is known as translational energy. b. Excited electronic states of the molecule. This is known as electronic energy. A molecule with two or more atoms can also have energy due to I. the rotation of the molecule. This is known as rotational energy. II. the movement or vibration of the bonds between atoms of a molecule. This is known as vibrational energy. Any chemical reaction we have an initial state (the reactants) and the final state (the products) For the difference between these two we define the mathematical function Δ which is the difference between the value of the final state(2) and the initial state (1). Therefore we have ΔU = U2 – U1 (3) Consider the reaction S(s) + O2(g) → SO2(g) (4) The energy released during this reaction is ΔU = Uproducts – Ureactants, where U is the energy per mole of reactant or product. Conversion of Work and Heat The first law of thermodynamics can be expressed by the equation, ΔU = q + w, (5) where ΔU is the change in internal energy of a process (or reaction), q is the heat liberated or absorbed and w is the work done on or by the system. The convention used in calculations is a positive q is heat absorbed by the system while a negative q is heat added to the system. Work done on the system is positive while work done by the system is negative. These conventions are illustrated in the Table below. Constant Volume and Constant Pressure Processes Chemical reactions and be carried out under constant pressure or constant volume. Most chemical processes are carried out at constant pressure due to the fact that the external pressure on the reaction is simply atmospheric pressure and this pressure doesn’t vary much during the course of most chemical reactions conducted in the laboratory. Additionally most reactions in solids or in liquids do not have any appreciable change in volume. The one exception to this is a chemical reaction involving a gas. For a reaction where there is a change in volume the work done by such a reaction is w = -PΔV (6) where P is the external pressure and ΔV is the change in volume. When a chemical reaction occurs at constant volume, however, there is no work done and from reaction (5) we have ΔU = q. (7) for constant volume Enthalpy For constant pressure problems we define a new term called enthalpy (H) by the equation H = U +PV (8). For a change in H we therefore have ΔH = ΔU +ΔPV (9). For a constant pressure process we factor out the pressure and we have ΔH = ΔU +PΔV (10). Substituting (5) for ΔU in (10) we have ΔH = q + w +PΔV (11). substituting (6) into (11) ΔH = q + - PΔV +PΔV or for constant pressure problems ΔH = q for constant pressure (12) From this we can see that 1. ΔU represents the heat released for a chemical reaction at constant volume 2. ΔH represents the heat released for a chemical reaction at constant pressure Since most chemical reactions are performed at constant pressure we see many tables referred to as the heat of reaction or equivalently the enthalpy of reaction. State Variables, Functions and Thermodynamic Cycles In science, a the state of a system is defined by the macroscopic values of the properties of a system. These include pressure, temperature, composition, energy etc. For any system, a state function has only one value for a given state. A thermodynamic cycle is simply a process by which the state of the system is changed from one point to another through any series of steps but is finally returned to the initial state. An illustration of this is shown in Figure 1. In this process we change the pressure and temperature through four states 1→2, 2→3, 3→4 and 4→1. Figure 1 Thermodynamic cycle Since a state variable has only one value at each of the states, in a cycle its final value must be the same as its initial value since it begins and ends at the same state. Both of the variables U and H are state variables but q and w are not. For example, we can express this mathematically for the enthalpy ,H, the (for the cycle above by the equation) ΔH1→2 + ΔH2→3 + ΔH3→4 + ΔH4→1 = 0 (13) This relationship is important in science because scientists measure and compile values of ΔH for multitudes reactions and physical changes. Sometimes it is difficult or impossible to measure a particular reaction, but equation 13 allows us to determine its value by measuring the enthalpy change for all of the other reactions in the cycle and using equation 13 to determine the unknown enthalpy in the cycle. Specific Heat and Heat Capacity Specific heat and heat capacities are used to determine the heat q (= ΔH at constant pressure) when substances are heated. The defining equations are, q = msΔT (14) where m is the mass of a substance, s is the specific heat and ΔT is the temperature change. Also we have q = CΔT (15) where C is the heat capacity of a substance. Table 5.2 in your text shows values of the specific heat for various substances. Measurement of q Laboratory measurements of q are made using a calorimeter. In these measurements the calorimeter is a thermally insulated device in which a measured amount of substance is place in the calorimeter, the substance is heated and the specific heat or the heat capacity is determined using equations 14 or 15. The figure below shows such a device. Figure 2 Calorimeter Hess’s Law This law is an example of applying a cycle to determine the enthalpy of a reaction. Consider the combustion reaction below which forms liquid water. CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) (16) This reaction can be thought of as two steps in a cycle. The first reaction being the combustion reaction forming gaseous water (17) followed by the reaction where water condenses from the gas phase to the liquid phase. (18) CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol (17) ______________2H2O(g) → 2H2O(l) ΔH = -88 kJ/mol (18) . CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) ΔH = - 890.4 kJ/mol We can add the reactions (17) and (18) as shown above by canceling common molecules and adding the others to produce equation (16) and it’s ΔH which by the result of ΔH being a state function is equal to ΔH17 + ΔH18. The cycle for this system is demonstrated in the figure below. Figure 3 Example of Hess Cycle Standard Enthalpies of Formation As previously mentioned the enthalpy change that accompanies a reaction can be measured in a calorimeter. In adding, by applying the additive properties of ΔH as shown above, this enthalpy change can be calculated from a table of the enthalpies of all the reactants and products in a reaction. The standard enthalpy of reaction for any molecule is written as Δ𝐻𝑓.0 . The standard enthalpy of any element is defined as 0 for the most common form of that element at a given temperature. For example, oxygen is a gas at STP therefore the Δ𝐻𝑓0 of O2 = 0 whereas graphite (C) is the standard state of carbon at STP therefore Δ𝐻𝑓0 of C(graphite) = 0. The standard states of all the other molecules are determined using thermodynamic cycles and measured ΔH of various reactions that forms these molecules from the standard state of the elements of the molecule. Table 1 shows a typical example of various Δ𝐻𝑓0 . Table 1 Δ𝑯𝟎𝒇 of some molecules at 25°C Molecule Δ𝐻𝑓0 kJ/mol AgCl(s) -127.1 Br2(l) 0.0 Br2(g) 30.9 C(graphite) 0.0 CH4(g) -74.8 H2O(g) -242 I2(s) 0.0 NO2(g) 33.2 O2(g) 0.0 Standard energy of a reaction (Δ𝑯𝟎𝒓𝒙𝒏 ) The standard energy of a reaction is defined by the hypothetical reaction aA + bB → cC and dD (19) where a, b, c and d are the coefficients of the reactants (A and B) and the 0 products (C and D). Δ𝐻𝑟𝑥𝑛 is defined by the equation 0 Δ𝐻𝑟𝑥𝑛 = c Δ𝐻𝑓0 (C) + dΔ𝐻𝑓0 (𝐷) – a Δ𝐻𝑓0 (A) – bΔ𝐻𝑓0 (B) (20) 0 In this manner the Δ𝐻𝑟𝑥𝑛 of any reaction can be determined by a direct measurement of the enthalpy or by using data like that described in Table 1 to calculate the enthalpy.