Chapter 7 Chemical Reactions and Energy Flow

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1 Chapter 7 Chemical Reactions and Energy Flow Energy is the currency of the Universe. Chemical changes are usually accompanied by a redistribution of energy and not just matter. And whether or not a reaction will proceed depends upon the flow of energy. The study of the energy flow is called thermodynamics literally, heat movement but initially, we will be considering a subset called thermochemistry. The two topics are related and often intermixed. Chapter 7 1

2 Some reactions release heat when they occur; others do not. Indeed, some reactions absorb heat. How do we account for these observations? The model that we have developed is that energy is stored in chemical compounds and if the energy stored in the reactants is greater than the energy in the products, then some will be left over and released. (And vice versa). We call processes that release energy exothermic ( exo means out or outside, so exothermic means heat out ). Processes that absorb energy are then endothermic ( endo means in or inside). Chapter 7 2

3 During a chemical reaction, a shift from reactants to products will result in the release or absorption of energy. In an exothermic process, the initial state has more energy than the final state and the excess energy is released as heat. In an endothermic process, the final state has more energy than the initial state and heat is absorbed. Chapter 7 3

4 Energy is the capacity to do work to apply a force over a distance. Kinetic energy is the energy tied up with motion the faster a molecule is moving, the more kinetic energy it has. Potential energy is the energy of place for molecules, this means the relative amount of energy invested in the bonds within a molecule and the attractive/repulsive forces between atoms, ions, and molecules. Heat is manifested in changes in both kinetic and potential energy within a system and its surroundings. Chapter 7 4

5 Heating a container of water results in: 1) A change in kinetic energy. The individual molecules of water accelerate and move much rapidly within the solution. Some have sufficient kinetic energy that they are capable of overcoming their intermolecular attractions and leave the solution. 2) A change in potential energy. The molecules, on average, move further apart (which is why the density decreases with increasing temperature) and work is required to move the molecules against the forces of attraction. Chapter 7 5

6 This conversion of energy from one form to another occurs freely in all sorts of different systems. For example, chemical energy can be converted to electrical energy which manifests in the form of both light and heat (electromagnetic radiation). The law of conservation of energy or the first law of thermodynamics tells us that although energy can be converted from one form to another, the total energy is a constant. To put it another way you can never win you can never get more energy out of a system than is present in the system to begin with. Chapter 7 6

7 Energy units Energy is most often measured in scientific terms in joules which is the energy required to lift one kilogram one metre. A joule is a kg m 2 /s 2 or kg m 2 s -2. An older unit of heat energy was the calorie which is defined as the amount of energy required in order to raise the temperature of 1 gram of water by 1 C. The conversion factor is 1 cal = J (recall the specific heat capacity of water). This should not be confused with the food calorie (Cal.) which is actually a kilocalorie or the amount of food needed to raise one kilogram of water by 1 C. Just keeping our bodies warm requires about 2000 Cal per day. Chapter 7 7

8 A second consideration that is important in thermochemistry is what exactly are we measuring? Consider that the law of conservation of energy tells us that energy can be neither created nor destroyed that the amount of energy is constant. If that is the case, then how can we say that a reaction is exothermic? That it releases energy. This would imply that the reaction creates energy that is released. The answer is that in thermochemistry, we are talking about a system and when considering whether a reaction is exothermic or endothermic, we are considering whether energy is leaving or entering the system. That total energy is a constant. Chapter 7 8

9 We define the system as the thing that we are studying a chemical reaction, the beaker in which it occurs, the instruments monitoring it or whatever. We then define the surroundings as everything else in the Universe. System + Surroundings = Universe energy of a system + energy of surroundings = constant Chapter 7 9

10 An open system is one in which there is the free exchange of both heat and matter between the system and surroundings. Think of a pot of boiling water on a stove. Heat is entering from the stove s element and matter is leaving in the form of steam (water vapour). A closed system is one in which heat is freely exchanged but matter is not. Think of a pressure cooker filled with water. The lid ensures that even when boiling, none of the water is released. (Most of the time, this is what we are talking about.) An isolated system is one in which neither heat nor matter is exchanged with the surroundings. Doesn t actually exist except in the sense that the entire Universe is an isolated system. However, theoretically this is a useful concept. Chapter 7 10

11 So, heat is a measure of the flow of energy between the system and its surroundings. An object or solution or chemical compound does not contain heat. Rather, there is thermal energy within a system that can manifest as heat. Wood, for example, has less thermal energy than coal on a mass bases. But in either case, reacting the fuel with oxygen results in a lot of heat to the surroundings. Temperature refers to how hot something is to the average kinetic energy of the molecules or atoms or ions within a system. A system at a high temperature can transfer energy in the form of heat to surroundings that are at a lower temperature. Temperature is an intrinsic property it doesn t depend on how much substance is present. Heat is not intrinsic. Chapter 7 11

12 Heat transfer occurs between any two objects when they come in contact until they reach thermal equilibrium. Heat is said to flow from the object with the higher temperature to the object with the lower temperature. This is an important distinction, because it is different from the way we view this in our daily lives. We often talk about the cold creeping in when in reality, it is the heat flowing out. That is, holding an ice cube results in the loss of heat from your hand to the ice cube not the cold from the ice cube flowing into your hand although that is what appears to be happening. Thermal equilibrium is achieved when both objects have the same thermal energy and the same temperature. Chapter 7 12

13 The energy content of a system is the sum of all of the kinetic and potential energy in the molecules, atoms, or ions within a system. This is referred to as the internal energy (U). The internal energy depends on the amount of matter (it is an extrinsic property ) as each ion, atom, or molecule in a system contributes to the total. Internal energy is also a state function a function that depends only on the state of a system and not on its history. We can t measure the internal energy of system but we can measure the change in the internal energy: ΔU system = U final - U initial Chapter 7 13

14 Heat and work are both forms of energy transfer between a system and its surroundings. The transfer of heat results in a change in temperature. Work must be accompanied by a change in volume against a constant pressure. (Work requires the expenditure of energy over a distance.) The change in internal energy is the sum of the energy transferred as heat and work: Δu system = q + w where q is heat and w is work. Chapter 7 14

15 Note that if we are talking about the amount of heat (i.e. 102 J) then we don t need to specify a sign. But when we are accounting for internal energy, we define q and w as positive if they increase the internal energy of a system. Most of the time, the direction or sign is apparent from the language used. Chapter 7 15

16 In a system at constant pressure a beaker open to the atmosphere we define a slightly different quantity for our discussion of energy. Enthalpy (H) is the amount of heat transferred between a system and its surroundings during a process that occurs at constant pressure (q p ), if no work other than that due to expansion of the system occurs. Enthalpy is a state function: ΔH = H final - H initial For exothermic processes, at constant pressure, ΔH < 0. For an endothermic processes, at constant pressure, ΔH > 0. Chapter 7 16

17 Changes in state require energy. Boiling water requires the input of heat but what is less obvious, perhaps, is that the condensation of steam releases an equivalent amount of heat. The energy involved is labelled for the conversion involved. The molar enthalpy change of fusion (ΔH fus ) is the energy involved in melting/freezing the conversion from a liquid to a solid and vice versa. The molar enthalpy change of vapourization (ΔH vap ) is the energy involved in boiling/condensation. There is also a molar enthalpy change of sublimation (ΔH sub ) which is the energy involved in sublimation/deposition. Chapter 7 17

18 Chapter 7 18

19 We can talk about the change in enthalpy for a reaction. It is defined as the difference in the sum of the enthalpy of the products minus the sum of the enthalpy of the reactants: ΔH rxn = Σ H products - Σ H reactants However, we can t actually use this equation because we can t measure the values of the enthalpies of the products or reactants. But we can measure the enthalpy of a reaction using a bomb calorimeter. We can also calculate H rxn using the molar enthalpies of formation. Chapter 7 19

20 Enthalpy diagrams for exothermic and endothermic reactions show the qualitative relationship between the reactants and products in a chemical reaction. Such diagrams can help visualize energy changes. Chapter 7 20

21 But, ideally, we would like to work with quantitative relationships how much energy can be get from a reaction? For example: CH 4(g) + 2O 2(g) CO 2(g) + 2H 2 O (g) ΔH f = kj/mol In this case, the enthalpy of the reaction is the amount released per mole of methane used. (Book mentions packets which is one way to think of it.) The magnitude of the enthalpy change depends on the amount. If we were to react 2 moles of methane, we would get 2 mol x kj/mol or kj. For 0.5 moles of methane, we only get kj. Chapter 7 21

22 The sign depends on the direction of the reaction. Turn the reaction around: CO 2(g) + 2H 2 O (g) CH 4(g) + 2O 2(g) ΔH f = kj/mol Which makes sense from our qualitative picture. If going one direction gives up energy, going the other direction requires the input of energy. Note that part of what it means to be a state function is that the reaction will generate the same amount of energy provided that methane is at 1 bar and 25ºC, regardless of the history of the methane or where the reaction takes place. Chapter 7 22

23 Calorimetry is a fairly simple method for measuring the enthalpy of a reaction. In principle, (and in first year labs) a calorimeter is simply a device (i.e. coffee cups and a thermometer) that isolates a reaction in a way that allows for a reproduce-able measurement of the amount of heat generated or consumed during a reaction The amount of heat is obtained from the change in the temperature of the water in the calorimeter. Chapter 7 23

24 We know the specific heat of water is J/K g and this leads to the expression: q = c x m x ΔT where m is the mass of water and c is the specific heat. For example, 50 grams of water, with a temperature change of 3.2ºC, requires: J/K g x 50 g x 3.2 K = J The accuracy of the calorimeter depends upon the accuracy of measuring the temperature and, in practical terms, coming up with a specific heat capacity for the calorimeter itself to account for heat losses. This is accomplished by using a reaction of known values to calibrate the device. Chapter 7 24

25 Instruments used in research laboratories (and upper level undergraduate laboratories) are a little more sophisticated. But they operate on the same principles and need to be calibrated before using. Chapter 7 25

26 A bomb calorimeter is calibrated by combusting 1.06 g of benzoic acid in excess oxygen resulting in a 4.63ºC temperature rise. A 1.83 g sample of an unknown is combusted resulting in a 3.86ºC rise. If the heat of combustion for benzoic acid is kj/g, what is the heat of combustion of the unknown? First, calculate c for the calorimeter: q = (26.43 kj/g)(1.06 g) = kj produces a 4.63ºC change which means that a temperature change of 3.86ºC is produced by: q = (3.86ºC/ 4.63ºC) x kj = kj which was produced by 1.86 g, so the heat of combustion is: ΔH combustion = kj/1.83 g = kj/g Chapter 7 26

27 If we are going to compare compounds or reactions with one another, we need to have a standard state since enthalpy depends on pressure, concentration, temperature, etcetera. Standard State: - For pure substances, the standard state is the most stable form and state of the substance at 1 bar at the temperature of interest (for most compounds, 25ºC). - For any gas, its state at a pressure of 1 bar. - For any aqueous species, its standard state when the concentration is exactly 1 M at a pressure of 1 bar (and usually 25ºC). For a reaction with reactants and products in their respective standard states, we have the standard enthalpy change of reaction. Chapter 7 27

28 We can utilize the standard enthalpy of reaction to work out the energy for any reaction or any sequence of reactions. Hess Law: If a reaction can be written as the sum of two or more steps, the enthalpy change of the overall reaction is the sum of the enthalpy changes of the reactions of the individual steps. Chapter 7 28

29 Hess s Law is a necessary consequence of the law of conservation of energy. The total energy of the steps must be the total energy of the overall reaction. Note that you must take stoichiometry into account in calculating the steps for a Hess s Law calculation. Chapter 7 29

30 The enthalpy of a reaction is equated with the heat that is given off from a reaction. It can be measured with instrumentation (a calorimeter). It can be assessed for reactions using Hess s Law. It can also be determined using the standard molar enthalpy change of formation (ΔH f ) which is: the enthalpy change accompanying the generation of a compound in its standard state from its constituent elements in their standard state and their stoichiometric proportions. The temperature must be specified. This works because all of the compounds in a reaction are then measured against a common point their elements. Chapter 7 30

31 For example, consider the combustion of sugar sucrose. C 12 H 22 O 11(s) + 12O 2(g) 12CO 2(g) + 11H 2 O (g) ΔH rxn = kj/mol The ΔH f of sucrose, carbon dioxide, and water are all required. Note that oxygen is the elemental form of oxygen and its standard state at 25ºC with ΔH f = 0 kj/mol. To calculate the other three values, we measure the reactions between the chemical species and their elements: 12C (s) + 12O 2(g) 12CO 2(g) 11H 2(g) + 5.5O 2(g) 11H 2 O (g) C 12 H 22 O 11(s) 12C (s) + 11H 2(g) + 5.5O 2(g) Chapter 7 31

32 Individually, these reactions are: C (s) + O 2(g) CO 2(g) ΔH f = kj/mol H 2(g) + O 2(g) H 2 O (g) ΔH f = kj/mol C 12 H 22 O 11(s) 12C (s) + 11H 2(g) + 5.5O 2(g) ΔH f = kj/mol But we need to take the stoichiometric factors into account, so the enthalpy for the overall reaction is then: ΔH rxn = 12 x kj/mol + 11 x kj/mol + 1 x kj/mol + 12 x O kj/mol = kj/mol Chapter 7 32

33 The standard enthalpy values for many substances are tabulated. Appendix C has a fairly extensive list. Chapter 7 33

34 The standard enthalpy of a reaction at any specified temperature can be defined by: ΔHº rxn = Σ n i ΔHº f (products) - Σ n i ΔHº f (reactants) Note that this is what we did with sucrose except here we are subtracting the total for all of the reactants and we use the signs, as written, in the tables provided. (subtracting a negative number is the same as adding a positive.) Also, we don t actually need to write out all of the equations. Chapter 7 34

35 Suppose we want to calculate the enthalpy change for the decomposition of calcium carbonate to calcium oxide and carbon dioxide at 25ºC. What is the value? CaCO 3(s) CaO (s) + CO 2(g) ΔHº rxn = Σ n i ΔHº f (products) - Σ n i ΔHº f (reactants) = [1x ΔHº f (CaO) + 1x ΔHº f (CO 2 )] [1x ΔHº f (CaCO 3 )] = [( kj/mol) + ( kj/mol)] [( kj/mol)] = kj/mol Note that this implies that it takes energy to separate carbon dioxide from limestone which is why lime won t work to sequester CO 2. Chapter 7 35

36 Despite extensive tables containing the standard enthalpy of formation for literally hundreds of chemical compounds, they are not sufficient. Many reactions are outside of the scope of the tables. However, we can approximate the energy by using the average bond energies for all of the chemical bonds involved. That is, if we know the amount of energy involved in each bond, we can work out an approximate value for each chemical species and work out the enthalpy of reaction from the difference. The bond energy (D) is the enthalpy change for breaking a particular bond in the molecules, assuming the reactants and products are in the gaseous state. Chapter 7 36

37 The energy difference is the energy of the bonds broken minus the energy of the bonds made: ΔHº f = Σ D(bonds broken) - Σ D(bonds made) This is simple a case of drawing an appropriate structural formula and then working through the bonds in the molecule: H 3 C-CH 3 H 3 C CH 3 ΔHº f = D = +346 kj/mol 6xH-C 6x[H C] ΔHº f = D = 6x +413 kj/mol D = 2824 kj/mol The bond energies are tabulated. Chapter 7 37

38 Chapter 7 38

39 Calculating the enthalpy of combustion of ethane gives: CH 3 CH 3(g) + 3.5O 2(g) 2CO 2(g) + 3H 2 O (g) For oxygen: For carbon dioxide: For water: D = 498 kj/mol D = 2x 783 kj/mol = 1566 kj/mol D = 2x 463 kj/mol = 926 kj/mol Which gives: ΔHº f = (2824 kj/mol + 3.5x498 kj/mol) (2x1566 kj/mol + 3x926 kj/mol) = kj/mol Note using the enthalpies from Table 7.2 gives: ΔHº f = (2x kJ/mol + 3x kJ/mol) -(1x-83.85kJ/mol + 3.5x0.0kJ/mol) = kj/mol Chapter 7 39

40 All sorts of reactions can yield useable energy but combustion is the most obvious. Burning propane and ethane light up our barbecues; burning wood provides the warm glow of a campfire; burning gasoline drives our cars; and burning food warms our bodies while providing the energy to live. The many different chemical reactions that food undergo in our bodies to provide energy and to provide the building blocks for many of our biomolecules fall into the area of biochemistry called metabolism. Primary amongst these reactions is the combustion of glucose (a carbohydrate): C 6 H 12 O 6(s) + 6O 2(g) 6CO 2(g) + 6H 2 O (l) ΔHº rxn = kj/mol Chapter 7 40

41 Of course, when we refer to this as combustion, we really are saying oxidation the carbon atoms in the glucose are oxidized to carbon dioxide. This is the underlying principle behind any combustion reaction. Further, if we were to use this energy directly, we would need to continuously stoke the fires. Instead, our bodies have evolved a mechanism that is common across all of life. We convert the energy of combustion from one mole of glucose to the formation of ATP (adenosine-5 -triphosphate) molecules via aerobic respiration. ATP then undergoes a hydrolysis reaction (literally, water breaking ) to produce ADP (adenosine-5 -diphosphate). Chapter 7 41

42 ATP (aq) + H 2 O (l) ADP (aq) + HPO 4 2- (aq) ΔHº rxn -24 kj/mol Chapter 7 42

43 Note that ATP doesn t have high energy bonds. Rather, the total energy of the reactants is greater than that of the products. And that energy must be loaded back into the system by the combustion of glucose. Also, that glucose is ultimately formed from the reaction of carbon dioxide and water in photosynthesis the reverse of the combustion reaction of metabolism. Chapter 7 43

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