Thermodynamics

1. Thermodynamics Chapters 5 and 19

2. Energy Energy is commonly defined as the capacity to do work or transfer heat. Work is defined as the energy used to cause and object to move. Heat is defined as the energy used to cause the temperature of an object to increase.

3. Types of Energy • Kinetic Energy: • Energy of motion • KE = ½ mv2 • Example: A car moving at 55 mph has a greater kinetic energy than a car moving at 40 mph. • All atoms and molecules are in motion and have kinetic energy. • Potential Energy: • Associated with the position of an object. • Chemical potential energy is the energy stored in chemical bonds.

4. Units of Energy The SI unit of energy is the joule (J) This is derived from the formula for kinetic energy. Another unit of energy is the calorie. 1 cal = 4.184 J

5. System and Surroundings Things in the universe we single out to study and observe are referred to as systems. Everything else is the surroundings. Systems can be: Open: Where matter and energy can be exchanged with the surroundings. Closed: Where energy but not matter can be exchanged with the surroundings. Isolated: Where neither matter nor energy can be exchanged with the surroundings.

6. Transferring Energy The two ways that we experience energy changes are work and heat. Work is defined as the energy used to move an object. ω = F xd The other way to transfer energy is heat. Heat is the transfer of energy from a warmer object to a cooler one.

7. The First Law of Thermodynamics The first law of thermodynamics states that energy cannot be created or destroyed, only transferred. Any energy “lost” by the system must have been transferred to the surroundings.

8. Internal Energy The internal energy of a system is the sum of ALL kinetic and potential energy of all of its components. The internal energy of a system is defined as E. We can usually never calculate the actual numerical value of E. We can calculated the change in the internal energy of a system (ΔE).

9. Relating ΔE to Heat and Work A closed system may exchange energy with the surroundings as heat or work. This would obviously change the amount of internal energy resulting in a positive or negative ΔE. The first law of thermodynamics can be written algebraically as: ΔE = q + ω

10. When heat is added to a system or work is done on the system, its internal energy would increase (ΔE = +) If heat is released from the system or the system does work on the surroundings, its internal energy would decrease (ΔE = -)

12. Example Two gases, A(g) and B(g), are confined in a cylinder and piston arrangement. Substances A and B react to form a solid product: A(g) + B(g) C(s). As the reaction occurs, the system loses 1150 J of heat to the surroundings. As the volume of the gas decreases under constant atmospheric pressure, the surroundings do 480 J of work on the system what is the change in the internal energy of the system?

13. Endothermic vs. Exothermic When a process occurs in which the system absorbs heat, the process is called endothermic. A process in which the system loses heat is called exothermic.

14. State Functions Internal energy is an extensive property. Meaning a 25 g sample of water at 25o C would contain less total internal energy than a 50 g sample of water at 25o C. Suppose we define our system as 50 g of water at 25o C. This system could have arrived at this state by cooling 50 g of water from 100o C, or by melting ice from 0o C. The internal energy after each process would be the same. A state function is a property of a system that depends only on it’s current state, not how it got there.

15. Suppose you drive from Chicago to Denver. Chicago is 596 ft above sea level; Denver is 5280 ft above sea level. No matter what rout you take your altitude change will be 4684 ft. Altitude is a state function. The rout you take however can have a big difference on the distance your travel.

16. ΔE is a state function but q and w are not Consider a battery…

17. Enthalpy Consider the reaction between zinc and an acid… Zn(s) + 2 H+(aq)  Zn2+(aq) + H2(g) If we carry this reaction out in an open beaker, we can see the hydrogen gas being evolved. It may not be obvious but the hydrogen gas is doing work on the surroundings. This is more evident if we add a cylinder and piston set up to the experiment.

18. This is the most common form of work discussed in chemistry. This is called pressure-volume (PV) work. When pressure is constant PV work is described as: w = -PΔV The thermodynamic function called enthalpy accounts for both the follow of heat into or out of a system as well as PV work. Positive enthalpy indicates a total increase in energy. Negative enthalpy indicates a total decrease in energy.

19. Example Indicate the sign of the enthalpy change, ΔH, in each of the following processes carried out under atmospheric pressure, and indicate whether the process is endothermic or exothermic. (a) An ice cube melts. (b) 1 g of butane (C4H10) is completely combusted in excess oxygen.

20. Enthalpies of Reaction Just like internal energy: ΔH = Hfinal –Hinital In a chemical reaction: ΔH = Hproducts – Hreactants When the combustion of hydrogen gas is controlled so that 2 mol of H2(g) burn to form 2 mol of H2O(g) at constant pressure the system releases 483.6 kJ of energy.

21. Thermochemical Equations Enthalpy is an extensive property. The magnitude of ΔH, therefore, is directly proportional to the amount of reactant consumed. CH4(g) + 2 O2(g)  CO2(g) + 2 H2O(l) ΔH = -890 kJ 2 CH4(g) + 4 O2(g)  2 CO2(g) + 4 H2O(l) ΔH = -1780 kJ

22. The enthalpy of a reaction is equal in magnitude but opposite in sign to the enthalpy of its reverse reaction. CO2(g) + 2 H2O(l)  CH4(g) + 2 O2(g) ΔH = 890 kJ The enthalpy of a reaction depends on the state of the reactants and products. CH4(g) + 2 O2(g)  CO2(g) + H2O(g) ΔH = - 802 kJ

23. Example How much heat is released when 4.50 g of methane gas is burned in a constant pressure system?

24. Calorimetry Calorimetry is the experimental determination of the ΔH for any physical or chemical process. In order to do a calorimetry experiment we need to know some background. Heat Capacity (C): Heat capacity, C, is the amount of heat energy required to raise the temperature of a substance by 1 K (1o C).

25. A substance with a high heat capacity requires more heat energy to raise its temperature than a substance with a low heat capacity. Heat capacity is an extensive property. 10 mL of water heat up much faster than 1 L of water. The heat capacity of one mole of a substance is called its molar heat capacity Cm. The heat capacity of one gram of a substance is called its specific heat capacity or just specific heat Cs.

26. Specific Heat Cs = Example: It requires 209 J of heat to increase the temperature of 50.0 g of water by 1.00 K. What is the specific heat of water?

27. Example (a) How much heat is needed to warm 250 g of water from 22o C to 98o C? The specific heat of water is 4.18 J/g-K. (b) What is the molar heat capacity of water?

28. Hess’s Law Many enthalpies of reactions have been tabulated by scientists. Having this information available and being able to use it allows us to calculate the heat of reaction for almost every chemical reaction. Because enthalpy change (ΔH) is a state function, reactions can be thought of as happening in one step or in a series of steps.

29. Example The combustion of methane (CH4) gas to produce carbon dioxide and liquid water happens in two steps.

30. Example The enthalpy of reaction for the combustion of C to CO2 is: C(s) + O2(g)  CO2(g) ΔH = -393.5 kJ The enthalpy of reaction for the combustion of CO to CO2 is: CO(g) + ½ O2(g)  CO2(g) ΔH = -283.0 kJ Use this information to calculate the enthalpy of reaction for the combustion of C(s) to CO(g)

31. Example Calculate ΔH for the reaction: 2 C(s) + H2(g)  C2H2(g) Given the following chemical equations and their respective enthalpy changes… C2H5(g) + 5/2 O2(g)  2 CO2(g) + H2O(l) ΔH = -1299.6 kJ C(s) + O2(g)  CO2 ΔH = -393.5 kJ H2(g) + ½ O2(g)  H2O(l)

32. Enthalpies of Formation Many different enthalpies of many different processes have been tabulated. We have already used the enthalpy of fusion and the enthalpy of vaporization. One other important type of enthalpy change that has been tabulated for many compounds in the enthalpy of formation. This is the heat change associate with the formation of a compound from its constituent elements.

33. Enthalpies of formation change depending on things like, pressure, temperature, and the physical states of the reactants and products. In order to compare different enthalpies of formations we need to study then under the same conditions. Most enthalpies of formation (an of other reactions as well) are tabulated under “standard conditions” standard conditions are defined as 1 atm and 298 K. Standard enthalpy change is that of a reaction where all of the components are in the physical state they would be in at standard conditions.

34. Standard Enthalpy of Formation The standard enthalpy of formation of a compound (ΔHof) is the enthalpy change for the reaction that forms one mole of the compound at standard state. Elements (in standard state)  1 mole of Compound (in standard state) The value of ΔHofis always reported as kJ/mol The standard enthalpy change for any element in its standard state is 0 kJ/mol.

35. Using ΔHof The enthalpy of any reaction can be calculated from the addition of the tabulated ΔHoffor all the components. Example: Calculate the standard heat of reaction for the combustion of propane (C3H8) with oxygen to from CO2 and water.

36. Spontaneous Processes A spontaneous process is one that occurs without any outside assistance. The melting of ice at temperatures higher than 0o C is a spontaneous process. Any process that is spontaneous is one direction is not spontaneous in the reverse direction. Think about trying to freeze water at 25o C. Not impossible but not easy. The majority of spontaneous processes are exothermic. All spontaneous processes are considered to be irreversible. A reversible process is one where the system and the surroundings can be converted back to their original states without any net change.

37. Entropy and The Second Law of Thermodynamcs Now that we know what a spontaneous process is we can start to predict if an unfamiliar process will be spontaneous or not. We will use the thermodynamic quantity of entropy (S) to do this. In general we will define entropy as randomness. The more free the molecules are to move in random order, the higher the entropy of the system.

38. Entropy Change Just like E, and H, entropy (S) is a state function. We can also not calculate the specific value of S for any system. We can only calculate the change in S. ΔS = Sfinal – Sinitial In the special case of an isothermal process ΔS is equal to the heat that would be transferred in the reverse process divided by the temperature.

39. ΔS for Phase Changes The melting of a substance at its melting point and the vaporization of a substance at it’s boiling point are isothermal processes. We achieve these changes by adding a certain amount of heat from the surroundings. (ΔHfus or ΔHvap) The ΔS for these processes can be calculated easily because these are isothermal processes.

40. Example The normal freezing point of mercury is -38.9 oC, and its molar enthalpy of fusion is ΔHfusion= 2.29 kJ/mol. What is the entropy change of the system when 50.0 g of Hg(l) freezes at the normal freezing point?

41. The Second Law of Thermodynamics We saw that in the first law of thermodynamics energy is always conserved. Entropy is different. The entropy change in any spontaneous process will always be positive. If we calculate the entropy change of one mole of ice melting to liquid water we get:

42. ΔS and Spontaneity In the last example we saw that the total entropy change of the universe was positive. This corresponds to a spontaneous and irreversible process. If the sum of theΔS of both the system and surroundings equal zero the process is reversible.

43. Making Qualitative Predictions about ΔS There are three properties of matter that we can use to predict the sign (+ or -) of ΔS: Temperature Volume The number of independently moving particles. Think of these three factors and how they affect the movement and disorder of molecules.

44. Examples When water vaporizes the molecules spread out into a larger volume. This results in ΔS = + Consider the reaction: 2 NO(g) + O2(g)  2 NO2(g) In this process we are combining two molecules into one. The result of this is less total movement of molecules in the system and a negative entropy.

45. In general we expect entropy to increase when: Gases are formed from either solids or liquids. Liquids or solutions are formed from solids. The number of gas molecules increases during a chemical reaction.

46. Examples Predict whether ΔS would be negative or positive for each of the following processes. H2O(l)  H2O(g) Ag+(aq) + Cl-(aq) AgCl(s) 4 Fe(s) + 3 O2(g)  2 Fe2O3(g) N2(g) + O(g)  2 NO(g)

47. The Third Law Of Thermodynamics As we cool a substance down the molecules begin to move slower. If we continue to cool a substance down to absolute zero (0 K) the molecules will have no kinetic energy. The third law of thermodynamics states that the entropy of a pure crystalline solid substance at absolute zero is 0.

48. Entropy Changes In Chemical reactions We talked about how calorimetry is used to determine the enthalpy change for a reaction. No such type of experiment exists to determine the entropy change of a reaction. The absolute value of S can however be determined through complex experimentation.

49. The Tabulation of Entropies The entropies of substances in their standard states are usually tabulated as molar quantities: As you can see, unlike enthalpies of formation, the molar entropy of a pure element is NOT zero. The standard molar entropies of gases are, in general, greater than those of liquids and solids. Standard molar entropies generally increase with increasing molar mass. Standard molar entropies generally increase with an increasing number of atoms in the formula of a substance.

50. Calculating The Entropy Change In A Chemical Reaction Just like using the standard heats of formation to calculate the enthalpy change in a reaction, we can use the standard molar entropies in the same way. ΔSo =