Chemical Thermodynamics -1

1. Chemical Thermodynamics -1 Lecture 23

2. In This Chapter, We Will Discuss: • Spontaneous porcesses • Entropy and the 2nd law of thermodynamics • Molecular interpretation of entropy • Entropy changes in chemical reactions • Gibb’s free energy • Free energy and temperature • Free energy and equilibrium constant

3. First Law of Thermodynamics Energy cannot be created or destroyed. Therefore, the total energy of the universe is a constant. Energy can be transferred between a system and the surroundings and can be converted from one form to another, but the total energy of the universe remains constant. We expressed this law mathematically as: DE = q + w where DE is the change in the internal energy of a system, q is the heat absorbed (or released) by the system from (or to) the surroundings, and w is the work done on the system by the surroundings, or on the surroundings by the system.

4. Remember that q>0 means that the system is absorbing heat from the surroundings, and w>0 means that the surroundings are doing work on the system. Experience tells us that certain processes always occur, even though the energy of the universe is conserved.Ice melts when left outside a freezer, for instance, and if you touch a hot object, heat is transferred to your hand. The first law guarantees that energy is conserved in these processes, and yet they occur without any outside intervention. We say that these processes are spontaneous. A spontaneous process is one that proceeds on its own without any outside assistance.

5. Spontaneous Processes Spontaneous processes are those that can proceed without any outside intervention. For example, a gas confined inside a vessel will spontaneously effuse to the outside, if a pinhole opening exists. Look at the situation where such a gas confined to vessel A and not allowed to escape to vessel B. Now if the stopcock is opened, the gas in vessel A will spontaneously effuse into vessel B, but once the gas is in both vessels, it will not spontaneously return to vessel A.

7. Spontaneous Processes Processes that are spontaneous in one direction are nonspontaneous in the reverse direction.

8. Spontaneous Processes Processes that are spontaneous at one temperature may be nonspontaneous at other temperatures. Above 0 C, it is spontaneous for ice to melt. Below 0 C, the reverse process is spontaneous.

9. Identifying Spontaneous Processes Predict whether each process is spontaneous as described, spontaneous in the reverse direction, or in equilibrium: (a) Water at 40 °C gets hotter when a piece of metal heated to 150 °C is added. (b) Water at room temperature decomposes into H2(g) and O2(g). (a) This process is spontaneous. Whenever two objects at different temperatures are brought into contact, heat is transferred from the hotter object to the colder one. The final temperature, after the metal and water achieve the same temperature (thermal equilibrium), will be somewhere between the initial temperatures of the metal and the water. (b) Experience tells us that this process is not spontaneous—we certainly have never seen hydrogen and oxygen gases spontaneously bubbling up out of water! Rather, the reverse process—the reaction of H2 and O2 to form H2O—is spontaneous

10. Predict whether each process is spontaneous as described, spontaneous in the reverse direction, or in equilibrium: (a) Benzene vapor, C6H6(g), at a pressure of 1 atm condenses to liquid benzene at the normal boiling point of benzene, 80.1 °C. (b) At 1 atm pressure, CO2(s) sublimes at –78 °C. Is this process spontaneous at –100 °C and 1 atm pressure? • The normal boiling point is the temperature at which a vapor at 1 atm is in equilibrium with its liquid. Thus, this is an equilibrium situation. If the temperature were below 80.1 °C, condensation would be spontaneous. • (b) No, the reverse process is spontaneous at this temperature

11. Criteria of Spontaneity A brick falling from your hand loses potential energy. The loss of some form of energy is a common feature of spontaneous change in mechanical systems. It was suggested that the direction of spontaneous changes in chemical systems is determined by the loss of energy., and thus, all spontaneous chemical and physical changes are exothermic!!! (wrong statement). It takes only a few moments, however, to find exceptions to this generalization. For example, the melting of ice at room temperature is spontaneous and endothermic. Similarly, many spontaneous dissolution processes, such as the dissolving of NH4NO3, are endothermic.

12. Spontaneity: Enthalpy is NOT the Whole Story!!! We will see that reactions involve not only changes in enthalpy but also changes in entropy. Our discussion of entropy will lead us to the second law of thermodynamics, which provides insight into why physical and chemical changes tend to favor one direction over another. We do not expect a brick to spontaneously rise from the ground to our hand, or to gather with other bricks to form an organized building!!!.Thermodynamics helps us understand the significance of this directional character of processes, regardless of whether they are exothermic or endothermic.

13. Reversible Processes Carnot considered what an ideal engine, one with the highest possible efficiency, would be like. He observed that it is impossible to convert the energy content of a fuel completely to work because a significant amount of heat is always lost to the surroundings. Carnot’s analysis gave insight into how to build better, more efficient engines, and it was one of the earliest studies in what has developed into the discipline of thermodynamics. An ideal engine operates under an ideal set of conditions in which all the processes are reversible. A reversible process is a specific way in which a system changes its state. Carnot concluded that a reversible change produces the maximum amount of work that can be done by a system on its surroundings.

14. Reversible Processes In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process. When two objects at different temperatures are in contact, heat flows spontaneously from the hotter object to the colder one. Because it isimpossible to make heat flow in the opposite direction, from colder object to hotter one,the flow of heat is an irreversible process. Given these facts, can we imagine any conditions under which heat transfer can be made reversible?To answer this question, we must consider temperature differences that are infinitesimally small, as opposed to the discrete temperature differences with which we are most familiar.

15. Consider a system and its surroundings at essentially the same temperature, with just an infinitesimal temperature difference dT between them. If the surroundings are at temperature T and the system is at the infinitesimally higher temperature T+ dT, then an infinitesimal amount of heat flows from system tosurroundings. We can reverse the direction of heat flow by making an infinitesimal change of temperature in the opposite direction, lowering the system temperature to T- dT. Now the direction of heat flow is from surroundings to system. Reversible processes are those thatreverse direction whenever an infinitesimal change is made in some property of the system.

18. Irreversible Processes Spontaneous processes are irreversible.

19. For a process to be truly reversible, the amounts of heat must be infinitesimally small and the transfer of heat must occur infinitely slowly; thus, no process that we can observe is truly reversible. Because real processes can, at best, only approximate the infinitely slow change associated with reversible processes, all real processes are irreversible. Further, a nonspontaneous process can occur only if the surroundings do work on the system (compression of a gas). Thus, any spontaneous process is irreversible.

20. Entropy and the 2nd Law of Thermodynamics How can we use the fact that any spontaneous process is irreversible to make predictions about the spontaneity of an unfamiliar process? Understanding spontaneity requires us to examine the entropy in more details. In general, entropy is associated either with the extent of randomness in a system or with the extent to which energy is distributed among the various motions of the molecules of the system.

21. Entropy Entropy (S) is a term introduced by Rudolph Clausius in the nineteenth century. Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered, (q/T), which he called entropy. Like total energy, E, and enthalpy, H, entropy is a state function. Therefore, S = SfinalSinitial

22. The Second Law of Thermodynamics In general, any irreversible process results in an increase in total entropy, whereas any reversible process results in no overall change in entropy of the universe. This statement is known as the second law of thermodynamics. The sum of the entropy of a system plus the entropy of the surroundings is what we refer to as the total entropy change, or the entropy change of the universe, DSUniverse.

23. We can therefore state the second law of thermodynamics in terms of two equations: Because spontaneous processes are irreversible, we can say that the entropy of the universe increases in any spontaneous process. This profound generalization is yet another way of expressing the second law of thermodynamics.

24. The second law of thermodynamics tells us the essential character of any spontaneous change—it is always accompanied by an increase in the entropy of the universe. We can use this criterion to predict whether a given process is spontaneous or not. Before seeing how this is done, however, we will find it useful to explore entropy from a molecular perspective. Throughout most of the remainder of this chapter, we will focus on systems rather than surroundings. To simplify the notation, we will usually refer to the entropy change of the system as DS rather than explicitly indicating DSsys.

25. The Concept of a Microstate Imagine taking a snapshot of the positions and speeds of all the molecules at a given instant. The speed of each molecule tells us its kinetic energy. That particular set of positions and kinetic energies of the individual gas molecules is what we call a microstate of the system. A microstate is a single possible arrangement of the positions and kinetic energies of the gas molecules when the gas is in a specific thermodynamic state. We could envision continuing to take snapshots of our system to see other possible microstates.

26. It is essential to define the concepts of microstate and macrostate. Lets us consider N unbiased identifiable coins. Each coin has two states: head (h) or tail (t). Lets us make N tosses. The strings of h and t are microstates. The number of microstates is 2N. Each microstate has probability (1/2)N. The sum of all microstates gives us a macrostate.

27. For a large number of particles, there would be such a very large number of microstates that taking individual snapshots of all of them is not feasible. Because we are examining such a large number of particles, however, we can use the tools of statistics and probability to determine the total number of microstates for the thermodynamic state. (That iswhere the statistical part of the name statistical thermodynamics comes in.) Each thermodynamic state (P, T, and n) has a characteristic number of microstates associated with it, and we will use the symbol W for that number.

28. Molecular Interpretation of Entropy To understand the concept of spontaneity, let us look at the expansion of a gas into a vacuum, which is a spontaneous process. Now, what really makes this expansion spontaneous? The answer is simple as it relates to the continuous motion of gas molecules described by the kinetic molecular theory. The expansion can be viewed as the ultimate result of the random movement of the gas molecules, throughout the larger volume.

30. From Probabilities The previous figure shows that with both flasks available to the molecules, the probability of the red molecule being in the left flask is two, and the probability of the blue molecule being in the left flask is the same. The probability that both gases are in either flask is (1/2)2 = (1/4) because there are 4 different ways to place the two gas molecules in the flasks. If we apply the same analysis to three gas molecules, we find that the probability that all three are in the left flask at the same time is (1/2)3 = (1/8).

31. Assume 4 Molecules Not 2 or 3 There are five possible arrangements: all four molecules in the left bulb (I); three molecules in the left bulb and one in the right bulb (II); two molecules in each bulb (III); one molecule in the left bulb and three molecules in the right bulb (IV); and four molecules in the right bulb (V). If we assign a different color to each molecule to keep track of it for this discussion (remember, however, that in reality the molecules are indistinguishable from one another), we can see that there are 16 different ways (24 = 16) the four molecules can be distributed in the bulbs, each corresponding to a particular microstate.

33. There are 16 different ways to distribute four gas molecules between the bulbs, with each distribution corresponding to a particular microstate. Arrangements I and V each produce a single microstate with a probability of 1/16. This particular arrangement is so improbable that it is likely not observed. Arrangements II and IV each produce four microstates, with a probability of 4/16. Arrangement III, with half the gas molecules in each bulb, has a probability of 6/16. It is the one encompassing the most microstates, so it is the most probable.

34. What about a mole of gas? Now let’s consider a mole of gas. The probability that all the molecules are in the left flask at the same time is (1/2)N, where N = 6.02*1023 molecules. This is a vanishingly small number! Thus, there is essentially zero likelihood that all the gas molecules will be in the left flask at the same time. This analysis of the microscopic behavior of the gas molecules leads to the expected macroscopic behavior: The gas spontaneously expands to fill both the left and right flasks, and it does not spontaneously all reside in one flask.

35. Boltzmann Distribution and Microstates The science of thermodynamics developed as a means of describing the properties of matter in our macroscopic world without regard to microscopic structure. In fact, thermodynamics was a well-developed field before the modern view of atomic and molecular structure was even known. The thermodynamic properties of water, for example, addressed the behavior of bulk water (or ice or water vapor) as a substance without considering any specific properties of individual H2O molecules.

36. To connect the microscopic and macroscopic descriptions of matter, scientists havedeveloped the field of statistical thermodynamics, which uses the tools of statistics and probability to link the microscopic and macroscopic worlds. Here we show how entropy, which is a property of bulk matter, can be connected to the behavior of atoms and molecules. Suppose we now consider one mole of an ideal gas in a particular thermodynamic state, which we can define by specifying the temperature,T, and volume, V, of the gas. What is happening to this gas at the microscopic level, and how does what is going on at the microscopic level relate to the entropy of the gas?

37. The Boltzmann Equation The connection between the number of microstates of a system, W, and the entropy of the system, S, is expressed in a beautifully simple equation developed by Boltzmann and engraved on his tombstone: In this equation, k is Boltzmann’s constant, . Thus, entropy is a measureof how many microstates are associated with a particular macroscopic state.

39. Entropy Change as Related to V and T suppose we increase the volume of the system, which is analogous to allowing the gas to expand isothermally. A greater volume means a greater number of positions available to the gas atoms and therefore a greater number of microstates. The entropy therefore increases as the volume increases. Second, suppose we keep the volume fixed but increase the temperature. How does this change affect the entropy of the system? An increase in temperature increases the most probable speed of the molecules and also broadens the distribution of speeds. Hence, the molecules have a greater number of possible kinetic energies, and the number of microstates increases. Thus, the entropy of the system increases with increasing temperature.

40. Molecular Motions and Energy Any real molecule can undergo three kinds of complex motion. The entire molecule can move in one direction, which is the simple motion we visualize for an ideal particle and see in a macroscopic object, such as a thrown baseball. We call such movement translational motion. The molecules in a gas have more freedom of translational motion than those in a liquid, which have more freedom of translational motion than the molecules of a solid. A real molecule can also undergo vibrational motion, in which the atoms in the molecule move periodically toward and away from one another, and rotational motion, in which the molecule spins about an axis.

41. The vibrational and rotational motions possible in real molecules lead to arrangements that a single atom can’t have. A collection of real molecules therefore has a greater number of possible microstates than does the same number of ideal-gas atoms. In general, the number of microstates possible for a system increases with an increase in volume, an increase in temperature, or an increase in the number and complexity of molecules because any of these changes increases the possible positions and motional energies of the molecules making up the system.

42. Entropy and Dissolution The ions in the solution move in a volume that is larger than the volume in which they were able to move in the crystal lattice and so possess more motional energy. This increased motion might lead us to conclude that the entropy of the system has increased.

43. We have to be careful, however, because some of the water molecules have lost some freedom of motion because they are now held around the ions as water of hydration. These water molecules are in a more ordered state than before because they are now confined to the immediate environment of the ions. Therefore, the dissolving of a salt involves both a disordering process (the ions become less confined) and an ordering process (some water molecules become more confined). The disordering processes are usually dominant, and so the overall effect is an increase in the randomness of the system when salts dissolve in water.

44. Chemical Thermodynamics -2 Lecture 24

45. Making Qualitative Predictions About DS In summary, we generally expect the entropy of a system to increase for processes in which: • The volume of a system increases. • The temperature increases. • The number of independently moving particles increases. • The number of atoms in a molecule increases Remember that: entropy increases when: 1. Solids or liquids are converted to gases.2. Solids are converted to liquids or solutions.3. The number of gas molecules increases during a chemical reaction.

46. In which phase are water molecules least able to have rotational motion?

47. If a process is nonspontaneous, does that mean the process cannot occur under any circumstances? A. Yes. Nonspontaneous processes can never occur under any circumstances. B. No. Nonspontaneous processes can occur with some continuous external assistance.

48. What kind of motion which a molecule can undergo that a single atom can not? A. Molecules and single atoms experience the same types of motion. B. A molecule can vibrate and rotate; a single atom undergoes neither. C. A molecule can undergo translational motion and rotate; a single atom undergoes neither. D. A molecule can vibrate and undergo translational motion; a single atom undergoes neither.

49. If a process is exothermic, does the entropy of the surroundings: • Always increase • Always decrease • Sometimes increase and sometimes decrease, depending on the process? A. Always increase B. Always decrease C. Sometimes increases and sometimes decreases, depending on the process

50. Consider a pure crystalline solid that is heated from absolute zero to a temperature above the boiling point of the liquid. Which of the following processes produces the greatest increase in the entropy of the substance? A. melting the solid B. heating the liquid C. heating the gas D. heating the solid E. vaporizing the liquid