DG 5 2 278 J Would this be considered a spontaneous process? Because the pressure is not kept
5.6 Amino Acid Equilibria 5.7 Summary
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132 Chapter 5 | Introduction to Chemical Equilibrium
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this system, we will have to put work into the system, but then the change is not spontaneous.
Now consider a chemical system. Think about a 1-cm3 cube of metallic sodium in a beaker of 100 mL of water. Is the system at equilibrium? Of course not! There ought to be a somewhat violent, spontaneous chemical reaction if we try to put a cubic centimeter of sodium in water. The state of the system as described origi- nally is not at chemical equilibrium. However, it’s not a question of gravitational potential energy now. It is a question of chemical reactivity. We say that this Na-in-H2O system is not at chemical equilibrium.
The sodium metal will react with the water (which is in excess) via the following reaction:
2Na (s)12H2O (,) h 2Na1 (aq)12OH2 (aq)1H2 (g)
Once that reaction is over, there will be no further change in the chemical iden- tity of the system, and the system is now at chemical equilibrium. In a sense, it is very much like the rock and mountain. The sodium in water represents a rock on the side of a mountain (Figure 5.1a), and the aqueous sodium hydroxide solution (which is an accurate description of the products of the above reaction) represents the rock at the bottom of the mountain (Figure 5.1b).
Consider another chemical system, this one a sample of water, H2O, and heavy water, D2O, in a sealed container. (Recall that deuterium, D, is the isotope of hydro- gen that has a neutron in its nucleus.) Is this a description of a system at equilib- rium? Interestingly, this system is not at equilibrium. Over time, water molecules will interact and exchange hydrogen atoms, so that eventually some of the mole- cules will have the formula HDO—a result that can easily be verified experimen- tally using, say, a mass spectrometer. (Such reactions, called isotope exchange reactions, are an important part of some modern chemical research.) This process is illustrated in Figure 5.2. Other processes like precipitation of an insoluble salt from aqueous solution are also examples of equilibrium. There is a constant balance between ions precipitating from solution and ions dissociating from the solid and going into solution:
PbCl2 (s) h Pb21(aq)12Cl2 (aq) Pb21(aq)12Cl2 (aq) h PbCl2 (s)
No net change: chemical equilibrium
The rock on the side of the hill that becomes the rock at the bottom of the hill is an example of an equilibrium, but this is an equilibrium where nothing is happening. This is an example of a static equilibrium. Chemical equilibria are different. The chemical reactions are still occurring, but the forward and reverse reactions are occurring at just the same rate so that there is no overall change in the chemical identity of the system. This is called a dynamic equilibrium.
All chemical equilibria are dynamic equilibria. That is, they are constantly moving, but going nowhere.
(a) (b)
Figure 5.1 (a) A rock on the side of a mountain represents a simple physical system that is not at equilibrium. (b) Now the rock is lying at the bottom of the mountain. The rock is at its minimum gravitational potential energy. This system is at equilibrium.
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5.2 | Equilibrium 133
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O
D D
O
D D
O
D D
O
D D
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D D
O
H H
O
H H
O
H H
O
H H
O
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H D
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H D
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H D
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H H
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H D
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H H
Figure 5.2 Sometimes it is difficult to know whether a system is at chemical equilibrium. An equimolar mixture of H2O and D2O—water and heavy water—might appear to be at equilibrium when mixed initially, because both substances are simply water. But in reality, hydrogen exchange occurs to mix the isotopes of hydrogen among the water molecules. At equilibrium, the predominant molecule is HDO.
Why does any system come to equilibrium? Consider the rock on the side of the mountain in Figure 5.1a. From physics, we know that gravity is attracting the rock, and the slope of the mountain is not sufficient to counter that attraction and keep the rock from moving. So the rock tumbles down the side of the moun- tain until it gets to the bottom (Figure 5.1b). At this position, the ground coun- teracts the force of gravity, and the situation becomes a stable, static equilibrium.
One way of considering this system is from the perspective of energy: A rock on the side of the hill has excess gravitational potential energy that it can get rid of by moving down the side of the hill. That is, the rock will spontaneously move to a position that decreases its (gravitational potential) energy. From a physical standpoint, the minimum-energy equilibrium is described in terms of Newton’s ExamplE 5.1
Describe the following situations as either static or dynamic equilibria.
a. The level of water in a fishtank, as the water is constantly passing through a filter
b. A rocking chair that has stopped rocking
c. Acetic acid, a weak acid, that is ionized only to the extent of about 2% in aqueous solution
d. A bank account that maintains an average monthly balance of $1000 despite numerous withdrawals and deposits
Solution
a. Because there is constant motion of the material at equilibrium—the water—this is an example of a dynamic equilibrium.
b. A stopped rocking chair isn’t moving at all at the macroscopic level, so this situation is an example of a static equilibrium.
c. The ionization of acetic acid is a chemical reaction, and like all chemical reactions at equilibrium, it is a dynamic one.
d. Because money is moving in and out of the account, even though the average monthly balance maintains the equilibrium amount of $1000, it is a dynamic equilibrium.
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134 Chapter 5 | Introduction to Chemical Equilibrium
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first law of motion. There are balanced forces acting on the rock, so it remains at rest: at equilibrium.
What about chemical reactions? Why do chemical systems eventually reach equilibrium? The answer is analogous to that for the rock: There are balanced
“forces” acting on the chemical species in the system. These forces are actually energies—chemical potentials of the different chemical species involved in the system at equilibrium. The next section introduces chemical equilibrium in those terms.