Thermal Buffers: An Illustrative Analogy Every student who passes through a general chemistry course must inevitably do battle with the concept of aeid-base buffer systems. Yet even after developing the ability to solve the appropriate equations and calculate resulting pH, many students emerge without an appreciation of how the buffer system actually works. We offer below an analogy between acid-base buffer behavior and the thermal behavior of a two-phase (solid and liquid) system. T a begin, let'ssummarize the behavior of an aeid-base buffer. We haveasolution containinga soluble weak acid (HA) and its conjugate base (A-) in comparable amounts. That the acid is weak implies two things: HA is dissolved but only slightly dissociated (-1% in the absence of added A-), and A- is a relatively strong base. The pH of this solution is given by pH = pK. -log- [HA1 [A-I The huller action arisrs when a strong acd w r hnsel iiaddcd to ihr irlutim, nmvrrting A- tu HI\ !lur H.4Io A-I. Althwph the mtio HA ,\- inrrrnws (ur decrtairs) rather suhstantislly. lhe pH rcmninr relatively unallrcred. n m p n r e d lu dddiny the same amount of strong acid (or base) t o pure water. Of course if one adds too much strong acid (or base), virtually all the A- (or HA) will be exhausted. With the "buffer capacity" thus exceeded, the pH will begin to fall (or climb) rapidly. These situations are shown graphically in Figure 1. I
heat camcity d liquid
PC-10
(1.0callg degl
30 -1
-40 :
1.0
-
0.5
0
0.5
1.O
moles acid added j moles base added
Figure 1. Buffer curve far 1.0 I of a solution containing 1.0 male HA (K, = 1 X lo@) and 1.0 mole A-.
60
-
40
20
0
20
40
- heat removed (callheat added (call -
M1
Figwe 2. Temperalure of a midure of ice and water (0.5g each) as a functionof heat absorbed or liberated.
Now consider an equilibrium salid-liquid mixhre of any pure substance, e.g., ice and water, with comparable amounts in each phase. Such a mixture must, by definition, he a t the melting paint of the solid (or freezing point of the liquid). Now suppose we add (or remove) heat from this mixture while maintaining equilibrium and noting the temperature. As heat is absorbed by the system, some of the ice is converted to water, the actual amount being governed by the heat of fusion (AHf) of ice. Conversely if heat is removed from the system, liquid water is converted to ice (again in an amount eontrolled by M f ) . But as long as there is some liquid in equilibrium with the solid (or "ice verso), the temperature will remain steadfastly a t 0°C. However, once sufficient heat is added (or removed) to completely melt (or freeze) the mixture, further additian (or removal) of heat will cause the temperature of the system to rise (or fall) in accordance with the heat capacity (C)of the liquid (or solid). This behavior is shown in Figure 2. Thus the water-ice mixture responds to the addition or removal of heat much like a weak acid-conjugate base buffer resounds to the addition of strane acid or base. The one significant difference, af course, is that the middle of the graph is strictly flat for a two-component mixture, while only relatively flat in the buffer system University of Cincinnati Cincinnati, OH 45221
710 1 Journal of Chemical Education
Roger S. Macomber
