edited bv GEORGEL. GILBERT Denison University Granville. Ohio 43023
Ice under Pressure Raymond Chang and James F. Sklnner' Willlams College WllliamsIown, MA 01267
The most interesting prediction made from a study of the nhase diaeram of water is that an increase in nressure on ice decreases its melting point. The practical consequence of rhe neeative s l o ~ e dPldT. . for the ice-liauid houndarv line is mentioned in most general and physiial chemistritexts in connection with ice skating. Presumably the pressure exerted by the skates melts the ice underneath and the water that forms permits the ease of movement over ice. However, Loucks in this Journal has pointed out that pressure alone is generally insufficient to produce the melting needed for ice skating2. He suggests that one must also take into account the thermal energy provided by the friction of the skate in contact with ice. While themelting of ice under pressure is clearly possible, i t occurs over a rather limited temperature range (between 0 and -22 "C). Below -22 OC, ice (I), the stable form of ice a t pressures up to about 2000 atm, cannot be in equilibrium with liquid water. Nevertheless, a straightforward demonstration of the phenomenon does not appear t o have been presented in this column. Such a demonstration on a scale suitable for a large or small classroom is described here. I t can be used to illustrate several fundamental principles. A bread-baking pan (10 X 25 cm) is filled with water to a depth of about 2.5 cm, and the water is frozen. A 1-kg weight is tied to each end of a 40-cm piece of steel music wire (-0.005 in. in diameter). The block of ice is placed on edge in the wooden holder illustrated in Figure 1 and the weighted wire looped over the edge of the ice. Depending on the room temperature and on how long the ice has been out of the freezer, the wire should pass through the block in 5-30 min, while leaving the block intact. The Clapeyron equation can be written as where AHf is the molar heat of fusion, Tfis the freezing (or melting) point, and AVr is the change in molar volume on melting. I t is the negative value for AVfthat causes the slope, or dPldT, to be negative for water. The equilibrium is endothermic in the forward direction. Increased pressure shifts the equilibrium toward the state that has the smaller molar volume, H20(1), but this requires the transfer of thermal energy, cooling the surrounlling ice, which in turn will result in the refreezing of water once the wire has passed. Loucks gives avalue of 125 atm per degree for the negative slopez. For the demonstration described, the pressure on the ice is estimated to be 50 atm, giving an equilihrium freezing point of about -0.4 "C. In observing this demonstration, an interesting misconception was voiced by several students. They suggested that the pressure of the wire produced heat,
' Deceased.
L. F. J. Chem. Educ. 1986, 63,115-1 16. LOUC~S,
10 cm.
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Figure 1. Front view (left) and side view (right) of the anangemem for melting ice ucder pressure.
Figure 2. me phase diagram of water.
which melted the ice. T o test this hypothesis, lead and Styrofoam blocks were nlaced on the lecture bench. and i t was emphasized that the temperature under the blbcks on the bench was the same. reeardless of the nressure exerted on the spot. Work can,of course, produce heat, but pressure alone cannot. A portion of the phase diagram (not to scale) is shown in Figure 2. Point A (0.01 O C , 0.0060 atm) is the triple point of water. Point B (0 OC, 1.0 atm) is the normal melting point, and point C (--0.4 OC a t a pressure of 60 atm) is the melting point in the demonstration. Note that, if the temperature remained a t 0 O C as the pressure had been increased from 1 to 50 atm (point D), the system would not have been at equilibrium and the ice would have melted. To maintain the equilibrium a t the high pressure, the temperature must drop to -0.4 OC (point C). Two additional demonstrations may be of interest. First, in very cold climate regions (temperature below -22 OCJ the wire-over-ice-blockdemonstration can he set up outdoors to Volume 67 Number 9
September 1990
789
show that ice does not melt under pressure as explained above. Second. it is instructive to comnsre the effect of pressure on melting point using another substance that has a oositivedPldT. Asuitahlechoice is cvclohexane, which hasa normal melting point of 6.6 "C. ~ p ~ r o x i m a t 40 el~ mL of cvclohexane is degassed and then frozen in a test tube (about i c m i.d.). w a r m k g the test tube to room temperature for a few minutes will permit the removal of the solid rod. A weighted wire will mechanically fracture the solid cyclobexane, hut there is no refreezing of the two portions of the rod as is found with the ice block. In this case an increase in pressure actually increases the melting point. ~~
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Shear
Visoelastic Surfactant Solutions: A Demo To Catch the Student's Attention SUBMITTEDBY
Steven Jon Bachofer
St. Mary's College of California Moraga, CA 94575 CHECKED BY
Paul Krause University of Cedrai Arkansas Conway. AK 72032 Can physical chemistry be fun? It can explain what clearly appear to he magical properties. A specific example is viscoelasticity, which is a rheological phenomenon (I). The viscoelastic effect can he observed upon subjecting a disordered svstem with a shear force that orders it. stopnine the shear. a i d viewing the system as it relaxes back to ihLdisordered state. This phenomenon is easilv observable if air bubbles are entrapped in this fluid ~ p o ~ s w i r l i nthe g contents (applying the shearing force) since in the relaxation period, the air bubbles stop and flow backwards to the initial direction of shear (2).Karol Mysel noted viscoelasticity is observable in egg albumin (egg whites), although we do not normally notice i t (I). This observation is so directly opposite to our fundamental understanding of materials (e.g., aqueous solutions) that it draws in the students to understand what is inuolued. The excitement to understand this phenomenon can be utilized to start serious investigations of colloidal systems that are easily understood through physical chemical measurements. The students gain an appreciation that they are developing skills that can he utilized to solve present day chemical questions. The remarkable appearance of viscoelasticity has been .. explained ft,r a number of colloidal systems containing pn)late niirelles (rod-shaped aggregates) (31. The pmlate rnicelles are a disorderedmicelfar system, which can be considered analogous to a spring about to be compressed. The compression force (which in this case is a shear) orders the system. Upon removal of the shear, the prolate micelles recoil hack to the disordered state just as a compressed spring would recoil. (See figure.) This phenomenon is also observed in numerous polymer aggregate-medium matrices, although they are not our primary focus (4). We here report on a svstem discovered in our own research that is easilv prepared for a lecture demonstration to encourage underaradustes that physical chemistry can be utilized to explain . . even unusual phenomena. T h e determination of critical micelle constant' is a stratphtforward euperimrnt that an undergraduate can do atrer viewing his demonstration. Numerous methods for determination of a cmc value can be applied and have been listed in this Journal (5). Preparatlon of Demonstration Sample 'The viscot~laitirdemcmrrnrion $ample is prepared wrth a 1.1 rtoirhmnrtric mixture oftus, mlls; the caticmr surfactant, cetyllrimethyhmmunium bnmrdefC'l'.AHI a n d the uenk ncld standard.
790
Journal of Chemical Education
Pictorial representation of prolate miceliar aggregates. The prolate micelles are initially in a disordered state (A), then in an ordered state under the shear (B),and return to the disordered state upon removal of the shear (A). This pictorial representation is used only in an analogy.
potassium hydrogen phthalate(KHP) (6).Both materials are commercially available and can be used without further purification. The 1:l mixture that is prepared above the critical micelle constant concentration(cmc) at 10 mM in each reagent salt demonstrates a viscoelastic effect. The solubility of the catianie surfactant is very low at room temperature since its Kraft point (temperature where its solubility increases strongly) is slightly above room temperature. In preparing a concentrated stock solution of CTAB, one can either sonicate or warm the solution to obtain the supersaturated stock. Crystalline potassium hydrogen phthalate(KHP) also dissolves slowly and therefore should be prepared ahead of time. Equal volumes of 20 mM solutions of each stock salt will yield a solution that will exhibit viseaelasticity. The rheological effect isclearly demonstrated (if the audience is within 20 f t of the demonstrator1fillins a 25- hv 150-mm test tuhe approximately half iull and nirer entrapping a icw air bulhles hy shaking the aamplr; swirling the tcsl tube wrll genemcra aigmfirant shenr gradient to provide the uhr~rwtiun Explaining the Demonstratlon The 1:l mixture forms an aggregate of the two oppositecharged materials (surfactant quaternary ammonium cation and hydrogen phthalate anion). The aggregate is formally a mixed micelle. T h e mixed micelle is a prolate (rod-shaped) micelle since the hydrogen phthalate anion situates itself a t the interface neutralizing the charge repulsionof thequaternary ammonium cation head groups of the surfacranr (3a). The anion not only changes the el&trostatic free energy of the interface by charge neutralization but also decreases the surface area to volume ratio of the micelle and therefore prescribes the change in aggregate ~ h a p e . The C'TAB:KHP system and analorous svstems with ~ h . er substituted benzoate anions are sirongiy dependent on pH, ionic strength, the substituent groups, and temperature (3, 6). The p H dependence is understood considering protonation of the carboxylate group eliminates the anionic charge, which enhances the charge-neutralization of the micellar interface. An ionic strength change perturbs the counterion bindine eauilibria and can even eliminate the ~~~-viscoelastic effrrt."wr? have srudied this counterion binding for numeroussubstituted beneoates with CTAH and have found an empirical correlation between the cmc value and the appearance of viscoelasticitv (6). Another clarifvine . ~ o i nist to show the appearance of &oelasticity in a sample shove the cmc and the disappearance of visroelastirity upon dilu~
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