ROBERT C. PLUMB
chemical principles exemplified
Freezing Ice Cream and Making Caramel Topping Illustrating principles of thermodynamics Suggested by John Otto Olson Uniuersity of Maine a t Fort Kent a n d Leo H. Bowman Southwest Minnesota State College The term "colligative properties"' has a mysterious, ahstract ring to it; the obscurity can be dispelled by the two exempla which follow. Althoueh there are now ice cream makers which vou " place inside your home freezer, the old-fashioned way of freezine ice cream with a salt-ice mixture is very effectiveand a Gt of fun. Why is an ice-salt bath colde; than an ice bath? Does it depend on the ice being colder than 0°C prior to the addition of salt? If not, where does the heat go when the mixture gets cold? Leo Bowman related the following experience to his students as an exam question Recently my wife shanghaied me into stirring the ingredients of a caramel tapping, while she continued the rest of her work. She directed me to stir the mixture of sugar, milk. . . constantly until the temperature reached 235°F. I obediently began the process without really considering the directive. In a brief duration the temperature of the boiling fluid leveled off at approximately 215-F. Again, without careful analysis, I remarked that her directions were foolish-"the content is an aqueous mixture and it is not possible to heat it above the slightly elevated boiling point". Eventually, of course, the 235OF level was attained. Why?
not vary with temperatures. Further, when the honds in ice are broken and liquid water is formed the molecules are relatively freer to move around and the liquid water is more disordered and hence has a higher entropy. The entropy change, ASo, when ice melts to form pure water a t a constant pressure of 1.0 atm is +5.28 cal mole-' deg-'. T h e change in the entropy of the system is also approximately independent of temperature because the difference in order between solid ice and pure liquid water depends on the difference in structure between the two and not on the temperature. For equilibrium between ice and water a t a pressure of 1.0 atm to exist, the tendency to seek a low energy state, ice, and the tendency to seek a high entropy state, water, must exactly balance. The change in Gibbs free energy for the reaction will then be zero and the reaction will be a t equilibrium. In quantitative terms this is expressed by the equation A G O
= AH' - TAS' = 0
where the enthalpy term and the entropy term exactly cancel each other. At what temperature will this cancellation take place? =
=
ASo
1436 eal mol-I = 273'K 5.28 cal mol-' deg-'
At, that is, the normal melting point of ice. Now suppose
Bv and laree, - . in introductorv chemistry courses all that is done to explain these phenomena is to say that freezing ~ 0 i n t are s lowered and boiling-uoiuts elevated hv the addi. tion of solutes. It is natural to inquire then-why are the freezing point and boiling point affected by the addition of solutes? Why is one lowered and the other elevated? I t would seem that these are such common phenomena, widely known to non-scientists as well as scientists that the chemistry teacher should he prepared to explain them in the simplest possible terms. The author finds the following explanation useful after students have studied some elementary thermodynamics. When ice melts, intermolecular bonds are broken increasing the intermolecular potential energy and hence the euthalpy of the system. Thus, when ice melts a t a constant pressure of 1.0 atm
H,O(I) pure Tb=lOOOC
HuO(s)= HgO(l)
,Hp(l)in IOFsol. Tf=-19-12
AHo = +I436 cal mole-'
4
* at4OO'C
nH,OII) p u r e >=O'C
The amount of thermal energy required to melt a mole of ice a t constant pressure, AHo, is approximately independent of temperature since most of that energy is used to break the honds in ice and the strength of the honds does 'That is, properties which depend on the number of particles present in a solution rather than on the kind of particles.
Entropy diagram tor pure water compared to water in 10 Fsalution.
Volume 53,Number 1. January 1976 / 49
that instead of pure water we have a salt solution in contact with the ice. If the solution is dilute the salt will not have a significant effect on the energy required to hreak the bonds in ice; that is, it will not affect the AHo for the reaction. However, instead of there being water molecules at any arbitrary point in space in the liquid there will now be some finite probability that there will be an ion of Na+ or C1- instead of a water molecule. Qualitatively then we see that the entropy of water in the salt solution is greater than the entropy of pure water. This is shown in the accompanying figure. Of course, if the salt increases the entropy of the water in the solution the entropy driving force of the reaction
must also be increased, as shown. At what temperature will there he equilibrium between ice and a salt solution? Qualitativelv we see that since AS for the reaction is lareer the temperature of equilibrium must be lower, i.e., the freezing ooint is deoressed. T o describe the deoressine effect of salt &antitati;ely one needs to know how mucLdifferent the entropy of water in the solution is from the entropy of pure liquid water. If it is considered to he an ideal solution the entropy is larger by an amount -Rln X, where X , is the mole fraction of solvent. This is just the effect of "diluting" the water with salt. With some mathematical manipulation, hut no further physical insights into the prohlem, this expression for the difference in entropy of a solvent in a solution may he combined with the previous expression for the temperature at which solid and liquid will be in equilibrium t o produce a quantitative expression for the freezing point lowering. In the simolest thermodvnamic laneuaee the temoera" ture of equilibrium between-ice and water is lowered dy the addition of salt because the entroov .. drivine" force for the fusion reaction is increased by the salt "diluting the water". When the temperature drops, a balance is restored in
50 / Journal of Chemical Education
which the competing driving forces of low intermolecular potential energy and maximum molecular disorder are balanced. And-in physical terms-where does the heat go when ice and salt at 0°C are mixed and the temperature drops to say -5"C? The answer-heat energy is converted to intermolecular potential energy and stored that way-that is, the heat energy is used to hreak bonds between molecules in ice. The intensity of thermal kinetic motion in the system a t 0°C is reduced to that characteristic of a temperature of -5"C, this decrease in thermal kinetic energy being halanced by an increase in the potential energy of the water. Liquid water represents a higher intermolecular potential energy state than ice because of less bonding than in the solid state. The first law of thermodynamics is satisfied; energy is conserved, being only converted from a thermal to potential form. And why does the addition of a non-volatile solute such as sugar raise the boiling point? The solute increases the entropy of water in the solution by making the water more dilute, just as it does a t the freezing point. However, as shown in the accompanying figure, increasing the entropy of water in the solution decreases the change of entropy for the reaction. HpO(l) = H 2 0 ( g )
In pure water a t 1.0 atm pressure, A H D and ASo for this reaction are balanced a t 373'K. If the entropy change for the reaction is decreased a higher temperature is required to produce equilibrium. Thus sugar and other solutes elevate the boiling point of water. As the caramel topping is cooked water boils off and the solution becomes more concentrated. As the concentration increases the entropy of the water in the solution increases and the temperature rises further. The cook, perhaps unwittingly, uses the boiling point as a quality control to determine exactly when the concentration of sugar has reached the ideal caramelization condition.
