# Why isn't 0°F the lowest possible temperature for a salt/ice/water mixture?

In your Web page Why can adding salt to ice water make the ice melt slower? it says that "A mixture of rock salt, ice, and water packed in the bucket around the ice cream mix can bring the temperature down as low as -21°C." I am confused by this number. -21°C = (-21)*(9/5)+32 = -5.8 °F but I thought the Fahrenheit scale was defined such that the lowest temperature achievable by a water/ice/salt mixture was 0 degrees F (-17.8 degrees C).

What's going on? Is the "-21" a typo, or is rock salt somehow different from what Fahrenheit used, or is there some transient effect not reflected in Fahrenheit's procedure, or is it something else I have not thought of?
Rik Littlefield, Senior Research Scientist, Pacific Northwest National Laboratory 4/22/01

 Vocabulary equilibrium eutectic mixture freezing point depression melting point phase diagram solute

Daniel Gabriel Fahrenheit's temperature scale doesn't place 0°F at the lowest freezing point of salt water (-21.12°C, or -6.02°F). There are at least three reasons for that.

1. Fahrenheit didn't actually use the lowest freezing point of an NaCl solution as a natural calibration point on his temperature scale. He calibrated 0°F as "the limit of the most intense cold obtained artificially in a mixture of water, of ice, and of sal-ammoniac or even of sea-salt" [1]. Sal-ammoniac is ammonium chloride, and sea-salt is not just NaCl. The eutectic points for ammonium chloride and sea salt mixtures are not at exactly -21.12°C (the eutectic point for NaCl and water), and they are not exactly equal to each other.
2. Fahrenheit abandoned the original 0°F calibration point. He chose new calibration points twice. He first adjusted the scale to make 32 the ice melting point and 96 the temperature of "the blood of a healthy man" [1]. It's easy to mark scale divisions that are multiples of two with simple tools, and the adjustment produced a scale with 64 divisions between the ice melting point and blood temperature.

He eventually replaced the upper calibration point at blood temperature with the boiling point of water. He discovered that the boiling point of water could be reliably used as a calibration point if atmospheric pressure was fixed, a fact that earlier temperature scale architects had overlooked. The boiling point at normal atmospheric pressure was set to 212°F, exactly 180 degrees between the freezing point of water and the boiling point of water, perhaps because 180 degrees is the number of degrees between opposite poles.

3. Fahrenheit was a victim of Hofstader's Law,, which states:

It always takes longer than you think it's going to take, even when you take into account Hofstadter's Law.

 Phase map for salt water. Drawn from a diagram by R. E. Dickerson (Note 3)
As ice begins to freeze out of the salt water, the fraction of water in the solution becomes lower and the freezing point drops further. This does not continue indefinitely, because eventually the solution will become saturated with salt. The lowest temperature possible for liquid salt solution is -21.1°C. At that temperature, the salt begins to crystallize out of solution (as NaCl·2 H2O), along with the ice, until the solution completely freezes. The frozen solution is a mixture of separate NaCl·2H2O crystals and ice crystals, not a homogeneous mixture of salt and water. This heterogeneous mixture is called a eutectic mixture. The eutectic mixture makes a wonderful calibration point for a temperature scale because, at equlibrium, salt and ice and water co-exist at one temperature and at one temperature only. If you see all three substances present in a mixture, and their amounts are not changing over time, you must be at -21.1°C.

By mixing salt, ice, and water so that at least 23.3% of the mixture was salt, Fahrenheit should have reached the eutectic point- in theory. But in practice:

• Salt dissolves very slowly in cold water.
• Salt dissolves very slowly in solutions that already contain high concentrations of salt.
• The salt dissolves more slowly if it has not been finely ground, and if the mixture is not stirred.
When these factors combine, a salt/ice/water mixture can take many days to come to equilibrium. Fahrenheit probably didn't wait that long.

### References and Notes

1. D. G. Fahrenheit,Phil. Trans. (London) 33, 1, 1724. Carmen Giunta provided the excerpts quoted at http://webserver.lemoyne.edu/faculty/giunta/fahrenheit.html.
2. From Douglas R. Hofstadter's excellent book The saltwater phase diagram is based on Figure 6-59, p. 376 of R. E. Dickerson's Molecular Thermodynamics (Pasadena, California), 1969.
3. For a thermodynamic explanation of freezing point depression, see How can freezing point depression be explained in terms of free energies?

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! Why isn't 0°F the lowest possible temperature for a salt/ice/water mixture?