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
-
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.
- 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.
- 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.
- 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.
![Saltwater phase diagram]() |
| 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
- D. G. Fahrenheit,Phil. Trans. (London) 33, 1, 1724. Carmen
Giunta provided the excerpts quoted at http://webserver.lemoyne.edu/faculty/giunta/fahrenheit.html.
- 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.
- For a thermodynamic explanation of freezing point depression, see How
can freezing point depression be explained in terms of free energies?
Author: Fred Senese
[EMAIL PROTECTED]
General
Chemistry Online! Why isn't 0�F the lowest possible temperature for a
salt/ice/water mixture?
Copyright � 1997-2004 by Fred
Senese
Comments & questions to [EMAIL PROTECTED]
Last
Revised 02/28/04.URL: http://antoine.frostburg.edu/chem/senese/101/measurement/faq/print-zero-fahrenheit.shtml
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