# Ice point

The ice point (also freezing point of water or melting point of water ) is the temperature at which air-saturated but otherwise pure liquid water under a pressure of one atmosphere (1013.25  hPa ) is in equilibrium with both its ice and its vapor . This temperature is approximately 273.15 K on the Kelvin scale and approximately 0 ° C on the Celsius scale .

Air-saturated but otherwise pure liquid water freezes when its temperature falls below the ice point at a pressure of 1013.25 hPa (and no supercooling delays the freezing). Air-saturated but otherwise pure water ice melts when its temperature at this pressure exceeds the ice point.

Before the definition of the Celsius scale was linked to the definition of the Kelvin scale in 1954 , the ice point (by definition 0 ° C) and the boiling point (by definition 100 ° C) of water served as their defining fixed points.

The linguistic usage is inconsistent: The respective point in the phase diagram of the water is sometimes referred to as the “ice point” (ie the pair of numbers 273.15 K and 1013.25 hPa), and sometimes the respective temperature (as it were, the “point” on the temperature scale). The same is true for the triple point .

## Explanation

### Transition from triple point to ice point

The triple point temperature of water is the temperature at which pure water and pure ice are in equilibrium with their vapor under the condition that the pressure in all three phases is equal to the saturation vapor pressure of the water at this temperature. There is exactly one point in the pressure-temperature diagram of pure water at which this equilibrium is possible, namely at around 273.16 K and 611 Pa. If one assumes a different pressure than the water's own saturation vapor pressure, then the three phases are in equilibrium at a different temperature. Another pressure can be generated by adding an additional, inert gas to the gas phase of the system.

If this added gas is in particular air and the pressure is set so that the total pressure of air and water vapor is 1013.25 hPa, then liquid water, water ice and water vapor are in equilibrium at a temperature around 0.01 Degrees lower than the triple point temperature. This shift in equilibrium temperature has two causes.

### Influence of the increased pressure

Schematic phase diagram of water.

Because the melting curve in the phase diagram of water is inclined to the left, the increase in pressure causes a drop in the freezing point of around 0.0075 degrees: If the pressure is increased from the triple point while the temperature is initially kept constant, the system leaves the triple point and enters the liquid area Water. Here the ice phase is not stable and melts. Once a pressure of one atmosphere has been reached, the temperature must be reduced by 0.0075 degrees so that the system returns to the melting curve and the coexistence of liquid water and ice is possible again.

### Influence of the dissolved air

Because part of the pressure-generating air goes into solution in the water , this is no longer a pure substance, but a mixture. The lowering of the freezing point in mixtures means that the temperature has to be lowered by a further 0.0025 degrees in order to regain phase equilibrium.

The ice point is less fundamental than the triple point because it is a property of the multicomponent system “air-saturated water”, while the triple point is a property of the pure substance system “water”.

## Ice point temperature

Simplified estimated values ​​for the two mentioned contributions to the lowering of the freezing point are easy to obtain.

### Influence of the increased pressure

${\ displaystyle {\ frac {\ mathrm {d} p} {\ mathrm {d} T}} \, = \, {\ frac {\ Delta h} {T \, \ Delta v}}}$

describes the slope of a phase boundary line in the p - T diagram. In order to determine the slope of the melting curve of water at the triple point, the melting enthalpy of ice and the change in the specific volume during melting must be used: ${\ displaystyle \ Delta h}$${\ displaystyle \ Delta v}$

${\ displaystyle \ textstyle \ Delta h = 333 {,} 43 \, \ mathrm {\ frac {kJ} {kg}}}$
${\ displaystyle \ textstyle \ Delta v = -0 {,} 000091 \, \ mathrm {\ frac {m ^ {3}} {kg}}}$
${\ displaystyle \ textstyle T = 273 {,} 16 \, \ mathrm {K}.}$

Dissolved after results for the change in pressure , the freezing point change ${\ displaystyle \ mathrm {d} T}$${\ displaystyle \ textstyle \ mathrm {d} p = 101325 \, \ mathrm {Pa} -611 \, \ mathrm {Pa} = 100714 \, \ mathrm {Pa}}$

${\ displaystyle \ mathrm {d} T_ {p} = - 0 {,} 0075 \, \ mathrm {K}}$

assuming that the slope does not change noticeably in the entire swept pressure area.

### Influence of the dissolved air

The lowering of the freezing point due to the dissolved gases is a colligative property , i.e. it does not depend on the type of dissolved particles, but only on their number and the type of solvent. For water as a solvent the cryoscopic constant is . At atmospheric pressure and 0 ° C, 0.00046 moles of oxygen and 0.00081 moles of nitrogen dissolve from the air in one kilogram of water. The molal concentration of 0.00127 mol / kg of the dissolved atmospheric gases causes a depression of the freezing point ${\ displaystyle \ textstyle 1 {,} 86 \, \ mathrm {\ frac {K} {mol / kg}}}$

${\ displaystyle \ mathrm {d} T_ {l} = - 1 {,} 86 \, \ mathrm {\ frac {K} {mol / kg}} \ cdot 0 {,} 00127 \, \ mathrm {\ frac { mol} {kg}} = -0 {,} 0024 \, \ mathrm {K}}$.

### Ice point temperature

The result is a precise calculation that also takes into account other atmospheric gases, the temperature dependence of the solubilities, the non-idealities of the dissolved substances and the pressure and temperature dependencies of the thermophysical properties of the water

${\ displaystyle T _ {\ mathrm {ice cream}} \, = \, (273 {,} 150019 \ pm 0.000005) \, \ mathrm {K}}$.

This numerical value is usually rounded to 273.15 K.

## Freezing point at other pressures

The calculation can also be carried out for other pressures; the following table lists some examples. For comparison, it is supplemented by the triple point:

Pressure

hPa
Freezing point of
pure water
K
Solution
effect
mK
Freezing point of
air-saturated water
K
1050 273.152246 −2.591 273.149655
1013.25 273.152519 −2,500 273,150019
1000 273.152618 −2.468 273.150150
0900 273.153360 −2.220 273.151140
0800 273,154103 −1.973 273.152131
0600 273,155589 −1.477 273.154112
0400 273.157075 −0.981 273.156093
0006.11 273.16 00- 000 -

The ice point should not be confused with the frost point, which is analogous to the dew point temperature, or frost point, below which frost is deposited.

## Remarks

1. The calculation results in the following molar proportions in the solution for the dissolved gases at the ice point temperature : 14.95 × 10 -6 for N 2 , 8.22 × 10 -6 for O 2 , 0.40 × 10 -6 for Ar, 0.54 x 10 -6 for molecular weight dissolved CO 2 , 0.05 x 10 -6 for each of HCO 3 - - and H + ions in the sum of 24.21 × 10 -6 dissolved for all gases.
2. The uncertainty mentioned above, the following from the input data and the calculation method uncertainty is the temperature spacing between the triple point and freezing point. At the time of these investigations, the triple point temperature as a defining fixed point had an exactly given numerical value, the uncertainty mentioned was therefore also the uncertainty for the absolute position of the ice point temperature on the Kelvin scale. Since the new definition of the Kelvin (2019), the triple point temperature is no longer a defining fixed point; it now has to be measured and therefore itself has a certain uncertainty. When the new definition was introduced, this uncertainty was 0.1 mK (see → triple point ). The uncertainty in the distance between the triple point and the ice point is still the same, but the uncertainty in the absolute position of the ice point is now greater by the uncertainty of the position of the triple point.

## Individual evidence

1. a b entry on melting point. In: Römpp Online . Georg Thieme Verlag, accessed on May 23, 2019.
2. CF Bohren, BA Albrecht: Atmospheric Thermodynamics. Oxford University Press, New York, Oxford 1998, ISBN 978-0-19-509904-1 , p. 222.
3. U. Grigull: Technical Thermodynamics. 3rd edition, de Gruyter, Berlin / New York 1977, ISBN 3-11-006405-7 , p. 118
4. MS Owen (ed.): 2013 ASHRAE Handbook Fundamentals - SI edition. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (ASHRAE), ISBN 978-1-936504-46-6 , Table 3.
5. ^ AF Holleman , N. Wiberg : Inorganische Chemie . 103rd edition. Volume 1: Basics and main group elements. Walter de Gruyter, Berlin / Boston 2016, ISBN 978-3-11-049585-0 , p. 741 (reading sample: Part A - Basics of the chemistry of hydrogen. Google book search ). "1 liter of water at 0 ° C dissolves - regardless of the gas pressure [...] - 23.2 cm³ nitrogen or 49.1 cm³ oxygen."
6. ^ A b AH Harvey, MO McLinden, WL Tew: Thermodynamic Analysis and Experimental Study of the Effect of Atmospheric Pressure on the Ice Point. AIP Conference Proceedings, vol. 1552, issue 1, 221-226 (2013), doi : 10.1063 / 1.4819543