# Protecting Citrus Trees from Freezing with Freezing Water


## Protecting Plants from Frost

When a temporary frost is expected in usually mild climates, managers of citrus orchards and vinyards may spray plants with microspray (fogging) irrigation systems to keep plant wet with water near 0 °C[1].

Figure $$\PageIndex{1}$$ Ash canker caused by Pseudomonas syringae, which is responsible for frost damage[2]

Paradoxically, the cold water is very effective at providing heat to trees from freezing[3][4]. Surprisingly, six times as much heat (about 6 kJ) is released as a mole (18 g) of water freezes at 0°C, than can be supplied when the same 18 g of "warm" water cools from 15°C to 0°C (about 1.1 kJ)[5].

## Enthalpy of Fusion

There is no temperature change as the water freezes at 0°C, so the heat that is released is called the "Latent Heat of Fusion" (or "Latent Enthalpy of Fusion"). The word fusion means the same thing as “melting”, and it's called the "latent" heat because it is "hidden" (not evident) because there is no temperature change. If air at temperatures below about -1°C moves into orchards, plants may be damaged[6] (water in the cells freezes a little below 0°C because dissolved substances cause freezing point depression). The temperature at which plant damage occurs depends on the season and other variables[7]. But if plants are covered with water at 0°C, heat is removed preferentially from the water as intermolecular H2O-H2O bonds form exothermically, and the plant is protected.

Frost damage in plants is actually promoted by a bacterium,Pseudomonas_syringae,

Figure $$\PageIndex{2}$$ Pseudomonas syringae cultures[8]

which was discovered by chance in 1961 when only corn plants dusted with a fungus preparation suffered frost damage. The bacterium catalyzes freezing of water by creating "nucleation sites" where ice crystal form, and the ice crystals then damage the cells. A concentration of about 107 to 108 bacteria per milliliter[9] is necessary to promote freezing (at slightly below 0°C), so ice crystals form in plant pores and crevices where they are more damaging than surface ice from irrigation. "Ice-minus" bacteria which do not catalyze freezing have recently been developed by recombinent DNA methods, to protect plants [10].

This macroscopic behavior demonstrates quite clearly that energy must be supplied to a solid in order to melt it, and energy is released when a liquid freezes. On a microscopic level, melting involves separating molecules which attract each other, increasing their potential energy and breaking a kind of bond. The bonds form during freezing, releasing energy.

When 1 mol of ice, for example, is melted, we find from experiment that 6.01 kJ are needed. The molar enthalpy of fusion of ice is thus +6.01 kJ mol–1, and we can write

$\ce{H2O (s) -> H2O (l)}\nonumber$

(0°C) ΔHM = 6.01 kJ mol–1

Selected molar enthalpies of fusion are tabulated below. Solids like ice which have strong intermolecular forces have much higher values than those like CH4 with weak ones.

## Enthalpy of Vaporization

Spraying fruit trees with water is tricky, because if the relative humidity is low, the water vaporizes, and this causes a reduction in temperature in already cold orchards[11].

This effect is familiar--it also causes cooling of our skin when we perspire. When 18 g (1 mole) of water vaporized at 100°C, 40.67 kJ of energy must be absorbed from the surroundings to break bonds between water molecules, so it is an endothermic (cooling) process. Note that it takes 7.5 times more energy to vaporize water as it takes to melt it. The quantities of heat are similar, but somewhat different when the water vaporizes from your skin at 37°C than when it boils at 100°C.

When a liquid is boiled, the variation of temperature with the heat energy supplied is similar to that found for melting. When heat is supplied at a steady rate to a liquid at atmospheric pressure, the temperature rises until the boiling point is attained. After this the temperature remains constant until the enthalpy of vaporization has been supplied. Once all the liquid has been converted to vapor, the temperature again rises. In the case of water the molar enthalpy of vaporization is 40.67 kJ mol–1. In other words

$\ce{H2O (l) -> H2O (g)}\nonumber$

(100°C) ΔHM = 40.67 kJ mol–1

Table $$\PageIndex{1}$$: Molar Enthalpies of Fusion and Vaporization of Selected Substances.
Substance Formula ΔH(fusion)
/ kJ mol1
Melting Point / K ΔH(vaporization) / kJ mol-1 Boiling Point / K (ΔHv/Tb)
/ JK-1 mol-1
Neon Ne 0.33 24 1.80 27 67
Oxygen O2 0.44 54 6.82 90.2 76
Methane CH4 0.94 90.7 8.18 112 73
Ethane C2H6 2.85 90.0 14.72 184 80
Chlorine Cl2 6.40 172.2 20.41 239 85
Carbon tetrachloride CCl4 2.67 250.0 30.00 350 86
Water* H2O 6.00678 at 0°C, 101kPa
6.354 at 81.6 °C, 2.50 MPa
273.1 40.657 at 100 °C,
45.051 at 0 °C,
46.567 at -33 °C
373.1 109
n-Nonane C9H20 19.3 353 40.5 491 82
Mercury Hg 2.30 234 58.6 630 91
Sodium Na 2.60 371 98 1158 85
Aluminum Al 10.9 933 284 2600 109
Lead Pb 4.77 601 178 2022 88

Heat energy is absorbed when a liquid boils because molecules which are held together by mutual attraction in the liquid are jostled free of each other as the gas is formed. Such a separation requires energy. In general the energy needed differs from one liquid to another depending on the magnitude of the intermolecular forces. We can thus expect liquids with strong intermolecular forces to have larger enthalpies of vaporization. The list of enthalpies of vaporization given in the table bears this out.

Two other features of the table deserve mention. One is the fact that the enthalpy of vaporization of a substance is always higher than its enthalpy of fusion. When a solid melts, the molecules are not separated from each other to nearly the same extent as when a liquid boils. Second, there is a close correlation between the enthalpy of vaporization and the boiling point measured on the thermodynamic scale of temperature. Periodic trends in boiling point closely follow periodic trends in heat of vaporiation. If we divide the one by the other, we find that the result is often in the range of 75 to 90 J K–1 mol–1. To a first approximation therefore the enthalpy of vaporization of a liquid is proportional to the thermodynamic temperature at which the liquid boils. This interesting result is called Trouton’s rule. An equivalent rule does not hold for fusion. The energy required to melt a solid and the temperature at which this occurs depend on the structure of the crystal as well as on the magnitude of the intermolecular forces.

From ChemPRIME: 10.9: Enthalpy of Fusion and Enthalpy of Vaporization

## References

1. http://biomet.ucdavis.edu/frostprotection/Principles%20of%20Frost%20Protection/FP005.html
2. en.Wikipedia.org/wiki/Pseudomonas_syringae
3. www.fshs.org/Proceedings/Pass...0(PARSONS).pdf
4. www.wateright.org/960803.asp
5. We'll explain this later Heat Capacities
6. ucce.ucdavis.edu/files/reposi...8100-54166.pdf
7. www.sidney.ars.usda.gov/Site_...Low%20Temp.pdf
8. en.Wikipedia.org/wiki/Pseudomonas_syringae
9. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC186742/?page=2
10. en.Wikipedia.org/wiki/Ice-minus_bacteria
11. www.sidney.ars.usda.gov/Site_...Low%20Temp.pdf