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How can I predict oxygen solubility in water?

The solubility of oxygen is affected by temperature and by the partial pressure of oxygen over the water.

How does temperature affect dissolved oxygen levels? The solubility of oxygen is greater in colder water than in warm water. Oxygen slips into "pockets" that exist in the loose hydrogen-bonded network of water molecules without forcing them apart. The oxygen is then caged by water molecules, which weakly pin it in place. The dissolution is exothermic overall, so cooling shifts the equilibrium towards the dissolved form .

How does oxygen partial pressure affect dissolved oxygen levels? Oxygen in water obeys Henry's law rather well; the solubility is roughly proportional to the partial pressure of oxygen in the air:

pO2 = KO2 xO2

where pO2 is the partial pressure of oxygen in Torr, xO2 is the mole fraction of oxygen in oxygen-saturated water, and KO2 is the Henry's law constant for oxygen in water (about 3.30 × 107 K/Torr for at 298 K ). Higher air pressure means higher partial pressure of oxygen, so waters at sea level can contain dissolve slightly more oxygen than mountain streams at the same temperature. High humidity very slightly lowers the fraction of oxygen in the air, and so lowers saturated dissolved oxygen levels slightly.

Many empirical equations are available to accurately estimate oxygen solubility as a function of temperature, pressure, and humidity. The more accuracy you require, the more complex the equations are.

Here are some very simple empirical equations that give the saturated dissolved O2 concentration (DO) in mg O2/L water. They apply to oxygen in distilled water at a barometric pressure of P (in torr), at a temperature of t (°C), with a water vapor pressure of p (in torr) :
0°C < t < 30°C
 DO = (P-p) × 0.678 35 + t
30°C < t < 50°C
 DO = (P-p) × 0.827 49 + t

Here's a quick DO calculator based on these functions. Just enter the barometric pressure in torr, and the water temperature in °C. Hit the Calculate button to see the saturated water vapor pressure and the predicted DO concentration.

 BarometricPressure (torr) Water Temperature (°C) Water Vapor Pressure (torr) Saturated DO Concentration (mg/L)
The saturated water vapor pressure is estimated by linear interpolation from a table of experimental values, and is reliable to 3-4 figures. The DO concentration is reliable to 2-3 figures.

Notes and References

1. See "Why do gas solubilities usually fall when temperature rises?
2. P. W. Atkins, Physical Chemistry, 6th ed., Oxford University Press, 1998. Henry's law constant for oxygen taken from Table 7.1 on page 174.
3. Standard Methods for the Examination of Water and Wastewater, 12th ed., American Public Health Association, New York, 1965. The empirical equations given above are taken from pp 408-410. Standard Methods also includes a table showing the solubility of oxygen in equilibrium with water-saturated air for solutions of different chlorinities.