Wednesday, March 30, 2011

Cold Facts About Dissolved Oxygen

By Dr. Scott Rudge

What’s the solubility of oxygen in water? Everyone knows that the answer to this question is “low”, and that’s enough to know for many practical applications. But it’s high enough to rust unprotected metal surfaces, and high enough to grow cells, provided that it’s replenished at some rate. It’s easy to find a number on the internet, at a temperature and pressure that the author of the internet resource thinks is interesting. But my interesting condition always varies from the internet’s, and finding the constants that I need to calculate the actual value is always difficult.

Most references that you can find say that the solubility of oxygen in water follows Henry’s Law. Henry’s Law is a very simple expression that says the concentration of a substance in a liquid phase is related to the partial pressure of that substance in the gas phase by a “constant”. Constant is a relative term in thermodynamics, because the constant in this and most cases varies with temperature and other components in both phases. But we’ll go with it.

In this equation, kH is Henry’s constant, p is the partial pressure of the substance in the gas phase and c is the corresponding concentration of that substance in the liquid phase. Partial pressure is simply the amount of the total pressure due to that substance. In a room full of air at sea level, the partial pressure of oxygen is approximately 21% of the atmospheric pressure, or 0.21 atmospheres (159.6 torr or mm Hg, or 3.1 psi). At 25°C, Henry’s constant for oxygen in pure water is 769.2 L*atm/mol.

To correct for temperature, an approximation using a reference temperature can be used, although the results will not be exact. The correlation is:

Where Tr is the reference temperature. Again, the use of these equations will give approximate values.

Adding salt to the water further decreases the solubility of oxygen, such that in sea water the solubility of oxygen is about 80% of that in pure water. In fermentation medium, the saturation concentration is probably even less.

For those who don’t like math, here’s the table for the dissolved oxygen concentration under air atmospheres containing 21% oxygen (dissolved oxygen concentrations in moles/L):