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, k_H 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 T_r 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):

Bending the Curve

By Dr. Scott Rudge

To understand the best ways to develop preparative and industrial scale adsorption separations in biotechnology, it’s critical to understand the thermodynamics of solute binding. In this blog, I’ll review some basics of the Langmuir binding isotherm. This isotherm is a fairly simplistic view of adsorption and desorption, however, it applies fairly well to typical protein separations, such as ion exchange and affinity chromatography.


A chemical solution that is brought into contact with a resin that has binding sites for that chemical will partition between the solution phase and the resin phase. The partitioning will be driven by some form of affinity or equilibrium, that can be considered fairly constant at constant solution phase conditions. By “solution phase conditions”, I mean temperature, pH, conductivity, salt and other modifier concentrations. Changing these conditions changes the equilibrium partitioning. If we represent the molecule in solution by “c” and the same molecule adsorbed to the resin by “q”, then the simple mathematical relationship is:

If the capacity of the resin for the chemical is unlimited, then this is the end of the story, the equilibrium is “linear” and the behavior of the adsorption is easy to understand as the dispersion is completely mass transfer controlled. A example of this is size exclusion chromatography, where the resin has no affinity for the chemical, it simply excludes solutes larger than the pore or polymer mesh length. For resins where there are discrete “sites” to which the chemical might bind, or a finite “surface” of some kind with which the chemical has some interaction, then the equilibrium is described by:

and the maximum capacity of the resin has to be accounted for with a “site” balance, such as shown below:

Where S_tot represents the total number of binding sites, and S₀ represents the number of binding sites not occupied by the chemical of interest. The math becomes a little more complicated when you worry about what might be occupying that site, or if you want to know what happens when the molecule of interest occupies more than one site at a time. We’ll leave these important considerations for another day. Typically, the total sites can be measured. Resin vendors use terms such as “binding capacity” or “dynamic binding capacity” to advertise the capacity of their resins. The capacity is often dependent on the chemical of interest. The resulting relationship between c and q is no longer linear, it is represented by this equation:

When c is small, the denominator of this equation becomes 1, and the equilibrium equation looks like the linear equilibrium equation. When c is large, the denominator becomes K_eqc, and the resin concentration of the chemical is equal to the resin capacity, S_tot. When c is in between small and large, the isotherm bends over in a convex shape. This is shown in the graph below.

There are three basic conditions in preparative and industrial chromatographic operations. In the first, K_eq is very low, and there is little or no binding of the chemical to the resin. This is represented by the red squares in the graph above. This is the case with “flow through” fractions in chromatography, and would generally be the case when the chemical has the same charge as the resin. In the third, K_eq is very high, and the chemical is bound quantitatively to the resin, even at low concentrations. This is represented by the green triangles in the graph above. This is the case with chemicals that are typically only released when the column is “stripped” or “regenerated”. In these cases, the solution phase conditions are changed to turn K_eq from a large number to a small number during the regeneration by using a high salt concentration or an extreme pH. The second case is the most interesting, and is the condition for most “product” fractions, where a separation is being made. That is, when the solution phase conditions are tuned so that the desired product is differentially adsorbing and desorbing, allowing other chemicals with slightly higher or lower affinities to elute either before or after the desired product, it is almost always the case that the equilibrium constant is not such that binding is quantitative or non-existent. In these cases, the non-linearity of the isotherm has consequences for the shape of the elution peak. We will discuss these consequences in a future blog.

In a “Quality-by-Design” world, these non-linearities would be understood and accounted for the in the design of the chromatography operation. An excellent example of the resulting non-linearity of the results was shown by Oliver Kaltenbrunner in 2008. 

Relying on linear statistics to uncover this basic thermodynamic behavior is a fool’s errand. However, using basic lab techniques (a balance and a spectrophotometer) the isotherm for your product of interest can be determined directly, and the chromatographic behavior understood. This is the path to process understanding!