Why is partial pressure used as a metric for oxygen in blood? I know haemoglobin basically acts as an oxygen buffer. But when we talk about non-bound oxygen in blood (or water), we're referring to the amount of O2 in solution (aqueous state). From a biochemistry point of view, the concentration seems like a good metric to me.

So why is it that medical papers report blood oxygenation in terms of partial pressure pO2 instead of concentration? 

What does a partial pressure inside a liquid even mean? I tried interpreting the arterial pO2 value of 11% atm (i.e. about 11kPa). When using the formula P = CRT at 310K (body temp), I found an oxygen concentration of about 4.3 mM. This value is 20× higher than the maximum O2 concentration for water according to Henry's law. For those more familiar with DO values in mg/L, it would be 137.6 mg/L.

According to Henry's Law there is a limit to the amount of O2 that can dissolve into water at a given pressure and temperature. I know the lungs experience a slightly lower partial pressure than the atmosphere. So how can the oxygen concentration be so high? Does their metric include the oxygen bound by haemoglobin (which would be misleading at the least), or is my calculation off somewhere?

Or does a pO2 value correspond to the steady-state equivalent concentration at that pressure, in which case the arterial concentration in my example would be 0.14 mM (based on this table in wikipedia).

This similar question didn't answer my question:
What is the state of aggregation (gas, liquid) of oxygen in blood?
The equation P=CRT is the relationship for the oxygen concentration in the gas phase.  To get the mole fraction of oxygen the the liquid phase (blood), you first use the Henry's law constant.  Here is a link that can help:  https://www.google.com/webhp?sourceid=chrome-instant&amp;ion=1&amp;espv=2&amp;ie=UTF-8#q=henry%27s%20law%20constand%20for%20oxygen%20in%20blood

If, after applying Henry's law, you end up with a concentration in units of x ml per unit volume, this result implies that x is the volume that the mass of dissolved gas (solute) would have it were an actual gas at the same pressure as that in the gas phase.