biochemistry - What does pO2 of blood mean and why do we use it?

I understand the basic Dalton's law of partial pressures in gases. Also, Henry's law of diffusion, says, the concentration of gas dissolved in a fluid is proportional to the partial pressure above it.

So if we say that the $p(\ce{O2})$ of oxygenated blood is $\pu{100 mmHg}$, where is the free gas existing in equilibrium with dissolved gas? Does it mean that the blood has a concentration of oxygen equal to that when placed in a surrounding of $p(\ce{O2}) = \pu{100 mmHg}$? If yes, why don't we directly report in concentrations instead? Is it easier to measure?

Wikipedia also says that the Henry's law doesn't stand if the gas is reacting. But isn't oxygen reacting with the Haemoglobin?

Answer

There is a good explanation in Relating oxygen partial pressure, saturation and content: the haemoglobin–oxygen dissociation curve Breathe 2015; 11: 194–201

The partial pressure of oxygen (also known as the oxygen tension) is a concept which often causes confusion. In a mixture of gases, the total pressure is the sum of the contributions of each constituent, with the partial pressure of each individual gas representing the pressure which that gas would exert if it alone occupied the volume. In a liquid (such as blood), the partial pressure of a gas is equivalent to the partial pressure which would prevail in a gas phase in equilibrium with the liquid at the same temperature. With a mixture of gases in either the gas or liquid phase, the rate of diffusion of an individual gas is determined by the relevant gradient of its partial pressure, rather than by its concentration. While in a gas mixture, the partial pressure and concentration of each gas are directly proportional, with oxygen in blood the relationship is more complex because of its chemical combination with haemoglobin. This allows blood to carry an enormously greater concentration (content) of oxygen than, for example, water (or blood plasma). Measurement of $p_\ce{O_2}$, therefore, does not give direct information about the amount of oxygen carried by blood.

So blood $p_\ce{O_2}$ does not correspond to a particular concentration of oxygen, because the concentration of haemoglobin can vary, and most of the oxygen is bound to the heme iron.

$P_\ce{O_2}$ is the partial pressure of oxygen in a hypothetical gas phase which would make the blood oxygen and gas phase oxygen be in equilibrium.