# Arterial blood CO2 content, division and partial pressure

My lecturer cites Boron and Boulpaep's Medical Physiology (2nd edition) for the following claims:

• the total $\ce{CO2}$ content of arterial blood is $26.4$ mmol/L or $48\%$ v/v (not sure if these numbers convert)
• including $90\%$ as bicarbonate, $5\%$ as dissolved gas and 5% as carbamino compounds (specifically carbaminohaemoglobin)
• the arterial partial pressure of $\ce{CO2}$ is $40$mmHg

How does one get from the arterial partial pressure value to determining these proportions and figures?

What I've tried: Henry solubility constant for $\ce{CO2}$ in water, equilibrium constants for the hydration of $\ce{CO2}$, ionisation of carbonic acid, assumed carbaminohaemoglobin formation went to completion and only consumed $\ce{CO2(aq)}$. Still don't seem to completely match my lecturer's figures.