Given: During open heart surgery, an extracoporeal heart$-$lung machine pumps a patient$$s blood through a oxygenator between the vena cava and the aorta. Within the oxygenator, O$2$ is bubbled through the flowing blood where it is absorbed at a rate of V $$O$2=5$ mmol$/$min$.$ The O$2$ and CO$2$ contents $($C $$O$2,$ C $$CO$2)$ of blood entering the device are $15$ and $53$ ml$($STP$)/100$ ml$,$ respectively. The O$2$ content in the blood exiting the device is $20$ ml$($STP$)/100$ ml$.$ The RQ of the device is $0\mathrm{.}90.$ Consider the blood in the oxygenator $($excluding gas bubbles$)$ as the control volume with volumetric input and output flows Q$1$ and Q$2.$

Find: $($a$)$ Assuming that the mass density of blood is essentially constant, what is the relationship between Q$1$ and Q$2$ during steady state operation? $($b$)$ Write a steady$-$state molar balance for O$2$ around the control volume. From this, evaluate the volumetric blood flow. $($c$)$ Write a steady$-$state molar balance for CO$2$ around the control volume. What is the uptake relationship of to V $$CO$2$ to V $$O$2?$ With these equations, evaluate $($C $$CO$2)2$