Oxygenating Blood

When arterial blood enters a tissue capillary, it exchanges oxygen and carbon

dioxide with its environment, as shown in this diagram.

The kinetics of this deoxygenation of hemoglobin in blood was studied with the

aid of a tubular reactor by Nakamura and Staub $[$J$.$ Physiol., $173,161$

$(1967).$

$Hb{O}_2{K}_{-1}^{K_1}Hb+O_2$

Although this is a reversible reaction, measurements were made in the initial

phases of the decomposition so that the reverse reaction could be neglected.

Consider a system similar to the one used by Nakamura and Staub: the

solution enters a tubular reactor in diameter$)$ that has oxygen

electrodes placed at $5-cm$ intervals down the tube. The solution flow rate into

the reactor is $19\mathrm{.}6c\frac{m^3}{s}.$

Using the method of differential analysis of rate data, determine the reaction

order and the forward specific reaction rate constant $k$ for the deoxygenation

of hemoglobin.

If you were to take more data points, what would be reasonable points?, why?

$[$Hint: Estimate the inlet concentration of $Hb{O}_2$ by using typical values of

hemoglobin concentration in adult human blood, and by assuming that

hemoglobin is saturated with oxygen, consider the position of the electrode as

the time$]$