# Problem Set 4 Resipiratory – Why we need Hemoglobin

We need hemoglobin because our blood cannot carry enough dissolved O2 to support our cell activity. That’s the short answer. Let’s explore a quantitative answer.

## 4.1 How much O2 can dissolve into blood?

We can model what is going on in the alveoli using a beaker filled with water. Diffusion of gas molecules from the air into the water (“going into solution”) or the reverse (“coming out of solution”) is not simply a function of the concentration gradient of the gas between the air and the water because gasses have different solubilities in solution.

Equilibrium (when an equal amount of gas is going into and out of solution) is modeled by the following equation

$$$c_\mathrm{O_2} = h_\mathrm{O_2} P_\mathrm{O_2}$$$
• $$c_\mathrm{O_2}$$ is the concentration of O2 in the water
• $$P_\mathrm{O_2}$$ is the partial pressure of O2 in air (so a measure of concentration)
• $$h_\mathrm{O_2}$$ is Henry’s solubility coefficient (or “constant of proportionality”).

Scientists in different fields have different ways of expressing the relationship between $$c_\mathrm{O_2}$$ and $$P_\mathrm{O_2}$$ so you may land on a web page or a textbook that expresses the constant in something like $$\frac{1}{c_\mathrm{O_2}}$$ or even a dimensionless constant. I like this way for physiology because it pumps our intuition about how $$P_\mathrm{O_2}$$ controls our dissolved O2 levels.

This equation tells us how much O2 will dissolve in the water at different partial pressures of O2 in the air, or, switching back to the lung, how much O2 will dissolve in the blood plasma given the partial pressure of O2 in the alveolar air.

Below is a table of $$P_\mathrm{O_2}$$ of alveolar air and the resulting concentration of dissolved O2 at equilibrium.

P_O2 (mmHg) c_O2 (mL O2/dL blood)
20 0.066
30 0.091
40 0.137
50 0.156
60 0.195
70 0.220
80 0.257
90 0.281
100 0.307
110 0.349
2. Plot $$c_\mathrm{O_2}$$ (y-axis) against $$P_\mathrm{O_2}$$ (x-axis)
5. What is $$c_\mathrm{O_2}$$ in healthy arterial blood entering an organ (use $$P_\mathrm{O_2} = 97$$ mmHg)?
6. How much dissolved O2 is ejected from our left ventricle each minute? Again, use $$P_\mathrm{O_2} = 97$$ mmHg