Question

Why is it necessary to accomodate vapour pressure when calculating the partial pressure of oxygen in respiratory function?

Answer 1

What does this mean? For example, if we have a mixture of gases AA, BB and CC in an isolated room, then, according to Dalton's law, the pressure exerted by the gases will be the sum of their partial pressures :

P=pA+pB+pCP=pA+pB+pCwhere pApA, pBpB and pCpC are the partial pressures of each gas. Also, if we have a moles of AA, b moles of BB and c moles of CC, we can express the partial pressure of each gas as below:pA=aa+b+cPpA=aa+b+cPpB=ba+b+cPpB=ba+b+cPpB=ca+b+cPpB=ca+b+cP

Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.

As the definition states, if we took an equilibrium as A(l)↽−−⇀A(g)A(l)↽−−⇀A(g), where A(l)A(l) and A(g)A(g) are the liquid and the vapor state of the compound AA . The vapor pressure of AA is the pressure exerted by the gaseous state (A(g)A(g)) over the liquid state (A(l)A(l)). Now, if we have a mixture of AA, BB and CC, we'll have the equilibrium between the liquid and gaseous state : (A,B,C)(l)↽−−⇀(A,B,C)(g)(A,B,C)(l)↽−−⇀(A,B,C)(g)and the vapor pressure PvPv (I noted PvPv so there won't be any confusion between it and the total pressure PP I mentioned before). According to Raoult's law, the vapor pressure PvPv is the sum of the products between the vapor pressures of each compound taken separately and the molar fraction of the compound in the mixture (i.e. in the solution) :

Pv=xApvA+xBpvB+xCpvCPv=xApvA+xBpvB+xCpvC

This may look just like Dalton's law, but there are different pressures involved. The partial pressure of a gas is the pressure exerted by a gas in the volume occupied by a mixture of gases, while the vapor pressure of a gas is the pressure exerted by a gas over it's condensed phase. Although :

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial pressure.

The vapor pressure still refers to the pressure of a gas over it's liquid (or solid) phase in a phase transition (condensed phase↽−−⇀↽−−⇀non-condensed phase), while the notion of partial pressure can be extended to a mixture of gases only.

Now that we've discussed how concentration and pressure affect diffusion, let's consider what happens to the concentration of oxygen in our lungs. By the time the inspired air reaches the alveoli where gas exchange occurs, the concentration drops from about 21% to about 13%. At sea level, this reduces the partial pressure of oxygen from 160 mmHg to about 100 mmHg, as 13% of 760 mmHg is about 100 mmHg. What is responsible for this drop in partial pressure? The addition of water vapor and carbon dioxide to the inspired air decreases the percent composition of oxygen.