Physical Chemistry of Gases: Gas Exchange Linda Costanzo, Ph.D. OBJECTIVES: After studying this lecture, the student should understand: 1. Application of the gas laws to pulmonary physiology. 2. How to calculate the concentration of a gas in blood using Henry s law. 3. Diffusion of gases according to Fick s law and the concept of lung diffusion capacity. 4. The overview of gas exchange across the alveolar-pulmonary capillary barrier and the resulting values of P O2 and P CO2 in inspired air, alveolar air, mixed venous blood, and systemic arterial blood. 5. The mechanism of diffusion-limited gas exchange. 6. The mechanism of perfusion-limited gas exchange. I. GAS LAWS A. General Gas Law This one should be familiar! PV = nrt P is pressure (mm Hg), V is volume (L), n is the number of moles of gas, R is the gas constant, and T is temperature in Kelvin. B. Boyle s Law Boyle s Law says that a given temperature, pressure times volume for a gas is constant. P 1 V 1 = P 2 V 2 For example, if the volume of the lungs increases (e.g., during inspiration), the pressure must decrease to keep pressure times volume constant. C. Dalton s Law of Partial Pressures It is critically important that you understand Dalton s Law since, in respiratory physiology, we are always dealing with gases in mixtures. Dalton s law of partial pressures states that the partial pressure of a gas in a mixture of gases is the pressure that gas would exert if it occupied
the whole volume of the mixture. P x = P B x F P x is the partial pressure of the gas, P B is barometric pressure, and F is the fractional concentration of the gas. In humidified air, we correct for water vapor pressure, P H2O, which is 47 mm Hg at 37 C. P x = ( P B B - PH2O) x F In dry atmospheric air, there is 21% O 2 and 79% N 2 (no CO 2, always remember that!) and the respective partial pressures (mm Hg) at sea level are shown in the table below. When this air is humidified air it is corrected for the obligatory water vapor pressure and the respective partial pressures are, accordingly, decreased. Gas (F) Dry Air Humidified Tracheal Air O 2 (0.21) 160 150 CO 2 (0) 0 0 N 2 (0.79) 600 563 H 2 O 0 47 Total (barometric) 760 mm Hg 760 mm Hg D. Henry s Law for Dissolved Gases Henry s law applies to concentrations of gases dissolved in solution. This is relevant since both O 2 and CO 2 are dissolved in blood. Important point: if equilibration has occurred, partial pressure of a gas in the liquid phase is equal to the partial pressure in the gas phase. Do not read further until you have understood this point! Henry s law is then used to convert the partial pressure of gas in the liquid to concentration of gas in the liquid. Henry s law calculates the concentration of dissolved gas that is free in solution and does not include any gas that is present in bound form (e.g., bound to hemoglobin). C x = P x x solubility C x is concentration of dissolved (free) gas in units of ml gas/100 ml blood (also called volume %), P x is the partial pressure of the gas in mm Hg, and solubility is the solubility of the gas in units of ml gas/100 ml blood/mm Hg.
Solubilities of O 2 and CO 2 in blood are as follows: O 2 CO 2 Solubility in blood (ml gas/100 ml blood/mm Hg) 0.003 ml O 2 /100 ml blood/mm Hg 0.07 ml CO 2 /100 ml blood/mm Hg II. FORMS OF GASES IN SOLUTION In air there is only one form of gas, the gaseous form (!), which is expressed as a partial pressure in units of mm Hg. In blood, gases can be carried in dissolved form (Henry s law), bound to proteins such as hemoglobin, or chemically modified. Dissolved gas. All the relevant gases (O 2, CO 2, and N 2 ) are carried to some extent in dissolved form. Henry s law relates concentration of the gas to its partial pressure. One corollary of Henry s law is that only dissolved gas creates a partial pressure; bound and chemically modified forms do not contribute to the partial pressure of the gas. N 2 is only found in the dissolved form, it is never bound or chemically modified. Bound gas. O 2, CO 2, and CO are bind to hemoglobin, which contribute significantly to their carriage in blood. CO 2 also binds to plasma albumin. Chemically modified. The most important example of a chemically modified gas is the conversion of CO 2 to HCO 3 - in red blood cells. III. GAS EXCHANGE A. Diffusion of gases Fick s Law V x = D A ΔP Δx V x is volume of gas transferred per unit time, D is the diffusion coefficient for the gas, A is surface area, ΔP is partial pressure difference for the gas, and Δx is the thickness of the membrane (e.g., the alveolar-capillary barrier). The driving force for gas diffusion is the partial pressure difference of the gas (ΔP) across the membrane or capillary wall. For example, if the P O2 of alveolar gas is 100 mm Hg and the P O2 of mixed venous blood
entering the pulmonary capillaries is 40 mm Hg, then the driving force for diffusion of O 2 is the difference in partial pressures across the alveolarpulmonary capillary barrier, or 60 mm Hg. O 2 will diffuse until the P O2 of pulmonary capillary blood is 100 mm Hg, at which point the partial pressure gradient is dissipated and there is no more driving force for O 2 diffusion. The diffusion coefficient of the gas, D, is inversely correlated with the molecular weight of the gas and directly correlated with the solubility of the gas. For example, D CO2 is >> D O2 (20 times greater). In respiratory physiology, we combine diffusion coefficient, surface area, and membrane thickness in the Fick equation into a single term called lung diffusing capacity (D L ). B. Lung diffusing capacity D L As noted above, several factors (D, A, and Δx) from Fick s diffusion equation are combined into the lung diffusing capacity, D L. D L also takes into account the time required for gas (e.g., O 2 ) to combine with proteins such as hemoglobin. D L is measured with CO (i.e., DL CO) because CO transfer across the alveolar-capillary barrier is limited exclusively by diffusion. (In the measurement, called the single breath method, a single inspiration of a dilute mixture of CO is made, and the rate of disappearance of CO from alveolar gas is measured.) V x = D L x ΔP Increases in D L. D L is increased in exercise, where there are more open capillaries and more surface area for gas exchange. Decreases in D L. D L is decreased when there is an increased diffusion distance (e.g., fibrosis and pulmonary edema) or decreased surface area for diffusion (e.g., emphysema). D L also is decreased in anemia where the decreased hemoglobin concentration in blood decreases the hemoglobinbinding component of the D L measurement.
IV. OVERVIEW OF GAS EXCHANGE IN THE LUNGS Figure 1.
Figure 2. The first figure shows an alveolus and a pulmonary capillary. The pulmonary capillary is perfused with mixed venous blood from the right heart. Gas exchange occurs across the alveolar-pulmonary capillary barrier -- O 2 diffuses from alveolar gas into pulmonary capillary blood and CO 2 (produced in the tissues) diffuses from pulmonary capillary blood into alveolar gas. Pulmonary capillary blood exits the lungs by the pulmonary vein, goes to the left heart and becomes systemic arterial blood. The second figure shows the average values for P O2 and P CO2 in various locations. Dry inspired air has a P O2 of 160 mm Hg, but no CO 2. When this air enters the trachea, it is humidified and the P O2 is lowered to 150 mm Hg because of the obligatory P H2O of 47 mm Hg ([760 mm Hg - 47 mm Hg] x 0.21 = 150 mm Hg). In alveolar gas, the values for P O2 and P CO2 change significantly. (The notation small capital A indicates alveolar gas.). PA O2 is 100 mm Hg because O 2 has diffused from alveolar gas into pulmonary capillary blood until equilibration occurs. PA CO2 is 40 mm Hg because CO 2 has diffused from capillary blood into alveolar gas until equilibration occurs. In the steady state, the amounts of O 2 and CO 2 transferred correspond to the amounts of O 2 consumed and CO 2 produced by
the body. Thus, pulmonary capillary blood, which becomes systemic arterial blood, normally equilibrates with alveolar gas and has a Pa O2 of 100 mm Hg and a P CO2 of 40 mm Hg. This blood circulates to the tissues, where O 2 is consumed and CO 2 is produced, and mixed venous blood has a Pv O2 of 40 mm Hg and a Pv CO2 of 46 mm Hg. V. DIFFUSION- AND PERFUSION-LIMITED GAS EXCHANGE A. Diffusion-limited gas exchange In diffusion-limited gas exchange, the total amount of gas transferred across the alveolar-capillary barrier is limited by the diffusion process (driven by the partial pressure gradient for the gas). The partial pressure gradient for the gas is maintained along the length of the capillary. Diffusion-limited gas exchange is illustrated by the transport of O 2 during strenuous exercise, in lung diseases such as emphysema and fibrosis, and by the transport of CO (shown in the figure below, Panel A). In the figure, the shaded area shows the partial pressure gradient for CO between alveolar gas (PA) and pulmonary capillary blood (Pa) along the length of the capillary. Blood entering the capillary has no CO and there is a huge partial pressure gradient for CO diffusion from alveolar gas into capillary blood. As CO diffuses into the blood, it binds to hemoglobin with a high affinity and very little CO is left free in solution. Thus, the partial pressure of CO rises very little along the length of the capillary, the partial pressure gradient is maintained for the entire capillary, and diffusion continues. There is no equilibration of CO! B. Perfusion-limited gas exchange In perfusion (or blood flow)-limited gas exchange, the amount of gas transferred is limited by blood flow. The partial pressure gradient for the gas is not maintained, i.e., there is equilibration of the gas at some point along the pulmonary capillary. In these cases, the only way to transfer more gas is by increasing blood flow. Perfusion-limited gas exchange is illustrated by the transfer of O 2 (resting conditions) and CO 2, and by the transfer of N 2 O (shown in the figure below, panel B). N 2 O is not bound in the blood at all, it is only present in the free, dissolved form that creates a partial pressure. Blood entering the pulmonary capillary initially has no N 2 O. N 2 O diffuses down its partial pressure gradient from alveolar gas into pulmonary capillary blood. The partial pressure of N 2 O in blood rises rapidly (because none is bound); when it equals the partial pressure in alveolar gas, there is no more transfer of N 2 O. The only way to transfer more N 2 O is to increase blood flow.
Figure 3. C. O 2 sometimes perfusion-limited, sometimes diffusion-limited O 2 transport is normally perfusion-limited. That is, O 2 equilibrates between alveolar gas and pulmonary capillary blood and the partial pressure gradient (driving force for diffusion) dissipates. The only way to increase the amount of O 2 transferred is to increase blood flow. However, this is not the whole story. Under certain conditions (usually pathologic, but also including strenuous exercise), O 2 does not equilibrate; the O 2 partial pressure gradient is maintained along the length of pulmonary capillary, and O 2 transfer converts to a diffusion-limited process.
Figure 4. In fibrosis, O 2 transfer converts to a diffusion-limited process (Panel A). Let s assume that mixed venous P O2 is the usual value of 40 mm Hg. This blood enters the pulmonary capillaries. The diffusion process is seriously impaired, however, because of thickening of the alveolar membranes, which decreases D L. O 2 does not equilibrate between alveolar gas and pulmonary capillary blood and the blood leaving the pulmonary capillaries and becoming systemic arterial blood has a very reduced P O2. At high altitude, the person with fibrosis is in even worse shape. Now the alveolar P O2 is reduced (because of the decrease in barometric pressure). For illustration, alveolar P O2 in this example is shown as 50 mm Hg. People with normal lungs will equilibrate O 2 (albeit more slowly because of the decreased partial pressure gradient), and their arterial P O2 will be 50 mm Hg. People with fibrosis, however, will not equilibrate O 2 and their arterial P O2 will be less than 50 mm Hg (in this example, 30 mm Hg).
VI. PRACTICE QUESTIONS 1. If barometric pressure is 740 mm Hg, and the fractional concentration of O 2 is 21%, of N 2 is 79%, and CO 2 is 0, what are the partial pressures in a humidified mixture of these three gases? 2. If alveolar gas has a partial pressure of O 2 of 150 mm Hg, what is the concentration of dissolved O 2 in blood that is equilibrated with that alveolar gas? 3. A person at sea level breathes a mixture containing 0.1% carbon monoxide (CO). The uptake of CO was measured in the single breath method to be 28 ml/minute. What is the lung diffusing capacity for CO (DL CO )? ( Hint: V CO = DL x ΔP) 4. In perfusion-limited O 2 exchange, the P O2 at the end of the pulmonary capillary is A. Less than the P O2 in alveolar air. B. Equal to the P O2 in mixed venous blood. C. Equal to the P O2 in alveolar air. D. Greater than the P O2 of alveolar air. E. Greater than the P O2 of systemic arterial blood. EXPLANATIONS 1. P O2 = (740-47) x 0.21 = 145.5 mmhg P N2 = (740-47) x 0.79 = 547.5 mmhg P CO2 = (740-47) x 0 = 0 2. Pa O2 = 150 mmhg Dissolved O 2 = 150 mmhg x 0.003 ml O 2 /100 ml blood/mmhg = 0.45 ml O 2 /100 ml blood, or 0.45 vol% 3. Answer: 39.3 ml/min/mm Hg 4. Answer = C. Begin by reminding yourself of the definition/description of perfusion-limited gas exchange as applied to O 2 (i.e., O 2 moves from alveolar gas into pulmonary capillary blood). Perfusion-limited means the gas equilibrates across the alveolar-pulmonary capillary barrier. Thus, the P O2 of pulmonary capillary blood equilibrates with, and becomes equal to, the P O2 of alveolar air. Additional comment on this question: Choice D (greater than P O2 of alveolar air) is a particularly bad answer because it implies that pulmonary capillary blood can achieve a higher P O2 than alveolar gas it can t! It can go as high as, but never higher!