gas. Also, a gram-mole of any gas (defined as its molecular weight in grams) should have a specific number of molecules. This number is called Avogadro’s number and is equal to approximately 6.022 x 10 molecules per gram-mole. Also related is that one gram-mole of any gas will occupy a volume of about 22.4 L (0.791 ft3) at standard temperature and pressure (0°C and one atmosphere). With this information, it is possible to determine the approximate density of any gas or gas mixture at any pressure. For example, what is the density of standard air assuming that air is 21% oxygen, 78% nitrogen, and 1% argon? From the periodic table or a table of molecular weights, we find that the molecular weight of oxygen (O2) is 31.999, the molecular weight of nitrogen (N2) is 28.014, and the molecular weight of argon (Ar) is 39.948. Density is mass per volume, and one grammole of any gas at standard temperature and pressure occupies 22.4 liters. Density of oxygen = 31.999 g/mole x 1 mole/22.4 L = 1.429 g/L Density of nitrogen = 28.014 g/mole x 1 mole/22.4 L = 1.251 g/L Density of argon = 39.948 g/mole x 1 mole/22.4 L = 1.783 g/L Dalton’s law of partial pressures tells us that we can sum the fractions of oxygen, nitrogen, and argon to obtain the density of the mixture we call air. Density of air = (0.21 x 1.429 g/L) + (0.78 x 1.251 g/L) + (0.01 x 1.783 g/L) = 1.294 g/L at standard temperature and pressure. The density of the gas breathed by a diver increases with increasing depth. Denser air is “thicker” and requires more work to breathe. What would be the density of the air breathed by a diver at a depth of 55 meters in the ocean? First find the absolute pressure at 55 msw: Pabsolute = (55 msw x 1 atm/10 msw) + 1 atm = 6.5 ata Chapter 3- Diving Physics Then find the density of the air, which is directly proportional to the pressure: Density = 1.294 g/L x 6.5 = 8.4 g/L The generally accepted limit in recreational diving for partial pressure of oxygen breathed by a diver is 1.4 ata. What is the partial pressure of oxygen in air at 55 msw? The partial pressure of oxygen in the air is 21% of the absolute pressure. PO2 = 0.21 x 6.5 = 1.37 ata This is less than the normal recreational O2 partial pressure limit. The calculations are similar using U.S./Imperial values. The General Gas Law Boyle’s law, Charles’ law, and Amontons’ law can be combined into a relationship called the General Gas Law, which can be used to predict the behavior of any quantity of gas in terms of pressure, volume, and temperature. Expressed mathematically, the formula for the General Gas Law is: P1V1 = P2V2 T1 T2 where P, V, and T are the absolute pressure, volume, and absolute temperature. If five of the six variables are known, the value of the sixth can be determined. If one set of variables remains constant, then the General Gas Law becomes a statement of one of the other gas laws. For instance, if the temperature does not change, it expresses Boyle’s law. Sample problems: SI/metric A cylinder contains 2,840 liters of air at the surface and a temperature of 23°C. What volume of air will be deliverable from the cylinder at a depth of 25 msw and a temperature of 30°C? First determine appropriate absolute values. Remember that the volume of air in the cylinder is the volume the air would occupy if it were allowed to expand to one atmosphere of pressure: Diving Physics 91 23
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