The formula for finding the partial pressure of any component gas of a mixture is: Ppartial = Fractiongas x Ptotal This can be manipulated to provide the formula to find the total pressure at which a component gas will reach a certain partial pressure: Ptotal = Ppartial Fractiongas A useful diagram to help remember the relationship and to solve for any value is: Partial Pressure Total Pressure Fraction Cover the value you want to know and the remaining two will show the proper relation (“divided by” or “times”). Sample Problems: SI/metric: What is the partial pressure of the oxygen in air at sea level in kilopascals? Answer: PO2 = 0.21 x 101.3 kPa = 21.3 kPa U.S./Imperial: What is the partial pressure of the oxygen in air at sea level in pounds per square inch? Answer: PO2 = 0.21 x 14.7 psi = 3.1 psi To find the partial pressure of a component of one’s breathing gas at depth, first convert the depth to absolute pressure, then multiply the absolute pressure by the fraction of the gas in the mixture. Sample Problems: SI/metric: What is the partial pressure of oxygen in bars in air breathed at a depth of 40 meters of seawater? Answer: First find the absolute pressure at depth. Pdepth = (40 msw x 1.005 bars )+ 1.013 bars = 5.03 bars 10 msw Then find the partial pressure of the oxygen. PO2 = 0.21 x 5.03 bars = 1.06 bars U.S./Imperial: What is the partial pressure of oxygen in atmospheres in air breathed at a depth of 150 feet of seawater? Answer: Chapter 3- Diving Physics First find the absolute pressure at depth. Pdepth = (150 fsw x 1 atm ) + 1 atm = 5.55 ata 33 fsw Then find the partial pressure of the oxygen. PO2 = 0.21 x 5.55 ata = 1.16 ata Dalton’s law is important to divers because the air (or other breathing mixture) that a diver breathes at depth is delivered by the regulator at ambient pressure, and the diver is subjected to that pressure. As the diver descends the partial pressure of each component gas increases as the absolute pressure increases. This is true not only of nitrogen, and oxygen, but also of any other gas, whether added intentionally, as helium might be, or present as a contaminant, such as carbon monoxide. At sufficient partial pressures, gases breathed, whether nitrogen, oxygen, or contaminants, can have adverse or dangerous effects on a diver. Gas toxicity is discussed in the “Physiology” chapter. Also, as ambient pressure increases, quantities of the gases breathed will begin to pass into solution in the body’s tissues, as discussed later in this chapter (Henry’s Law) and in the chapter on “Decompression.” KINETIC THEORY OF GASES The molecules of any gas are in constant motion, traveling in random directions at high speeds. They collide with each other and with the walls of their container, rebounding in new directions only to collide again. This concept forms the basis for the kinetic theory of gases, which relates the motion of the molecules to the mechanical and thermal properties of gases, such as pressure, volume, temperature, and heat conductivity. The kinetic theory of gases was actually formulated several times in the past, but it did not find acceptance until the third quarter of the nineteenth century. As early as 1738, Daniel Bernoulli, a Swiss mathematician and scientist, published the mathematical model for the kinetic theory of gases. In the following century other researchers also developed and published versions, but the scientific interest and understanding of the time was Diving Physics 85
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