Gas Laws Gas Laws One of the most amazing things about gases is that, despite wide differences in chemical properties, all the gases more or less obey the gas laws. The gas laws deal with how gases behave with respect to pressure, volume, temperature, and amount. Pressure Gases are the only state of matter that can be compressed very tightly or expanded to fill a very large space. Pressure is force per unit area, calculated by dividing the force by the area on which the force acts. The earth's gravity acts on air molecules to create a force, that of the air pushing on the earth. This is called atmospheric pressure. The units of pressure that are used are pascal (Pa), standard atmosphere (atm), and torr. 1 atm is the average pressure at sea level. It is normally used as a standard unit of pressure. The SI unit though, is the pascal. 101,325 pascals equals 1 atm. For laboratory work the atmosphere is very large. A more convient unit is the torr. 760 torr equals 1 atm. A torr is the same unit as the mmHg (millimeter of mercury).

It is the pressure that is needed to raise a tube of mercury 1 millimeter. The Gas Laws: Pressure Volume Temperature Relationships Boyle's Law: The Pressure-Volume Law Boyle's law or the pressure-volume law states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant. Another way to describing it is saying that their products are constant. PV = C When pressure goes up, volume goes down. When volume goes up, pressure goes down. From the equation above, this can be derived: P1V1 = P2V2 = P3V3 etc. This equation states that the product of the initial volume and pressure is equal to the product of the volume and pressure after a change in one of them under constant temperature. For example, if the initial volume was 500 mL at a pressure of 760 torr, when the volume is compressed to 450 mL, what is the pressure?

Plug in the values: (760 torr)(500 mL) = P2(450 mL) 760 torr x 500 mL/450 mL = P2 844 torr = P2 The pressure is 844 torr after compression. Charles' Law: The Temperature-Volume Law This law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. V Same as before, a constant can be put in: V / T = C As the volume goes up, the temperature also goes up, and vice-versa. Also same as before, initial and final volumes and temperatures under constant pressure can be calculated. V1 / T1 = V2 / T2 = V3 / T3 etc. Gay-Lussac's Law: The Pressure Temperature Law This law states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. P Same as before, a constant can be put in: P / T = C As the pressure goes up, the temperature also goes up, and vice-versa.

Also same as before, initial and final volumes and temperatures under constant pressure can be calculated. P1 / T1 = P2 / T2 = P3 / T3 etc. Avogadro's Law: The Volume Amount Law Amedeo Avogadro (1776-1856) Gives the relationship between volume and amount when pressure and temperature are held constant. Remember amount is measured in moles. Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract. If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases.

V FW = gRT / PV ; V = (0.1000 g)(0.0821 L-atm / mole-K)(295.3 K) / (0.0928 atm)(0.256 L) = 102 g / mole FW of CHF2 = 51.0 g / mole ; 102 / 51.0 = 2 ; C2H2F4 If the equation above is rearranged further, g / V = P x FW / RT = density you get an expression of the density of the gas as a function of T and FW. EXAMPLE 3: Compare the density of He and air (average FW = 28 g/mole) at 25.0 oC and 1.00 atm.

dHe = (4.003 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(298 K) = 0.164 g / L dair = (28.0 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(298 K) = 1.14 g / L EXAMPLE 4: Compare the density of air at 25.0 oC and air at 1807 oC and 1.00 atm.

dHe = (28.0 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(298 K) = 1.14 g / L dair = (28.0 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(2080 K) = 0.164 g / L Partial Pressures Dalton's Law of Partial Pressures states that the total pressure of a mixture of nonreacting gases is the sum of their individual partial pressures. Ptotal = Pa + Pb + Pc + ... Ptotal = naRT / V + nbRT / V + ncRT / V + ... or Ptotal = (na+ nb+ nc+ ... )RT / V The pressure in a flask containing a mixture of 1 mole of 0.20 mole O2 and 0.80 mole N2 would be the same as the same flask holding 1 mole of O2. Partial pressures are useful when gases are collected by bubbling through water (displacement).

The gas collected is saturated in water vapor which contibutes to the total number of moles of gas in the container. EXAMPLE 5: A sample of H2 was prepared in the laboratory by the reaction: Mg(s) + 2 HCl(aq) MgCl2(aq) + H2(g) 456 mL of gas was collected at 22.0 oC. The total pressure in the flask was 742 torr. How many moles of H2 were collected? The vapor pressure of H2O at 22.0 oC is 19.8 torr. nH2 = PH2V / RT ; nH2 = (0.9503 atm)(0.456 L) / (0.0821 L-atm / mole-K)(295 K) = 0.0179 mole H2. Non-Ideal Gases Johannes Diderik van der Waals (1837-1923) The ideal gas equation (PV=nRT) provides a valuable model of the relations between volume, pressure, temperature and number of particles in a gas.

As an ideal model it serves as a reference for the behavior of real gases. The ideal gas equation makes some simplifying assumptions which are obviously not quite true. Real molecules do have volume and do attract each other. All gases depart from ideal behavior under conditions of low temperature (when liquefaction begins) and high pressure (molecules are more crowed so the volume of the molecule becomes important). Refinements to the ideal gas equation can be made to correct for these deviations. In 1873 J. D. van der Waals proposed his equation, known as the van der Waals equation. As there are attractive forces between molecules, the pressure is lower than the ideal value. To account for this the pressure term is augmented by an attractive force term a/V2. Likewise real molecules have a volume. The volume of the molecules is represented by the term b. The term b is a function of a spherical diameter d known as the van der Waals diameter. The van der Waals equation for n moles of gas is: The values for a and b, below, are determined empirically: Boyle law - definition of Boyle law by The Free Dictionary Boyle law - definition of Boyle law by The Free Dictionary (boilz) n.

The physical law stating that at a constant temperature the volume of a confined ideal gas varies inversely with its pressure. [After Robert Boyle.] Boyle's law n (General Physics) the principle that the pressure of a gas varies inversely with its volume at constant temperature [C18: named after Robert Boyle] Boyle's′ law′ n. the principle that, for relatively low pressures, the pressure of an ideal gas kept at constant temperature varies inversely with the volume of the gas. [after R. Boyle ] Boyle's law The principle that the volume of a given mass of gas will increase as its pressure decreases, and will decrease as its pressure increases, as long as its temperature remains constant. Compare Charles's law . Boyle's law The principle that at a constant temperature the volume of a given mass of gas is inversely proportional to its pressure. ThesaurusAntonymsRelated WordsSynonymsLegend: The Gas Law Four variables are usually sufficient to define the state (i.e.

condition) of a gas: Temperature, T Volume, V Quantity of matter, usually the number of moles, n The equations that express the relationships among P, T, V and n are known as the gas laws The Pressure-Volume Relationship: Boyle's Law Robert Boyle (1627-1691) Studied the relationship between the pressure exerted on a gas and the resulting volume of the gas. He utilized a simple 'J' shaped tube and used mercury to apply pressure to a gas: He found that the volume of a gas decreased as the pressure was increased Doubling the pressure caused the gas to decrease to one-half its original volume Boyle's Law: The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure The value of the constant depends on the temperature and the amount of gas in the sample A plot of V vs.

1/P will give a straight line with slope = constant The Temperature-Volume Relationship: Charles's Law The relationship between gas volume and temperature was discovered in 1787 by Jacques Charles (1746-1823) The volume of a fixed quantity of gas at constant pressure increases linearly with temperature The line could be extrapolated to predict that gasses would have zero volume at a temperature of -273.15ï¿½C (however, all gases liquefy or solidify before this low temperature is reached In 1848 William Thomson (Lord Kelvin) proposed an absolute temperature scale for which 0ï¿½K equals -273.15ï¿½C In terms of the Kelvin scale, Charles's Law can be restated as: The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature Doubling the absolute temperature causes the gas volume to double The value of constant depends on the pressure and amount of gas The Quantity-Volume Relationship: Avogadro's Law The volume of a gas is affected not only by pressure and temperature, but by the amount of gas as well.

Joseph Louis Gay-Lussac (1778-1823) Discovered the Law of Combining Volumes: At a given temperature and pressure, the volumes of gasses that react with one another are in the ratios of small whole numbers For example, two volumes of hydrogen react with one volume of oxygen to form two volumes of water vapor Amadeo Avogadro interpreted Gay-Lussac's data Avogadro's hypothesis: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules 1 mole of any gas (i.e. 6.02 x 1023 gas molecules) at 1 atmosphere pressure and 0ï¿½C occupies approximately 22.4 liters volume Avogadro's Law: The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas Doubling the number of moles of gas will cause the volume to double if T and P remain constant 1996 Michael Blaber Boyle's Law: Volume and Pressure About Watch and Favorite Watch Watching this resources will notify you when proposed changes or new versions are created so you can keep track of improvements that have been made.

Favorite Favoriting this resource allows you to save it in the “My Resources” tab of your account. There, you can easily access this resource later when you’re ready to customize it or assign it to your students. Boyle's Law: Volume and Pressure Boyle's Law describes the inverse relationship between the pressure and volume of a fixed amount of gas at a constant temperature. Learning Objective Apply Boyle's Law using mathematical calculations. Key Points According to Boyle's Law, an inverse relationship exists between pressure and volume . Boyle's Law holds true only if the number of molecules (n) and the temperature (T) are both constant. Boyle's Law is used to predict the result of introducing a change in volume and pressure only, and only to the initial state of a fixed quantity of gas . The relationship for Boyle's Law can be expressed as follows: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume values, and P2 and V2 are the values of the pressure and volume of the gas after change.

Terms Full Text Boyle's Law Boyle's Law (sometimes referred to as the Boyle-Mariotte Law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains unchanged within a closed system . This can be stated mathematically as follows: $P_1V_1=P_2V_2$ History and Derivation of Boyle's Law The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. Boyle showed that the volume of air trapped by a liquid in the closed short limb of a J-shaped tube decreased in exact proportion to the pressure produced by the liquid in the long part of the tube. An animation of Boyle's Law, showing the relationship between volume and pressure when mass and temperature are held constant. The trapped air acted much like a spring, exerting a force opposing its compression. Boyle called this effect "the spring of the air" and published his results in a pamphlet with that title. The difference between the heights of the two mercury columns gives the pressure (76 cm = 1 atm), and the volume of the air is calculated from the length of the air column and the tubing diameter.

The law itself can be stated as follows: for a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional—that is, when one doubles, the other is reduced by half. Remember that these relations hold true only if the number of molecules (n) and the temperature (T) are both constant. Gases can be compressed into smaller volumes. How does compressing a gas affect its pressure? Run the model, then change the volume of the containers and observe the change in pressure. The moving wall converts the effect of molecular collisions into pressure and acts as a pressure gauge. What happens to the pressure when the volume changes? Example In an industrial process, a gas confined to a volume of 1 L at a pressure of 20 atm is allowed to flow into a 12-L container by opening the valve that connects the two containers. What is the final pressure of the gas? Set up the problem by setting up the known and unknown variables.

In this case, the initial pressure is 20 atm (P1), the initial volume is 1 L (V1), and the new volume is 1L + 12 L = 13 L (V2), since the two containers are connected. The new pressure (P2) remains unknown. P1V1 = P2V2 (20 atm)(1 L) = (P2)(13 L). 20 atom = (13) P2. An Explanation of Pressure and the Laws of Boyle, Charles, Dalton, and Henry c. 19051 lbs. Chose 'True' or 'False' for each of the following statements: 3. A cubic foot of air weighs less in Denver (altitude 5280 ft.) than in Miami (sea level). 4. A cubic foot of air contains fewer molecules in Denver than in Miami. 5. A given volume of air contains fewer molecules in Denver than in Miami. 6. Each of the first three miles of atmosphere (where people live) exerts the same pressure over earth's surface. TEST YOUR UNDERSTANDING Answers To further consider the concept of air pressure, open your hand palm upward.

The palm surface of an average-sized hand (with fingers closed) covers about 25 square inches. Now lift your hand quickly upward with the palm flat out (Figure 4). Assuming you are at sea level, and your hand is average-sized, you are lifting 25 x 14.7 or 368 pounds of air! Why, then, does your lifting seem so effortless? If you had to lift 368 pounds of anything with one hand you couldn't do it. It feels effortless because air pressure is evenly distributed around your hand, and the molecules of air are easily movable. At sea level, air pressure is 14.7 pounds per square inch on top of your hand, underneath your hand, and on all sides. Thus you don't really 'lift' 368 pounds, though that is the weight of air on top of your hand. As you lift your hand you move some air molecules out of the way and other molecules immediately come under and around your hand. The pressure surrounding your hand stays the same: 14.7 psi. Because the pressure is evenly distributed, you don't feel any weight in lifting your hand.

(There is resistance, however, as it takes time for air molecules to get out of the way. Resistance in the face of equal pressures is much better appreciated under water, since water is much denser than air.) Figure 4. Air pressure around your hand - or any object in the atmosphere - is evenly distributed. WHAT IS THE DIFFERENCE BETWEEN AMBIENT, BAROMETRIC AND ATMOSPHERIC PRESSURE? It can be confusing when different terminology is used to describe the same thing. One example is the use of multiple terms to indicate the pressure around us and the different measurement units for that pressure. The surrounding pressure, on land or under water, is referred to as the ambient pressure. If the surrounding pressure is from the weight of air, it is the atmospheric pressure. If the surrounding pressure is from the weight of water, it is the water pressure (Figure 5). Figure 5. Ambient Pressure on land and under water. When surrounded by air, ambient pressure = atmospheric pressure = barometric pressure. When surrounded by water, ambient pressure = water pressure.

Weather forecasters usually report air pressure in terms of a barometer reading in inches, e.g., "the barometer is currently 30 inches of mercury and rising." A barometer is an instrument for measuring atmospheric pressure, so barometric pressure is just another term for atmospheric pressure. WHAT ARE THE MEASUREMENT UNITS FOR THE AMBIENT PRESSURE? There are several units of measurement for ambient pressure. None is universally used, as different groups seem to prefer different terms to describe this pressure. The various terms are listed in Table 1, arbitrarily subdivided according to whether or not they are commonly employed in diving. Note that "bar" is commonly used in European diving. North Americans who rent air gauges in other countries may find them calibrated in bars. Thus a tank filled to 3000 psi would register 206 bars. TABLE 1. VARIOUS UNITS OF MEASUREMENT FOR AMBIENT PRESSURE (fsw = feet sea water; Hg = mercury) ambient pressure at: used in diving sea level 33 fsw psi 14.7 29.4 atmospheres 1 2 bar (non-U.S.

only) 1.01 2.02 used in other fields cm H2O 988 1976 inches Hg 29.92 59.84 mm Hg (torr) 760 1520 kilopascal 101.3 202.6 WHAT IS AN "ATMOSPHERE" OF PRESSURE? One atmosphere (atm.) is the air pressure at sea level and equals 14.7 psi. Note that the term "one atmosphere" is just a measurement; you don't have to be at sea level to be surrounded by one atmosphere. You could be in a submarine 330 feet under water and still be surrounded by one atm. of pressure (though the submarine hull would be surrounded by 10 atm. of water pressure). Similarly, two atm. is twice the sea level pressure. Two atm. = 29.4 psi, a pressure reached at 33 fsw (Table 1). You could also experience this pressure on land, in a hyperbaric chamber.

Conversely, the air pressure at 18,000 feet altitude = 7.35 psi, but this could be experienced at sea level as well, inside a chamber that can simulate altitude. Don't confuse "atmosphere," which is a unit of measurement, with "atmospheric pressure," which is a general term for the surrounding air pressure. Atmospheric pressure could be any value, e.g., one atm. (sea level pressure), one-half atm. (18,000 feet), zero (outer space), or three atm. (inside a hyperbaric chamber). Another important unit of measurement is millimeters of mercury, abbreviated mm Hg (Hg is the chemical symbol for mercury). Some texts refer to mm Hg by the term "torr," after the Italian Evangelista Torricelli (1608-1647), a pioneer in the measurement of atmospheric pressure; one mm Hg = one torr. Air pressure at sea level is 760 mm Hg (or 760 torr). In medicine and science, mm Hg is commonly used as the unit for partial pressures of gases.

Note that psi and mm Hg reflect different ways of measuring the same thing. At sea level air weighs 14.7 pounds per square inch of earth's surface, so the pressure is 14.7 psi. It is also true that this weight of air will support a column of mercury 760 mm high (Figure 6), so the air pressure is also 760 mm Hg. I also mentioned the weather forecaster's lingo, e.g., "the barometer is 30 inches of mercury and rising." Inches and millimeters are both measurements of length. In the United States, non-scientific measurements remain largely non-metric (many people would like to change that!). In most of the rest of the world the metric system is used for all measurements. Metric lengths are described in millimeters, centimeters, meters and kilometers. Table 2 lists some common units of measurement for average atmospheric pressure, shown for various altitudes. WHAT IS THE DIFFERENCE BETWEEN ABSOLUTE PRESSURE AND GAUGE PRESSURE? Sea water weighs about 64 pounds per cu. foot (the exact weight depends on the quantity of dissolved salt, which varies slightly in the world's oceans).

Using this value, 33 cu. feet of water weighs 33 x 64 = 2112 pounds. Dive to 33 feet depth, lay horizontal, and you will have 2112 pounds of water over every square foot of your body; this comes to 14.7 pounds per square inch, which is the atmospheric pressure at sea level. At 33 feet depth a diver is under two atmospheres of pressure: one atmosphere from the air above sea level and a second atmosphere from the 33 feet of water. The fact that 33 feet of sea water equals the pressure of the entire atmosphere is important in understanding the term "gauge pressure." Gauge pressure, discussed in some diving books, is the water pressure read by gauges that arbitrarily set sea level pressure to zero. Such instruments read the pressure at 33 feet depth as "1 atm. gauge," meaning that the pressure from water alone is 1 atm.

However, if the dive commenced at sea level, then at 33 feet the actual, real, absolute pressure on the diver is two atmospheres, one from earth's atmosphere (14.7 psi) and another from the water (also 14.7 psi). Unless you have one of these gauges don't be concerned about gauge pressure. You need to know the actual or absolute pressure as you dive. If you commence your dive at sea level the absolute pressure at 33 fsw is two atmospheres; at 66 fsw, three atmospheres; at 99 fsw, four atmospheres; etc. Figure 6. The weight of air at sea level will support a column of mercury 760 mm high. In a simple experiment shown by this figure, a tube longer than 760 mm, and closed at one end, is filled with liquid mercury. The tube is then inverted so that its open end is submerged in a pan of mercury, at which point mercury in the tube falls to a certain height. The height of the column of mercury in the inverted tube equals the pressure of air over the open pan of mercury.

At sea level the column of mercury is 760 mm high, so 760 mm Hg is the pressure of air at sea level. TABLE 2. AVERAGE ATMOSPHERIC PRESSURE AT VARIOUS ALTITUDES Measured in atmospheres (atm.), pounds per square inch (psi), millimeters mercury (mm Hg) and inches mercury (in. Hg); latter two are rounded to nearest whole digit. Location Ht (ft.) atm. psi mm Hg in. Hg Sea Level zero 1.00 14.7 760 30 Denver 5280 .75 12.3 640 24 Pikes Peak, Colorado 14410 .63 8.52 550 22 Andres Mtns. 18000 .50 7.35 380 15 Mt. Everest summit 29028 .25 4.12 253 10 Outer space (50 miles) 0 0 0 0 7.

What are the gauge and absolute pressures for a scuba diver at a depth of 132 fsw? 8. If you dive in a mountain lake where the atmospheric pressure is 3/4 that at sea, what is the absolute pressure (in atmospheres) at a depth of 34 feet (equivalent to 33 fsw)? a. 1 d. cannot determine from this information TEST YOUR UNDERSTANDING Answers WHAT CAUSES CHANGES IN ATMOSPHERIC PRESSURE? There are 25.4 millimeters to the inch, so a barometric pressure "30 inches of mercury" is the same as "762 millimeters of mercury." That amount of atmospheric pressure will support a column of mercury 30 inches or 762 mm high. The terms "rising" and "falling" as applied to barometric pressure refer to minor changes in atmospheric pressure with changes in weather. A "high pressure front" is one where the barometric pressure for a mass of air is slightly higher than average.

Although "high and low pressure" fronts may have profound consequences for the weather (e.g., a low pressure front portends bad weather), the pressure changes, per se, have little effect on people; the variations are usually too small to be of any significance. Barometric pressure at a specific location (e.g., the airport at Denver, the beach at Waikiki, the top of the Empire State Building) seldom fluctuates by more than 30 mm Hg (1.2 inches Hg) throughout the year. There is, of course, an average barometric pressure for any given location. At sea level throughout the world this average barometric pressure is 760 mm Hg. Fluctuations in barometric pressure at a specific location, used to predict the weather, are of course different from changes in barometric pressure that come about from changes in altitude or depth. Changes in pressure with altitude have nothing to do with the weather, but are due to the change in weight of air above you. The closer to the earth's surface, the greater the weight of air above you and the greater the air pressure.

Similarly, pressure changes in water are solely related to the change in weight of water above you; the deeper you dive, the greater the weight of water above you and the greater the water pressure. 9. List A shows barometric pressures recorded at four different locations. Match each pressure with a single location in list B where the pressure was most likely recorded. A B TEST YOUR UNDERSTANDING Answers WHAT IS THE COMPOSITION OF AIR? Air is a mixture of gases, mainly oxygen (21% by volume) and nitrogen (78% by volume). The other 1% of air is made up of several other gases such as carbon dioxide (CO2), argon, krypton and neon. The actual percentage composition of dry air (what scuba divers inhale) is shown in Table 3. For scuba diving purposes it is convenient to consider nitrogen as 79% of the air, since the other inert gases (principally argon) must also be considered in computing decompression schedules. Thus you will find many texts listing nitrogen as "79%" of the air. In any mixture of gases (e.g., air), the individual gases don't chemically combine with each other.

The gases maintain their individual identity and percentage regardless of how much or little pressure the mixture is subjected to. The percentages of gases shown in Table 3 are the same throughout the breathable atmosphere. They are also the same inside a tank of compressed air and in the air as it emerges from the tank on its way to the diver's lungs, regardless of depth. This fact takes on critical importance as water pressure increases with increasing depth because, although the percentages are unchanged, the total pressure exerted by each gas component increases proportionately. The increases in component gas pressures account for some of the major problems inherent in compressed air diving: nitrogen narcosis, decompression sickness and oxygen toxicity (see Sections G and I). TABLE 3. PERCENT COMPOSITION OF DRY AIR Nitrogen 78.084 Oxygen 20.948 Argon 00.934 Carbon Dioxide 00.031 Other Gases** 00.003 Total 100.00 ** Neon, helium krypton, xenon, hydrogen, ozone, nitrous oxide and methane. WHAT ARE THE GAS LAWS AND WHY ARE THEY IMPORTANT TO DIVING?

So far we have discussed pressure as it relates to air in the atmosphere. Scuba divers, of course, are interested in what happens to air under water. Air under water obeys the same laws as air in the atmosphere. I will introduce the gas laws in this section and, in Chapter 5, use them to further explain physiology under water. The four important gas laws are those of the Englishmen Robert Boyle (1627-1691), John Dalton (1766-1844), and William Henry (1774-1790), and the Frenchman Jacques Charles (1746-1823). The idea is not to belabor laws of physics, but to emphasize relationships that explain what happens when you dive. The four gas laws are useful because they predict changes in air pressure, volume and temperature as compressed air divers descend and ascend. WHAT IS BOYLE'S LAW? Boyle's law states: At constant temperature, the volume of a gas varies inversely with the pressure, while the density of a gas varies directly with pressure. Simplified: If temperature is kept constant, as air pressure increases the volume of a gas decreases, and vice versa.

Mathematically, where P and V are the pressure and volume, respectively, and K is a constant. Change P, and V will change in the opposite direction, so that their product is maintained at a constant value. Now let's illustrate this law. Suppose you have a container open on one end that is inverted over water; as the container is lowered in the water the trapped air will be compressed by the water pressure (Figure 7). Assume the container holds one liter of air at sea level pressure (one atmosphere). PV = 1 liter x 1 atm. = 1. Increase the air pressure to 2 atmospheres and Boyle's law predicts the volume of air in the container will be 1/2 liter (Figure 7). Figure 7. A container open on one end has one liter of air at one atmosphere. The air is compressed by taking it under water. Boyle's law predicts that at two atmospheres pressure (33 fsw) the volume of air in the container will decrease by one half and the density of air will double. At 3 atmospheres pressure, the volume of air will be 1/3 of that at sea level; and the density triples; etc.

Note that Boyle's law also relates to gas density. Increase the pressure of a fixed volume of gas and the density increases, and vice versa. This part of the law becomes particularly important on deep dives; it predicts that the inhaled air will become denser the deeper one goes. As a result of increasing air density, deep divers often notice greater difficulty breathing. Without doubt Boyle's is the most important law in scuba diving (but not the most important rule, which is never hold your breath). All certification courses stress Boyle's law. Don't leave home without it! 10. A balloon containing 6 liters of air at sea level is taken to a depth of 165 feet. What will the volume of air be in the balloon at the depth? What will be the change in gas density, compared to sea level? 11. A scuba diver takes an extra tank of compressed air to a depth of 99 fsw, which he does not breath from. Compared to sea level what are the density and volume of air in the tank? (Assume temperature is constant.) a. same Charles's law states: At a constant volume, the pressure of gas varies directly with absolute temperature.

Simplified: Given a constant volume of gas, the higher the temperature the higher the gas pressure, and vice versa. Mathematically, where P1 and P1 are the beginning and final pressures, and T1 and T2 are the beginning and final temperatures (remember, volume is kept constant). Compared to Boyle's law, Charles's law is not as important for scuba divers because temperature under water seldom changes enough to seriously affect air pressure. However, the law is useful to keep in mind when filling air tanks, especially when there is a large difference between air and water temperatures. Suppose you have a steel scuba tank holding 80 cu. ft. of air at a pressure of 3000 psi, filled when the air temperature was 90�F. Now you take the tank into water that is 75�F. Before you take your first breath of that tank's air, Charles's law predicts that the tank pressure will be...what? Lower than 3000 psi. Since T2 is less than T1, the law predicts that P2 will be less than P1.

(To know how much less you need to convert T1 and T2 into absolute temperatures by adding 460 to each fahrenheit temperature.) Scuba shop proprietors know about Charles's law, which is why they often fill tanks in a water bath where the temperature is about the same as the ocean (or wherever the diving will take place). 12. A tank is filled to 3000 psi when the air temperature is 85 degrees F. A diver takes the tank into the water and, while still on the surface, notices its pressure is only 2700 psi. Assuming no air has been inhaled from the tank, which one of the following statements is correct? a. The tank has less cubic feet of air than when it was filled. b. The tank has the same cubic feet of air but the air exerts less pressure than when the tank was filled. c. The tank has more air but under lower pressure than out of the water. TEST YOUR UNDERSTANDING Answers WHAT IS DALTON'S LAW?

Dalton's law states: The total pressure exerted by a mixture of gases is equal to the sum of the pressures that would be exerted by each of the gases if it alone were present and occupied the total volume. Simplified: The pressure of any gas mixture (e.g., air) is equal to the sum of pressures exerted by the individual gases (e.g., oxygen, nitrogen, and each of the minor gases). Mathematically, where PTOTAL is the total pressure of a gas mixture (e.g., air), and P1 and P2 are the partial pressures of component gases (e.g., oxygen and nitrogen). The term POTHER is used to signify partial pressures of all other gases in the mixture. WHAT IS PARTIAL PRESSURE? Partial pressure is a very important concept in scuba diving, in part because it aids in understanding Dalton's law. Partial pressure is the pressure exerted by an individual gas, whether that gas is part of a mixture (such as air) or dissolved in a liquid (such as blood) or in any body tissue.

Partial pressure of a gas (PG) is determined by the fraction of the gas in the mixture (FG) times the total pressure of all the gases (excluding any water vapor present): In air at sea level, the partial pressures of oxygen and nitrogen are: Note that we could have used any of the terms in Table 1 (page 58) to denote partial pressure. Thus, in mm Hg the partial pressures of oxygen and nitrogen at sea level are (assuming no water vapor): 13. True or False: The sum of partial pressures of all gases in a gas mixture can never add up to more than the total pressure of gas mixture. 14. True or False: While scuba diving with compressed air, the partial pressure of inhaled oxygen increases with increasing depth. 15. What is the partial pressure, in atmospheres, of oxygen and nitrogen in the lungs of a scuba diver at 66 fsw? 16. What is the partial pressure of oxygen (in mm Hg) at an altitude of 18,000 feet, where the ambient pressure is 380 mm Hg?

TEST YOUR UNDERSTANDING Answers WHAT DOES DALTON'S LAW PREDICT ABOUT CHANGES IN PARTIAL PRESSURE WITH CHANGES IN AMBIENT PRESSURE? (If you answered questions 13 and 14 correctly you already know the answer to this question.) The percentage of gases making up air is the same throughout the breathable atmosphere. Regardless of altitude, the composition of air is about 21% oxygen, 78% nitrogen, 1% other. Similarly, even though air is compressed in a scuba tank, the percentage of the individual gas components is the same. Given this fact and Dalton's law, we see that as air pressure increases or decreases, the partial pressure of each gas will do the same. With increasing altitude, for example, the partial pressure exerted by each gas in the air will decrease. With increasing depth, the partial pressure exerted by each gas in the air we breathe will increase. The lower partial pressures at altitude reflect the fact that there are less molecules of O2 and N2 per volume than at sea level. At the highest point on earth, the summit of Mt.

Everest, air still contains 21% oxygen and 78% nitrogen but the number of oxygen and nitrogen molecules per volume of air is only about 1/3 that at sea level (Figure 2); thus the partial pressures of oxygen and nitrogen are only 1/3 those of sea level. People who fly in unpressurized airplanes, or engage in mountain climbing or hot air ballooning, subject themselves to a decrease in air pressure as they ascend, and an increase in air pressure as they descend; the opposite, of course, happens to scuba divers. Since air at altitude contains fewer O2 molecules, a passenger plane that flies above a certain altitude must pressurize its cabin to the air pressure of a lower altitude than actually flown. When you fly at 30,000 feet, for example, the cabin is pressurized to an altitude of about 7000-8000 feet. At 7000 feet altitude, but not 30,000 feet, the air contains enough oxygen molecules for comfortable breathing at rest (albeit fewer than at sea level).

If the plane suddenly lost its artificial cabin pressure at 30,000 feet and did not descend immediately to a safer altitude, and there was no way to get extra oxygen to the passengers and crew, everyone aboard the plane would soon lose consciousness. If the problem remained uncorrected everyone would eventually succumb to hypoxia. As a practical matter people can live and work up to about 16000 feet; beyond that altitude hypoxia makes it difficult to breathe for long periods, particularly with any exertion. However, people have actually climbed to the summit of Mt. Everest without breathing extra oxygen, a feat of incredible endurance (some would say incredible foolishness). Two principle adaptations allow people to function at high altitude: increased blood volume (hemoglobin carries most of the blood oxygen, so the more blood the more of the scarce oxygen molecules can be taken up from the thin atmosphere); and hyperventilation, which is the medical term for over breathing. Hyperventilation lowers the blood carbon dioxide level and allows the mountain dweller to bring more oxygen molecules into the lungs. Hyperventilation is much more effective in adding oxygen to the blood when the blood is low in oxygen than when it is normally supplied.

(While hyperventilation is a positive adaptation for altitude, it can cause problems in divers, both breath-hold and scuba; see Chapter K.) 17. A sample of air is taken at 18,000 feet during a hot air balloon ride, and the partial pressures of oxygen and nitrogen are measured. Similar measurements are taken at sea level, and on air as it is inhaled by a scuba diver at a depth of 99 fsw. Using units of atm, complete the table with partial pressures of oxygen and nitrogen for the three sites. 99 fsw sea level 18,000 feet PO2 WHAT IS HENRY'S LAW? Henry's law states: The amount of any gas that will dissolve in a liquid at a given temperature is a function of the partial pressure of the gas in contact with the liquid and the solubility coefficient of the gas in that particular liquid. Simplified: As the pressure of any gas increases, more of that gas will dissolve into any solution with which it is in free contact.

Mathematically, where VG is the volume of a particular gas, VL is the volume of a particular liquid, a is the solubility coefficient for the gas in that liquid, and Pg is the pressure of the gas in contact with the liquid. Taken together, Henry's and Dalton's laws predict two very important consequences: 1)When ambient pressure is lowered (as at altitude), the partial pressure of oxygen and nitrogen in the body must fall, and there will be less molecules of each gas dissolved in the blood and tissues. 2)When ambient pressure is raised (as when diving), the partial pressure of oxygen and nitrogen in the body must rise, and there will be more molecules of each gas dissolved in the blood and tissues. The second statement is the physiologic basis for three important problems associated with compressed air diving: decompression sickness, nitrogen narcosis, and oxygen toxicity. These conditions are discussed in Sections G and I. 18. Listed below are the 12 statements that relate to the entire chapter. State which are true and which are false. a. Air pressure is due to the weight of the air. b. Water is much heavier than air and for this reason exerts a much greater pressure. c.

Partial pressure of gas is independent of the ambient pressure. d. The percent change in ambient pressure between 18000 feet altitude and sea level is the same as that between sea level and 33 feet of sea water. e. There are several ways to specify the measurement of air pressure, e.g., psi, mm. Hg, inches Hg, and atmosphere (atm.). Average air pressure at sea level = 1 atm. =760 mm. Hg = 14.7 psi. f. Gauge pressure and absolute pressure are the same. g. Air is a mixture of gases made up of approximately 21% oxygen, 78% nitrogen, and 1% other gases. These percentages are the same regardless of altitude, or of outside pressure exerted on air. h. When breathing compressed air, more oxygen will dissolve in blood at gg fsw than at 33 fsw. i. Boyle's law states that pressure of a gas (at constant temperature) is inversely related to its volume: if pressure increases volume decreases, and vice versa. j. For a given tank pressure, the density of inhaled gas is constant during scuba diving. k.

Henry's law explains why there is increased nitrogen in the tissues at depth when scuba diving. l. Charle's law predicts that the pressure of in a scuba tank will fall if the outside temperature falls. Answers to TEST YOUR UNDERSTANDING 1. c. Air pressure at sea level is 14.7 psi, which means the total column of air from sea level to outer space one inch square weighs 14.7 lbs. Since a square foot contains 12 x 12 = 144 square inches: 144 sq. in. x 14.7 lbs./sq. inch = 2116.8 lbs. 2. c. A square yard contains 9 sq. feet, or 9 x 144 sq. inches. Hence the column of air over a sq. yard weighs 9 x 144 x 14.7 = 19,051.2 lbs. 3. True 5. True 6. False 7. At 132 fsw absolute or total ambient pressure = 5 atm. Gauge pressure (pressure of water alone) = 4 atm. 8. b.

1.75 atm. 9. 253 mm Hg - summit of Mt. Everest 640 mm Hg - Denver 1520 mm Hg - inside hyperbaric chamber 10. Volume at 165 feet = 1 liter; density 6 times as great 11. a. The tank is a rigid structure. The compressed air is unaffected by ambient pressure until it leaves the tank. 12. b. 14. True 15. At 66 fsw, PO2 = .63 atm.; PN2 = 2.37 16. Partial pressure of oxygen is .21(380), or about 80 mm Hg. (This answer assumes dry air; any water vapor in the air will slightly lower the partial pressures of the other gases.) 17. 18. c, f, and j are false; the other statements are true. REFERENCES AND BIBLIOGRAPHY Quoted sources and general references are listed by section or sections, in alphabetical order. An asterisk indicates references that are especially recommended. Medical textbooks and journal articles can be obtained from most public libraries via inter-library loan.

For a list of companies that distribute free catalogs of diving books and videos, see Section U. SECTION D. An Explanation of Pressure and the Laws of Boyle, Charles, Dalton, and Henry For the sport diver, the training manuals of NAUI, PADI and SSI provide much useful information on physics and physiology of diving, as well as on all the diving skills. In addition, the following six books are highly recommended reference works for those who wish to read further on dive physics and physiology; the last three are textbooks marketed mainly to physicians and other medical professionals. *Hornsby A, Brylske A, Shreeves K, Averill H, Seaborn C. Encyclopedia of Recreational Diving. International PADI, Inc., Santa Ana, CA.; 1989. *NOAA Diving Manual, 3rd Edition. U.S. Department of Commerce, National Oceanic and Atmospheric Administration, Washington, D.C.; 1991. *U.S. Navy Diving Manual, Vol. 1 (Air Diving) and Vol 2 (Mixed-Gas Diving), Best Publishing Co., Box 30100, Flagstaff, AZ; 1993.

*Bennett P, Elliott D, editors. The Physiology and Medicine of Diving. 4th edition. W.B. Saunders Co., Philadelphia; 1993. *Bove AA, Davis JC, editors. Diving Medicine. 2nd Ed., W.B .Saunders., Philadelphia; 1990. *Edmonds C, Lowry L, Pennefather J. Diving and Subaquatic Medicine. Butterworth Heinemann, Oxford; 1992. Gas Laws – The Physics Hypertextbook Discussion introduction The gas laws are a set of intuitively obvious statements to most everyone in the Western world today. It's hard to believe that there was ever a time when they weren't understood. And yet someone had to notice these relationships and write them down. For this reason, many students are taught the three most important gas laws by the names of their discoverers. However, since the laws are known by different names in different countries and (more importantly) since I can never remember who gets credit for which law without referring to notes, I will not follow this convention. pressure-volume (constant temperature) What happens to the volume of a gas as the pressure on it changes.

Let's try the following experiment using equipment that might be found in your kitchen. Marshmallows in a kitchen vacuum pump. The volume of a marshmallow increases as the pressure on it decreases — and vice versa. Do try this experiment at home. Do it! Marshmallows are a mixture of sugar, air, and gelatin. Sugar makes them sweet, air makes them fluffy, and gelatin makes them elastic. Marshmallows are a frozen foam and are mostly air by volume. When placed in a vacuum pump, they expand as the pressure decreases. Break the seal on their container and they shrink during the return to normal atmospheric pressure. Since the vacuum pump pulls on the marshmallows hard enough to burst some of the air bubbles, they are actually a bit smaller and more shriveled at the end of this experiment. This illustrates a fundamental, yet important, property of gases. The pressure of a gas is inversely proportional to its volume when temperature is constant.

Symbolically… P ∝ or P1V1 = P2V2 = constant This correlation was discovered independently by Robert Boyle (1627–1691) of Ireland in 1662 and Edme Mariotte (1620–1684) of France in 1676. In Great Britain, America, Australia, the West Indies and other remnants of the British Empire it is called Boyle's law, while in Continental Europe and other places it is called Mariotte's law. Mariotte added the important provision that temperature remain constant. Boyle neglected to mention it, but the data he used to derive his law were most likely collected during a period in which the temperature did not experience any significant change. Since the gas needs to be in thermal equilibrium with its environment (or some other heat reservoir) to maintain an even temperature, the pressure-volume relationship normally applies only to "slow" processes. The marshmallow-vacuum experiment shown above is an example of a "slow" process. The pressure is reduced at a rate slow enough that heat from the environment is able to keep the jar and its contents at nearly room temperature.

Such a transformation that takes place without a change in temperature is said to be isothermal. Pumping a bicycle tire with a hand pump is an example of a "fast" process. The work done pushing the piston transforms into an increase in the internal energy (and thus an increase in the temperature) of the air molecules within the pump. People familiar with hand bicycle pumps will attest to the fact that they get hot after use. Likewise, when a gas is allowed to expanded into a region of reduced pressure it does work on its surroundings. The energy to do this work comes from the internal energy of the gas and so the temperature of the gas drops. You can experience this yourself without the aid of any apparatus other than your mouth. Purse your lips so that your mouth has only a tiny opening to the outside and blow hard. The air rushing from your mouth will be quite cool despite coming from the core of your body, which is normally quite hot (around 37 ℃). During a "fast" process like the ones just described, pressure and volume are changing so rapidly that heat doesn't have enough time to get into or out of the gas to keep the temperature constant.

Such a transformation that takes place without any flow of heat is said to be adiabatic. volume-temperature (constant pressure) What happens to the volume of a gas when its temperature changes? Let's try another kitchen experiment. Bread dough before and after baking. Increasing the temperature of bread dough increases its volume. Do try this experiment at home. Do it! [dough] [bread] Bread is made from wheat flour, water, yeast, and a bit of sugar. Yeast are tiny microorganisms. They are quite possibly the very first domesticated animals and, much like dogs and horses, yeast have been bred for different purposes. Just as we have guard dogs, lap dogs, and hunting dog; draft horses, race horses, and war horses; we also have brewer's yeast, champagne yeast, and bread yeast. Bread yeast have been selectively bred to eat sugar and burp carbon dioxide (CO2). When wheat flour and water are mixed together and kneaded, the protein molecules are mashed and stretched until they line up neatly to form a substance called gluten that, like chewing gum, is both elastic and plastic.

Let this special matrix sit and the the CO2 vented from the yeast get trapped in thousands of tiny resilient, stretchy pockets. As this process continues these tiny pockets expand, which causes the volume of the dough to expand or rise in a process called proofing. We now have a fluffy gummy blob ready for the oven. While there the dough expands again, but his time it's not due to the action of microorganisms (they all die around the boiling point of water). This time it's the heat, or rather the temperature. The temperature inside a bread oven is roughly 50% greater (in absolute terms) than the temperature outside. And similarly, the baked bread that comes out of a bread oven is also roughly 50% greater than the room temperature dough that goes in. This domestic example illustrates quite nicely a fundamental property of gases. The volume of a gas is directly proportional to its temperature when pressure is constant. Symbolically… V ∝ T (P constant) While no doubt known and understood informally by billions of bakers since the dawn of civilization, the precise mathematical relationship was first discovered by the French physicist Guillaume Amontons (1663–1705) in 1699.

The experiment was repeated much later by Jacques Charles (1746–1823) in 1787 and much, much later by Joseph Gay-Lussac (1778–1850) in 1802. Charles did not publish his findings, but Gay-Lussac did. It is most frequently called Charles' law in the British sphere of influence and Gay-Lussac's law in the French, but never Amonton's law. An isobaric process is one that takes place without any change in pressure. Let's recall what it means when two quantities are directly proportional like volume and temperature. Heat up a gas and it's volume will expand. Cool it down and it's volume will contract. The two quantities change in the same direction. More specifically, an increase in one results in a proportional increase in the other and a decrease in one results in a proportional decrease in the other. For example… Doubling the absolute temperature of the air in an engine cylinder will double its volume. Halving the absolute temperature of the air in a bag of potato chips will cause it to shrink to one half its original volume.

The absolute temperature of a bread oven is one and a half times that of room temperature. Therefore, the loaf of baked bread that comes out of an oven has 50% more volume than the ball of dough that went into it. There's a symmetry at work here somewhere. A symmetry is a change in one quantity that leaves another, more fundamental quantity unchanged. It's something like multiplying both the numerator and denominator of a fraction by the same thing. a Double room temperature, 293 K = 20 ℃, and you get 586 K = 313 ℃ not 40 ℃. a complete ideal gas law Proportionality statements aren't as popular today in the Twenty first Century as they were in the Nineteenth Century and earlier. We live in an era where it's all about the equation. There's good and bad in this focus. Equations convey a lot of information in a very few symbols, which is why they're so popular, but they're also a crutch; a device used to support a weak understanding and make it seem strong. Equations can be used by a student with no understanding to fake competency. "I put the numbers into the equation and I got the right answer.

Since I have the right answer, I am smart." Skilled? Certainly. Smart? Not necessarily. Still, it would be nice to have an equation around for those times when all you want to do is just get the job done with a minimum of hassle. Combine the three together.

Question: The principle that "the volume of a given quantity of gas varies inversely with the pressure when the temperature is constant", is whose law?
Answer: BOYLE'S LAW