In the final module of this chapter, a modified gas law will be introduced that accounts for the non-ideal behavior observed for many gases at relatively high pressures and low temperatures. The ideal gas equation contains five terms, the gas constant R and the variable properties P , V , n , and T. Specifying any four of these terms will permit use of the ideal gas law to calculate the fifth term as demonstrated in the following example exercises.
Using the Ideal Gas Law Methane, CH 4 , is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by g of CH 4. It would require L gal of gaseous methane at about 1 atm of pressure to replace 1 gal of gasoline. It requires a large container to hold enough methane at 1 atm to replace several gallons of gasoline.
Using the Combined Gas Law When filled with air, a typical scuba tank with a volume of Note: Be advised that this particular example is one in which the assumption of ideal gas behavior is not very reasonable, since it involves gases at relatively high pressures and low temperatures. Check Your Learning A sample of ammonia is found to occupy 0. Whether scuba diving at the Great Barrier Reef in Australia shown in [link] or in the Caribbean, divers must understand how pressure affects a number of issues related to their comfort and safety.
Pressure increases with ocean depth, and the pressure changes most rapidly as divers reach the surface. The pressure a diver experiences is the sum of all pressures above the diver from the water and the air. Divers must therefore undergo equalization by adding air to body airspaces on the descent by breathing normally and adding air to the mask by breathing out of the nose or adding air to the ears and sinuses by equalization techniques; the corollary is also true on ascent, divers must release air from the body to maintain equalization.
Buoyancy, or the ability to control whether a diver sinks or floats, is controlled by the buoyancy compensator BCD. The expanding air increases the buoyancy of the diver, and she or he begins to ascend.
The diver must vent air from the BCD or risk an uncontrolled ascent that could rupture the lungs. In descending, the increased pressure causes the air in the BCD to compress and the diver sinks much more quickly; the diver must add air to the BCD or risk an uncontrolled descent, facing much higher pressures near the ocean floor.
The pressure also impacts how long a diver can stay underwater before ascending. The deeper a diver dives, the more compressed the air that is breathed because of increased pressure: If a diver dives 33 feet, the pressure is 2 ATA and the air would be compressed to one-half of its original volume.
The diver uses up available air twice as fast as at the surface. We have seen that the volume of a given quantity of gas and the number of molecules moles in a given volume of gas vary with changes in pressure and temperature. Chemists sometimes make comparisons against a standard temperature and pressure STP for reporting properties of gases: At STP, an ideal gas has a volume of about Key Concepts and Summary The behavior of gases can be described by several laws based on experimental observations of their properties.
Sometimes leaving a bicycle in the sun on a hot day will cause a blowout. Explain how the volume of the bubbles exhausted by a scuba diver [link] change as they rise to the surface, assuming that they remain intact.
How would the graph in [link] change if the number of moles of gas in the sample used to determine the curve were doubled? The curve would be farther to the right and higher up, but the same basic shape. In addition to the data found in [link] , what other information do we need to find the mass of the sample of air used to determine the graph? Determine the volume of 1 mol of CH 4 gas at K and 1 atm, using [link]. Determine the pressure of the gas in the syringe shown in [link] when its volume is What is the temperature of an Calculate the volume of the gas at the higher temperature, assuming no change in pressure.
A balloon inflated with three breaths of air has a volume of 1. At the same temperature and pressure, what is the volume of the balloon if five more same-sized breaths are added to the balloon? A weather balloon contains 8. When the volume decreases, the pressure increases. This shows that the pressure of a gas is inversely proportional to its volume. It is named after 17th century scientist Robert Boyle. P 1 is the initial pressure. V 1 is the initial volume. P 2 is the final pressure.
The Interdependence between Ocean Depth and Pressure in Scuba Diving Whether scuba diving at the Great Barrier Reef in Australia shown in Figure 9 or in the Caribbean, divers must understand how pressure affects a number of issues related to their comfort and safety. Figure 9. Scuba divers, whether at the Great Barrier Reef or in the Caribbean, must be aware of buoyancy, pressure equalization, and the amount of time they spend underwater, to avoid the risks associated with pressurized gases in the body.
Chemistry End of Chapter Exercises Sometimes leaving a bicycle in the sun on a hot day will cause a blowout. Explain how the volume of the bubbles exhausted by a scuba diver Figure 8 change as they rise to the surface, assuming that they remain intact. How would the graph in Figure 4 change if the number of moles of gas in the sample used to determine the curve were doubled?
How would the graph in Figure 5 change if the number of moles of gas in the sample used to determine the curve were doubled? In addition to the data found in Figure 5 , what other information do we need to find the mass of the sample of air used to determine the graph? Determine the volume of 1 mol of CH 4 gas at K and 1 atm, using Figure 4.
Determine the pressure of the gas in the syringe shown in Figure 5 when its volume is What is the temperature of an Calculate the volume of the gas at the higher temperature, assuming no change in pressure. A balloon inflated with three breaths of air has a volume of 1. At the same temperature and pressure, what is the volume of the balloon if five more same-sized breaths are added to the balloon?
A weather balloon contains 8. What is the volume of the balloon under these conditions? The volume of an automobile air bag was What was the pressure in the bag in kPa? How many moles of gaseous boron trifluoride, BF 3 , are contained in a 4. How many grams of BF 3?
Iodine, I 2 , is a solid at room temperature but sublimes converts from a solid into a gas when warmed. What is the temperature in a How many grams of gas are present in each of the following cases?
A cylinder of medical oxygen has a volume of A large scuba tank Figure 8 with a volume of 18 L is rated for a pressure of bar. Calculate the mass of the gas remaining in the cylinder if it were opened and the gas escaped until the pressure in the cylinder was equal to the atmospheric pressure, 0.
How many moles of O 2 are consumed by a 70 kg man while resting for 1. The effect of chlorofluorocarbons such as CCl 2 F 2 on the depletion of the ozone layer is well known. The use of substitutes, such as CH 3 CH 2 F g , for the chlorofluorocarbons, has largely corrected the problem.
Calculate the volume occupied by Each alpha particle becomes an atom of helium gas. A balloon that is If the final volume of the balloon is If the temperature of a fixed amount of a gas is doubled at constant volume, what happens to the pressure?
If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure? For a gas exhibiting ideal behavior: The pressure decreases by a factor of 3. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately.
This relationship between the two quantities is described as follows:. Dividing both sides of Equation 6. The numerical value of the constant depends on the amount of gas used in the experiment and on the temperature at which the experiments are carried out. Hot air rises, which is why hot-air balloons ascend through the atmosphere and why warm air collects near the ceiling and cooler air collects at ground level. Because of this behavior, heating registers are placed on or near the floor, and vents for air-conditioning are placed on or near the ceiling.
The fundamental reason for this behavior is that gases expand when they are heated. Because the same amount of substance now occupies a greater volume, hot air is less dense than cold air. The substance with the lower density—in this case hot air—rises through the substance with the higher density, the cooler air.
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