ChemBytes - Chapter 5

January 26, 1998

CHEMByte 1: Scuba Diving and Boyle's Law
For the scuba diver, the proper application of Boyle's law is of vital interest. With every 10 meters of depth, divers experience an additional pressure of one atmosphere, which affects gases trapped anywhere in the body cavities, especially the middle ear, sinuses, and most importantly the lungs. If a diver descends without scuba gear, the amount of gas contained in the body cavities remains constant and the volume of these cavities decreases as the surrounding water pressure increases. However, a diver using scuba gear does not experience the crush of the great external pressure, because the regulator on the tank delivers air to the lungs at the same pressure as the surroundings. This means that at a depth of 30 meters, the air in the diver's lungs is at 4 atmospheres. Great care must be taken to breath out regularly while returning to the surface from such depth to prevent the trapped air in the lungs from expanding. Extreme distortion of the lungs can cause the small air sacks called alveoli to burst. This could allow air bubbles to enter the bloodstream and cause a dangerous blockage, followed by loss of consciousness, heart attack, or brain damage, and possibly death.

CHEMByte 2: "Lighter-than -Air Craft and Hot Air Ballooning."
Because the density of a gas is proportional to its molar mass, any gas with a molar mass significantly less than the average molar mass of air has potential lifting power. Air is composed of roughly 78% N2 which has a molar mass of 28.0 g/mol, 21% O2 with a molar mass of 32.0 g/mol, and 1% Ar with a molar mass of 40.0 g/mol. The average molar mass of air is 29.0 g/mol. Gases with lower molar masses include CH4 (16.0 g/mol) and NH3 (17.0 g/mol) as well as the even more buoyant He (4.0 g/mol) and H2 (2.0 g/mol).

A balloon will rise if the mass of the balloon and its contents is less than that of an equal volume of air. The balloon is pushed up through the air just as a submerged piece of cork is pushed up by the water. The lifting power of the balloon is the difference in mass between the filled balloon and that of the same volume of air. Helium is commonly used in balloons and blimps instead of hydrogen because the greater lifting power of hydrogen gas is more than offset by its extreme flammability. Hot air balloons take advantage of the lower density of heated air resulting from its increase in volume according to Charles/Gay-Lussac law.

CHEMByte 3: Jacques Charles and Joseph Gay-Lussac
On hearing about experiments on balloons, Jacques Charles, a professor at the Sorbonne and popular lecturer on science for the layman, realized that the element hydrogen, which had just been discovered a few years earlier, would be just the right gas for rising to new heights. It would be a far more efficient buoyant force than hot air. So in August of 1783, on the eve of the French Revolution, he constructed the first hydrogen-filled balloon, inventing the necessary devices for handling, filling, and manipulating it. He ascended several times, reaching heights of over a mile and in the process helped to establish what became the first aeronautical craze since Leonardo da Vinci's attempts at bird flight. Unfortunately, Louis XVI of France was fascinated by balloon flight and patronized Charles's expeditions, a fact which almost got Charles beheaded along with the Monarch in the French Revolution. But the popular lecturer talked his way out of it by reciting his long list of ballooning achievements to the cheering courtroom.

In 1804, the young Joseph Gay-Lussac made a balloon ascent with another French physicist, Jean Biot (1774-1862). Using a balloon left over from Napoleon's Egyptian campaign, the two of them, loaded down with an assortment of scientific instruments and a small collection of live animals, made one of the first ascents for strictly scientific purposes. In a later flight, Gay-Lussac reached a height of over four miles, higher than the tallest peak in the Alps.
Both Charles and Gay-Lussac made extraordinary contributions to the young science of chemistry in their exploration of the expansion of gases on heating. They also anticipated the space exploration of our time in their early attempts to rise above the Earth's surface.

CHEMByte 4: Helium Demand and Helium Storage
In the century since it was discovered as a trace ingredient of the uranium mineral clevit, helium, the second lightest of all elements, has become indispensable to science and technology. Scientists believe it could play a vital role in helping the world through future energy shortages. But the fear exists that the most economically exploited source of this nonrenewable substance will be depleted in 20 years or so. Although American producers recover about 3.3 billion cubic feet of helium from natural gas each year, another 3.2 billion cubic feet are thrown away through lack of separation, refinement, and storage capacity. A world shortage of helium a generation from now could obstruct the development of superconducting power lines, motors, generators, electricity storage systems, magnetically levitated trains, and many other applications not yet even imagined.

Helium is commercially recovered from natural gas reservoirs, mainly in the U.S.. Because it is a noninflammable gas with considerable lifting power, it was prized by airship builders and users following WW I, a conflict in which hydrogen-filled Zeppelin bombers proved to be death-traps. After that war, the US. banned the export of helium and began to stockpile the gas, creating a reserve now estimated to be 32 billion cubic feet. Unfortunately, the US. government is considering going out of the stock-piling business. And unless the government creates economic incentives, private industry is not likely to step in. With present world growth in demand for helium rising, that leaves us with a short, one-generation at most, supply.
Helium is separated from natural gas with which it is mixed by compressing and cooling the methane and other gases until all but the helium are liquefied. The helium, which remains a gas until it is chilled to minus 452 Fahrenheit, is then pumped off. The main obstacle to extracting and storing helium is the mismatch in market demands for natural fuel gas and helium. When demand for natural gas is heavy, as is normally the case in winter, large amounts of helium are withdrawn from wells along with the natural gas, but if there is little commercial demand for helium at that point, there is no economic incentive to extract and save it. Gas companies then generally save themselves the expense of separating the helium, which consequently remains mixed with the natural gas and is lost when the gas is burned.
As we write, the situation is unresolved!

CHEMBytes: Additional Problems on Gases

  1. A certain sample of gas has a volume of 0.452 L measured at 87°C and 0.620 atm. What is its volume at 1 atm and 0°C?
  2. Calculate the number of moles in a sample of an ideal gas whose volume is 0.452 L at 87°C and 0.620 atm?
  3. An ideal gas at 1 atm pressure was contained in a bulb of unknown volume V. A stopcock was opened which allowed the gas to expand into a previously evacuated bulb whose volume was known to be exactly 0.500 L. When equilibrium between the bulbs had been established, it was noted that the temperature had not changed, and that the gas pressure was 530 torr. What was the unknown volume V of the first bulb?
  4. It is found that 0.896 g of a gaseous compound containing only nitrogen and oxygen occupies 524 mL at a pressure of 730 torr and a temperature of 28.0°C. What is the molecular weight and molecular formula of the gas?
  5. Ethylene reacts with hydrogen in the presence of a platinum catalyst (according to the equation that follows), forming ethane:
    C2H4(g) + H2(g) —> C2H6(g)
    A mixture of C2H4(g) and H2(g) known only to contain more H2 than C2H4 had a pressure of 52 torr in an unknown volume. After the gas had been passed over the catalyst bed its pressure was 34 torr in the same volume and at the same temperature. What fraction of the molecules in the original mixture was ethylene?
  6. A gaseous compound known to contain only carbon, hydrogen, and nitrogen is mixed with exactly the volume of oxygen required for the complete combustion to CO2, H2O, and N2. Burning 9 volumes of the gaseous mixture produces 4 volumes of CO2, 6 volumes of water vapor, and 2 volumes of N2, all at the same temperature and pressure. How many volumes of oxygen are required for the combustion? What is the molecular formula of the compound?
  7. The valve between a 5-L tank in which the gas pressure is 9 atm and a 10-L tank containing a gas that is at 6 atm is opened, and the pressure equilibrium ensues at constant temperature. What is the final pressure in the two tanks?
  8. A sample of PCl5 weighing 2.69 g was placed in a 1.00 L flask and completely vaporized at a temperature of 250°C. The pressure observed at this temperature was 1.00 atm. The possibility exists that some of the PCl5 may have dissociated according to the equation
    PCl5 (g) = PCl3 (g) + Cl2 (g)
    What are the partial pressures of PCl5, PCl3, and Cl2 under these experimental conditions?
  9. Calculate the root-mean-square speed (in cm/s and at 25°C) of a free electron and of a molecule of UF6.
  10. Compare the root-mean-square speed (at 20°C) of He and the escape velocity of earth. Given the information in ChemByte 4, what do you conclude?
  11. A mixture of hydrogen and helium is prepared such that the number of wall collisions per unit time by molecules of each gas is the same. Which gas has the higher concentration?