ChemBytes - Chapter 6

February 2, 1998

CHEMByte 5: A Story Neils Bohr Liked to Tell
There was once a young man who was sent by his village to another town to hear a great rabbi talk. When he returned, he reported: "The Rabbi spoke three times; the first talk was brilliant, clear and simple. I understood every word and it was clear that the Rabbi was the master of his subject. The second talk was even better, deep and subtle. I didn't understand much but the Rabbi understood all of it. The third lecture was a truly great and unforgettable experience. I understood nothing and the Rabbi didn't understand much either."

CHEMByte 6: Looking at Liquid CO2
Carbon dioxide is a colorless, tasteless gas about 1.5 times as dense as air. Under certain conditions, carbon dioxide gas may be liquefied or even solidified. If the gas at a pressure of 20 atm is chilled to 0°F, it will liquefy. However, if it is not practical to chill the gas below room temperature it can still be liquefied by compressing the gas to 50 atm at about 68°F. The critical temperature for CO2 is 87.8°F and so it is impossible to liquefy the gas beyond this temperature, no matter what the pressure. In the simple classroom demonstration, pieces of dry ice were placed within a 6" inch length of half-inch diameter Tygon tubing (with 3/64" wall thickness) and then clamped at either end with Hoffman clamps and tightened with pliers to ensure a tight seal. As the dry ice vaporizes, the pressure increases and the carbon dioxide liquefies first into a slush and then into a clear liquid. But equilibrium is never achieved because soon the increasing pressure forces the Tygon tubing to fail as it first balloons into a great aneurysm which finally explodes with a bang.

CHEMByte 7: The Permanent Gases
Michael Faraday (British: 1791-1867) was the first to liquefy chlorine when he decomposed a chlorine compound in a sealed tube. A few drops of liquid chlorine condensed in the cold end. By immersing the cold end in a cooling mixture, Faraday was able to isolate and liquefy a number of gases that had previously resisted efforts to condense them. However, all attempts at condensing hydrogen, nitrogen, and oxygen were unsuccessful and many scientists of the day believed them to be "permanent gases." With advances in low temperature technology, all of the uncondensable gases of Faraday's generation have now been condensed to the liquid state. James Dewar liquefied hydrogen in 1898 and was subsequently able to solidify it in 1899 at a temperature only 14 degrees above absolute zero, a temperature at which all substances except helium are solids. Heike Kamerlingh-Onnes successfully condensed helium in 1908. It was the last of the "permanent gases" and the most difficult to liquefy.

James Dewar (Scottish: 1842-1923) was Fullerian Professor of Chemistry at the Royal Institution (London). His most important work in a long and successful career was in the field of low temperatures. In 1892, he constructed double-walled evacuated glass flasks generally shaped like large test tubes. The space between the walls was evacuated so that heat could not be transmitted by thermal conduction or convection due to air currents. Heat could be transferred only by radiation, and even that could be cut down by "mirroring" the walls with silver so that radiated heat would be reflected rather than absorbed. Today, these vessels are called Dewar flasks and are little changed from Dewar's original designs. One household variety is sold under the trade name of Thermos® bottle.
Returning to the Dutch university at Leiden after receiving his Ph.D. degree from Heidelberg, where he had studied under Bunsen, Heike Kamerlingh-Onnes (1853-1926) established the cryogenic (low temperature) laboratory which now carries his name. Here new depths of temperature were plumbed and Leiden became famous as the cold research center of the world. Kamerlingh-Onnes studied the behavior of gases at very low temperatures. To reach the very low temperatures required liquefied gases, which in turn brought his attention to problems in liquefaction, in particular, the one remaining gas that had defied all attempts to condense it, namely helium. Kammerlingh-Onnes built an experimental device that would cool helium intensively by means of vaporizing liquid hydrogen and then allowing the hydrogen gas produced to expand. Collecting the first drops of the liquid, he preserved it in a flask cooled by liquid hydrogen, which was in turn kept cool by being immersed in a still larger flask of liquid air. He reported a scant 4 K (-269°C) boiling point. After his death, students in his laboratory managed to solidify helium by using not only very low temperatures but the added trick of very high pressures. It froze at 1 K (-272°C) at a pressure of 26 atm.

CHEMByte 8:The Properties of Solutions
A century ago, the accurate determination of molecular weights was a major concern for chemists, and to be able to provide such data with simple scientific equipment such as barometers and thermometers was significant. What made this possible? As early as 1878, in his first published scientific paper, Francois-Marie Raoult (French: 1830-1901) hinted at the existence of a relationship between the molar mass of a dissolved substance and the vapor pressure of a dilute solution of that substance. Raoult showed that certain characteristic physical properties of solutions depended on the choice of solvent but not on the choice of solute. For example, he was able to demonstrate that the freezing point was depressed in proportion to the number -- not the kind -- of particles present in solution, and that, in turn could be used to find the molar mass of the dissolved particles.

Raoult was a professor at the French university of Grenoble, and although a number of scientists of the day had studied the effects of solutes on solutions before him, his was the definitive work. He was aided to a significant degree by the availability of a cleverly designed piece of apparatus known as the Beckmann thermometer in which the amount of mercury in the stem could be varied so as to change the temperature range, making it possible to measure differences in temperatures with a precision of 0.001°C. That degree of precision proved to be very important for measuring the small differences in temperature Raoult found in his freezing point depression and boiling point elevation studies.

CHEMByte 9: Osmotic Pressure and a Theory for Solutions
Jacobus Henricus van't Hoff (1852-1911), a Dutch physical chemist noted for his studies of osmotic pressure and winning the first Nobel Prize ever awarded in chemistry, had an interesting way of looking at the phenomenon. As he put it, the osmotic pressure was the pressure which the dissolved substance would exert if it existed as an ideal gas in the volume occupied by the solution, but with all the solvent removed. Van't Hoff's explanation was that the pressure was due to the collisions or impacts of the dissolved molecules with the semipermeable membrane. But when he studied electrolytes -- solutions that conduct an electric current -- the results were different, consistently deviating from the predicted behavior. Solutions of salts like sodium chloride, for example, produced nearly twice as large an effect as sugar solutions, behaving as though there were twice as many moles of particles present in the solution. The explanation for this appeared in the now famous Ph.D. thesis, written by a young Swedish chemist named Svante Arrhenius (1859-1927).

Much to the consternation of his teachers who represented the scientific establishment in chemistry at the time, Arrhenius had suggested that the marked deviation van't Hoff observed in the behavior of electrolyte solutions such a sodium chloride could be explained by assuming that the salt split into sodium ions and chloride ions. Thus, there would be twice as many particles and twice the effect in dilute solutions. Arrhenius was the first to postulate that electrolyte solutions result from a separation of apparently neutral species into positively and negatively charged atoms called ions. Because these ideas were in direct conflict with the prevailing theories of the day, he received the lowest possible passing grade on his thesis. Years later, so much hostility remained that Arrhenius was almost prevented from being appointed professor at Stockholm. But it was for this very work that he was awarded the Nobel prize for chemistry in 1903. Later in his career, Arrhenius was one of the most honored, important, and influential men of science in the world. For many years, he was the general secretary of the Nobel Committee and the Director of the Nobel Institute for Physical Chemistry.

CHEMByte 10: Treating Municipal Waste Waters
Efficient sewage disposal is important to the health of any community. In the past, the easy method of disposal -- dilution -- was utilized universally. Wastes were dumped into available large water bodies such as rivers, lakes, streams or coastal waterways. There, the ever present supply of oxygen would in time destroy the organic components of our municipal wastes, mostly human sewage. That solution, however, is no longer satisfactory, even in small, isolated communities.

The amount of treatment required of municipal sewage is determined by the quantity of suspended solids and the biochemical oxygen demand (BOD), the amount of molecular oxygen needed by a microbial population to stabilize biodegradable organic materials. Modern municipal sewage treatment methods fall into three categories:
  1. Physical (primary) treatment: removes 50-60% of suspended solids while reducing the BOD by an equivalent amount. The influent is screened to allow passage of solids of a certain maximum size (about 3-5 cm in diameter). Solids that settle out are then removed. Chemical additives like iron(III) sulfate or aluminum sulfate are added to increase the size and promote settling of fine, suspended particles. When only primary treatment is used, the clarified effluent is chlorinated to destroy bacteria and viruses before its return to natural waters.
  2. Biochemical (secondary) treatment: Primary treatment which was the total treatment 50 years ago is now considered inadequate because it leaves a great quantity of solids in the form of fine particles, as well as all of the dissolved substances. Secondary treatment reduces BOD by 90% by oxidizing dissolved organic substances. The process in which the water is exposed to microorganisms that eat up organic wastes is the equivalent of nature's own water purification. To speed the process, activated sludge containing aerobic microorganisms that digest raw sewage can be added. The removed solids can be burned for their energy content, or they can be sold and used as fertilizers after filtering and drying. The liquid effluents remaining after removal of the solids are then chlorinated to destroy any remaining harmful organisms.
  3. Advanced (tertiary) treatment: Where local conditions require it, further treatment beyond biochemical oxidation can be implemented. The need arises from the presence of specific pollutants not removed by primary or secondary treatment and also from discharge of the treated water into a sensitive environment. Tertiary treatment can, for example, remove heavy metals entering the wastewater from industrial plants. It is also required for removal of nitrogen compounds from waters released to estuaries such as the Chesapeake Bay or Long Island Sound. These compounds are plant nutrients and without treatment, decomposition of the additional aquatic plants deprives the waters of oxygen needed by fish and shellfish.

CHEMBytes: Additional Problems on Liquids and Solutions

  1. What are the molality and the molarity of a solution of ethanol (C2H5OH) in water (H2O) at 20°C if the mole fraction of the ethanol is 0.05? Assume that the density of the solution is 0.997 g/mL at 20°C.
  2. Concentrated nitric acid is 69% HNO3 by weight and has a density of 1.41 g/mL at 20°C. What volume and weight of concentrated nitric acid are needed to prepare 100 mL of 6 M acid?
  3. The freezing point depression constant for mercury(II) chloride (HgCl2) is 34.3. For a solution of 0.849 g of mercury(I) chloride (Hg2Cl2) in 50 g of mercury(II) chloride, the freezing point depression is 1.24°C. What is the molecular weight of mercury(I) chloride in this solution? What is its molecular formula?
  4. Ten liters of dry air were bubbled slowly through water at 20°C and the observed weight loss (of water) was 0.172 g. By assuming that 10 liters of saturated water vapor formed during the experiment, calculate the vapor pressure of water (in torr) at 20°C.
  5. Ethanol and methanol form a solution that is very nearly ideal. The vapor pressure of ethanol is 44.5 torr and that of methanol is 88.7 torr, at 20°C. (a) Calculate the mole fractions of methanol and ethanol in a solution obtained by mixing 60 g of ethanol with 40 g of methanol. (b) Calculate the partial pressures and the total vapor pressure of this solution, and the mole fraction of ethanol in the vapor.
  6. At 55°C, ethanol has a vapor pressure of 168 torr, and the vapor pressure of methyl cyclohexane is 280 torr. A solution of the two, in which the mole fraction of ethanol is 0.68 has a total vapor pressure of 376 torr. Is this solution formed from its components with the evolution or absorption of heat?
  7. The pressure of CO2 in a 1.0 L bottle of soda is 1.5 atm. On opening the bottle and letting the gas escape, the pressure falls to 1.0 atm. If the temperature is 20°C, what volume of gas at one atmosphere escaped? Henry's law constant KH = 1.26x106 torr.
  8. Assuming seawater to have a salt concentration of 0.52 M and a density of 1.024 g/cm3, determine what pressure in atmospheres is needed in order to cause seawater at 25°C to move through a semipermeable membrane in a reverse osmosis desalination plant. Consider only sodium and chloride ions in this calculation although seawater actually contains other ions such as calcium, magnesium and sulfate. At what temperature will the seawater freeze?
  9. Because of the marked sensitivity of osmotic pressure measurements, which produce relatively large values for very dilute solutions, molar masses for very large molecules such as proteins can be obtained. Now suppose that a typical synthetic nylon or natural protein was soluble to the extent of 0.1 g/L , and that the limit of your ability to measure osmotic pressure is 10-3 torr at 298 K. Estimate the highest molar mass you can measure by this method.
  10. What is the concentration of sap in a 200 foot tree?