In the Classroom
Sublimation of Iodine at Various Pressures
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Multipurpose Experiments in Inorganic and Physical Chemistry Ilya A. Leenson Department of Chemistry, Moscow State University, Moscow, 119899, Russia;
[email protected] Iodine is a dark purple (almost black) crystalline solid. It is commonly used as a tincture of iodine; its dark-brown color being due to charge-transfer complexes with the solvent molecules (1). Iodine crystals slowly sublime at room temperature, and when heated they turn into deep-purple vapors. These phenomena are described in many textbooks, and the authors of several articles (2–4) presented various modifications of the experiment.1 The aim of this article is to elucidate some interesting phenomena that can be observed in the process of heating solid iodine in closed vessels at various pressures and temperatures. The article and questions therein may be used in classroom discussion with students of general, inorganic, and physical chemistry (molecular– kinetic theory). Liquid Iodine in a Closed Vessel About 1 g of iodine crystals is placed in a sealed glass ampoule and gently heated on a hot plate. A layer of purple gas is formed at the bottom, and the iodine liquefies. If one tilts the tube this liquid flows along the wall as a narrow stream and solidifies very quickly.
Why does solid iodine sublime readily but liquid iodine is not usually visible if crystals are heated in the open air? Iodine melts at 112.9 ⬚C and boils at 183.0 ⬚C; its vapor pressure is 100 mm at 116.5 ⬚C (5). Van der Waals forces that link iodine molecules together in a crystal are relatively weak. That is why iodine usually sublimes very easily (that is, passes directly from the solid to the gaseous state) without going through the liquid state. But being heated very quickly, or in a closed vessel, crystalline iodine melts. Thus, it is necessary to attain the vapor pressure of about 100 mm to see liquid iodine. This is not simple in the open air (crystals may sublime completely before melting) but is easily achieved in a closed vessel. Iodine Crystals in a Closed Vessel It is interesting to observe iodine powder in a sealed tube over a long time period. Tiny crystals on the walls disappear and the larger crystals grow. Slow sublimation of iodine at room temperature produces within several years a single large crystal. In an evacuated tube, the growth of one crystal is faster than at atmospheric pressure. The “thermodynamic” reason of this phenomenon is the tendency to minimize the surface area and thus the surface energy. The moving force of this process is an increased vapor pressure above small crystals compared to larger crystals. Therefore the iodine evaporates from the surface of small crystals and condenses on the surface of large crystals. In the presence of air this process is slower so the growth of one crystal in this circumstance may take many years. www.JCE.DivCHED.org
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Visibility of Iodine Vapor Iodine vapors are usually invisible at room temperature owing to very small pressure. It is interesting to estimate the temperature at which vapors above the solid iodine become visible. Scientists who are involved in photochemistry usually agree that human eye can detect traces of color of a liquid or gas if its absorbance, A, is of the order of magnitude of 0.1 (of course this value depends on the spectral region, the width, and the shape of absorption band). Iodine has a broad absorption band with a maximum in the green spectral region with λmax ≈ 520 nm (1) and it transmits light in the blue and red spectral regions. Suppose a glass tube with iodine crystals has the diameter of l = 1 cm (the absorption path length). The customary form of the Beer–Lambert law is A = εcl where ε is the molar absorption coefficient, c is concentration (mol L᎑1). For iodine vapors in air λmax = 520–530 nm, ε ≈ 700 L mol᎑1 cm᎑1 (6). This value is close to that of the solutions of iodine in noncomplexing (nonsolvating) solvents (ε = 920 L mol᎑1 cm᎑1; ref 1). To convert pressure, p, into concentration (with some approximation) we can use the formula for ideal gases: c = p兾RT, from which c = (0.016 mol L᎑1 mm ᎑1K ) p兾T. Dependence of p on T can be found in several reference books (see, for example, refs 7, 8 ). The first presents vapor pressures (in 10⬚ intervals) from ᎑50 to 160 ⬚C. The second gives formula log p = ᎑3578兾T − 2.51logT + 17.715. Both give similar results. At 20 ⬚C when p = 0.20 mm (7, 8) c = (0.016 × 0.20)兾293 ≈ 1.1 × 10᎑5 mol L᎑1, A = εcl = (700)(1.1 × 10᎑5) = 0.0077, and iodine vapors are invisible. This fact means that in all photos in the textbooks where violet vapors are shown visible above solid iodine (see, for example, ref 9) the bottom of the flask is inevitably heated even if the hot plate is not seen! At 50 ⬚C when p = 2.19 mm (7, 8) c = (0.016 × 2.19)兾323 = 1.1 × 10᎑4 mol L᎑1, A = (700)(1.1. × 10᎑4) = 0.077. Thus iodine vapors could be seen at temperatures just above 50 ⬚C. Experiments confirm this rough estimation. Iodine crystals in a sealed ampoule (o.d. 2 cm) heated to 40 ⬚C produce a barely noticeable pale purple color in the gas phase, which is in perfect agreement with the “theoretical” calculations because at 40 ⬚C, p = 1.03 mm. Heat of Sublimation of Iodine From the dependence of the vapor pressure of solid iodine on absolute temperature it is easy to deduce the heat (enthalpy) of sublimation (∆H ) using Clausius–Clapeyron equation (9, 10): lnp = constant – ∆H兾RT. Literature data (7, 8) in coordinates [lnp, 1兾T (from 20 to 120 ⬚C)] give a straight line. The value of ∆H from its slope (60.6 kJ mol᎑1) is in excellent agreement with the heat of iodine sublimation at the melting point, 14.48 kcal mol᎑1 or 60.57 kJ mol᎑1 (11).
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Lack of Visible Color when Heating Iodine If solid iodine is heated in an evacuated ampoule (pressure less than ∼10᎑3 mm) no noticeable color usually appears, and immediate condensation of tiny iodine crystals is visible higher up on the cold walls of the tube. The reason is simple: iodine molecules do not diffuse as they do in air—colliding with oxygen and nitrogen molecules. Instead they fly quickly along straight lines until they bump against the cold wall and condense there. The velocities of iodine molecules are extremely high. The root-mean-square velocity of a gas molecule, u, is (3RT兾M)1/2, where R is the gas constant (8.31 J mol᎑1 K᎑1), M is the molar mass (kg mol᎑1), and T is the absolute temperature (9, p 174). It is plausible to rewrite this equation as follows. If M is presented in g mol᎑1, then u = 158(T兾M)1/2. Students can use this equation to calculate how fast molecules of various substances move on average at room temperature (T = 293 K). For the lightest molecules, (H2, M = 2 g mol᎑1) u = 1912 m s᎑1. For the heaviest molecules, (UF6, M = 352 g mol᎑1) u = 144 m s᎑1; uranium hexafluoride is a volatile solid, its vapor pressure is 100 mm at 23 ⬚C (5). For iodine molecules, (M = 254 g mol᎑1) u = 170 m s᎑1 at 20 ⬚C and 175 m s᎑1 at 50 ⬚C. So it takes approximately only (0.1 m)兾(170 m s᎑1) = 0.6 ms for these molecules to pass 10 cm (0.1 m) from a crystal to the most remote wall of the ampoule. But if the rate of sublimation is high enough the color might appear in the evacuated tube (molecular beam of iodine molecules). This rate can be roughly calculated as follows. Suppose, as previously one could see the color of iodine when its pressure in the tube is 2 mm and concentration is 10᎑4 mol L᎑1. Let the cross section of an ampoule be 1 cm2, its length 10 cm, and its volume 0.01 L. The color of iodine vapor will be barely seen when c = 10᎑4 mol L᎑1 that is, 10᎑6 moles or 6 × 1017 molecules in an ampoule. At root-meansquare velocity of 170 m s᎑1 all of the iodine molecules disappear from this volume in approximately 6 × 10 ᎑4 s. Therefore to sustain constant concentration in this volume the rate of evaporation from the bottom should be (6 × 1017 molecules)兾(6 × 10᎑4 s) = 1021 molecules per second. (At such a rate one gram of iodine evaporates fully in only two seconds!) The rate of evaporation from solid substance into vacuum is related to its equilibrium vapor pressure as p = m(2πRT兾M)1/2兾St = G(2πRT兾M)1/2, where m is the mass evaporated, S is the surface of evaporation, t is the evaporation time, M is the molar mass, and G is the evaporation rate per unit surface (12). To express p in mm Hg, G in (g s᎑1 cm᎑2), and M in (g mol᎑1) we should use the following conversion factors: 1 mm = 133.3 Pa, 1 g = 10᎑3 kg, and 1 cm2 = 10᎑4 m2. Thus, p (mm) = G(10᎑3兾10᎑4)(2 × 3.14 × 8.31 × T兾10᎑3M )1/2兾133.3 = 17.14G(T兾M )1/2 (12). Alternatively, this can be written as p (mm) = 17.14G(T兾M )1兾2 and this can be rearranged to G = p(M兾T )1兾2兾17.14. Now it is possible to calculate n, the number of molecules that evaporate from 1 cm2 surface in 1 s: n = (G兾M )(6.02 × 1023) = p(M兾T ) 1兾2 (6.02 × 10 23 )兾(17.14M ) = (3.51 × 10 22 ) p(MT )᎑1兾2. With n = 1021 molecules s᎑1 cm᎑2 one can calculate that such an evaporation rate is achieved at approximately 80 ⬚C. It should be noted that equilibrium vapor pressure of iodine at this temperature equals 15 mm provided the whole 242
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ampoule is heated to this temperature. In a real experiment as previously described, only solid iodine and the nearest glass have this temperature. Thus, iodine vaporizes as a molecular beam directed to the cold walls. Thus, we have a much lower iodine concentration in the ampoule that corresponds to only 2 mm pressure (if the molecular beam would instantly stop). It is necessary also to point out that 80 ⬚C should be the temperature of the crystal itself (more precisely, its lower thin layer) and not only of the adjacent tube walls. The Knocking Phenomenon A very interesting phenomenon in the evacuated tube when its bottom is heated intensively, is quick jumping and “knocking” of iodine crystal on the bottom loudly enough to be heard at the distance of several meters. Iodine crystals evaporate only from their lower surface where they are in contact with the hot wall of the tube. Thus a jet power emerges, and this power can be evaluated. Let the mass of an iodine crystal be 1 g. The force needed to lift it is F = mg = (10᎑3 kg)(9.8 m s᎑1) ≈ 0.01 N. According to Newton’s second law mu = Ft or F = mu兾t where m兾t is the evaporation rate of a substance. Now we use again the formula G = p(M兾T )1兾2兾17.14 and calculate the “jet force” F that emerges at different temperatures. At 80 ⬚C (353 K) p = 15.1 mm (7), and G = (15.1兾17.14)(254兾353)1/2 ≈ 0.75 g s᎑1 = 7.5 × 10᎑4 kg s᎑1 (at evaporation area 1 cm2). At this temperature u = [(3)(8.31) (353)兾0.254]1兾2 = 186 m s᎑1 and F = (7.5 × 10᎑4 )(186) ≈ 0.14 N. If the evaporation area, S, of the lower part of the iodine lump is only 0.1 cm2, then F = 0.014 N, and this is just enough to lift the crystal a little; but in the same moment the lower part of the crystal loses contact with the hot glass, evaporation ceases quickly, the “rocket” falls down, and the process repeats all over again. (The density of iodine is about 5 g cm᎑1 so our crystal with m = 1 g has a volume 0.2 cm3 = 200 mm3, and if it has a shape of a square plate of 2 mm thickness its lower area would be 100 mm2 = 1 cm2, but the surface of the crystal contacting with the hot wall is inevitably less.) When temperature rises iodine vapor pressure p, evaporation rate G, and force F all increase rapidly. Thus, at 90 ⬚C p = 26.8 mm, G = 1.31 g s᎑1 cm᎑2, u = 189 m s᎑1, and F = 0.025 N (S = 0.1 cm2). At 100 ⬚C p = 45.5 mm, G = 2.19 g s᎑1 cm᎑2, u = 191 m s᎑1, and F = 0.042 N and so forth. This jumping of an iodine crystal is very similar to that observable in the degassing process of an organic liquid (for example, carbon tetrachloride) in a small round-bottomed bulb by freeze-pump-thaw cycle: during the first thawing, the frozen liquid may “jump” in the bulb vigorously. (Such degassing is necessary, for example, to free the solvent of oxygen for the ESR measurements.) But in this case, the jumping occurs for a different reason: it is the quick evolution of the dissolved air from the lower part of the organic “ice”. Collisions and Diffusion of Iodine The most challenging (and interesting) problem is the detailed behavior of iodine molecules: their collisions and diffusion. If the ampoule at the atmospheric pressure (or partly evacuated with a water aspirator to, for instance, 100
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mm) is placed in a thermostatted beaker with warm water, iodine vapors would diffuse into air from the bottom. The higher the temperature and the lower the pressure in the ampoule, the higher is the diffusion rate. Knowing the time t at which the upper boundary of vapors moves for the distance s, one could calculate such important quantities as mean free path of iodine molecules and their collision frequencies.2
Mean Free Path The kinetic–molecular theory is based on the postulate that molecules of a gas are in constant motion and collide with one another. After each collision, the direction in which a molecule moves changes randomly. Thus a molecule accomplishes the so-called random walk, a random process consisting of a sequence of discrete steps of a length λ. This value is called the mean free path. The random thermal perturbations of tiny particles in a liquid are responsible for the random walk phenomenon known as Brownian motion, and collisions of molecules in a gas are the random walk responsible for diffusion. The mean free path is the average distance a molecule travels between collisions with other particles. This value differs significantly from the mean distance between molecules. For instance, at an altitude of 1300 km the mean free path is about 3200 km while the average distance between particles (mainly N and O neutral and charged atoms) is only 0.076 mm (14). This parameter is of importance in temperature measurements at high altitudes. One can find some interesting figures concerning mean free path between collisions in the high atmosphere in Miller’s article (14). Thus, the mean free path λ equals only 0.086 µm at sea level (0 km, p = 760 mm), 2.1 µm (10 km, p = 210 mm), 0.078 mm (50 km, p = 0.76 mm), 0.93 mm (70 km, p = 0.055 mm), 2.1 cm (90 km, p = 2 × 10᎑3 mm), and 9.5 cm (100 km, p = 6 × 10᎑4 mm). These values for λ could be compared with those for vacuum attained by laboratory vacuum pumps and with dimension of the flasks used by chemists in experiments. For instance it is possible to obtain p = 2 × 10᎑3 mm using conventional vacuum-line technique and rotary oil-sealed forevacuum pump (supplied with a liquid nitrogen trap; this is necessary also to protect the pump from corrosive vapors). At this pressure, λ = 2 cm is sufficient to make it possible for molecules to reach the walls almost in a free flight without collisions. With a diffusion pump it is easy to obtain p = 6 × 10᎑4 mm when λ = 9.5 cm. Random Walk One can find an excellent description of random walk and diffusion in Feynman’s course (15). This can be adapted as follows. Let s be the displacement of a molecule moving with velocity u and experiencing N collisions in time t; its mean free path is λ and its root-mean-square velocity is u. It is obvious that the full path the molecule travels is L = ut = λN. On the other hand, a real displacement of the molecule from the initial position is s = λ(N )1兾2 (Feynman presents a very simple proof of this equation). Exclusion of N from the last two equations gives s2 = uλt, or λ = s2兾ut. The collision frequency is Z = N兾t = u兾λ = u2t兾s2. The larger number of collisions, N, the greater is the difference between the full path L and the real displacement s owing to diffusion. For instance, when u = 1 m s᎑1, λ = 1 www.JCE.DivCHED.org
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m, and N = 100, L = 100 m and s = 10 m; when N = 106, L = 106 m = 1000 km and s = 103 m = 1 km. For any molecule in a gas at ordinary pressure N is extremely large (Z is of the order of 109 s᎑1).
Diffusion Coefficient The value uλ is the measure of the diffusion coefficient D, the proportionality factor in Fick’s law (ref 12, Chapter 13.12). More precisely, D = 1兾3(uλ) (12). It is a physical constant dependent on molecular size and other properties of the diffusing substance as well as on temperature and pressure (16).3, 4 The following data were obtained in one experiment with iodine sublimation in an ampoule (o.d. 2 cm) at atmospheric pressure: T = 59 ⬚C = 332 K, s ≈ 6 cm, t = 2 min = 120 s. At this temperature, u = 180.5 m s᎑1, λ = s2兾(ut) = 1.7 × 10᎑7 m = 0.17 µm, Z = u兾λ = 1.1 × 109 s᎑1, D = uλ兾3 = 10᎑5 m2 s᎑1 = 0.1 cm2 s᎑1. It is noteworthy that in this experiment L = ut ≈ 22 km(!) as compared with only 6 cm for s. Of course, a lower pressure will enhance the λ value as mentioned above. It is interesting to compare these data with the known data for different gases. Thus, for Ar and Xe at 0 ⬚C and p = 1 atm, λ = 6 × 10᎑8 m; Z = 9 × 109 (NH3), 4 × 109 (Ar), 6.1 × 109 (CO2) and so on (5). The diffusion coefficient obtained is also of the same order as that found, for example, for diffusing oxygen in air (0.18 cm2 s᎑1) and for carbon oxide diffusing in hydrogen (0.64 cm2 s᎑1, both at 0 ⬚C and 1 atm) (12). A tentative value for the diffusion coefficient for bromine vapors diffusing in air at 28 ⬚C and atmospheric pressure has been found to be 0.105 cm2 s᎑1 (17). It is interesting also to compare D for gas molecules with molecular diffusion coefficients in a liquid; for example, D = 4.8 × 10᎑8 cm2 s᎑1 for hydrated cobalt ions in 1% agar solution (18).5, 6 The 1926 Nobel Prize in physics was awarded to Jean Baptist Perrin. By measuring the square of the tiny rubber latex particles displacement, s2, relative to the origin as a function of time, t, he was able to calculate the diffusion coefficient using D (20). From the Stokes–Einstein equation, D = (RT兾NA)兾3πµd (µ is the viscosity of fluid, d is the diameter of a particle), Perrin could calculate the Avogadro number NA. With the particle diameter of 0.1 µm, λ ∼ 5 × 10᎑4 µm, and t (time between collisions) ∼ 3 × 10᎑9 s in water at 20 ⬚C, NA is calculated to be 6.8 × 1023. This is another way to obtain this important value (21). The modern version of Perrin’s experiment that made it possible to project and observe on a television monitor the motions of latex microspheres and to plot at regular time intervals their position was proposed by H. Kruglak (22).7 Mean Free Path in Real Life As an interesting aside lets examine the mean free path in real life. Many stories tell about travelers who, without any landmarks to help them, lost their way in a small forest or froze to death in a field in a severe blizzard “only half a mile from the road (village etc.)”. The real reason is that a person cannot move in a straight line without landmarks (such as the sun, moon, stars, noise of a train or a highway, etc.). In such circumstances, his route resembles the molecular random walk with permanently changing directions of the movement and multiple crossings of his own trajectory.
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B. Gorobetz designed an interesting experiments using his students (23); Gorobetz placed a student in the middle of a stadium with his eyes blindfolded and asked him or her (in total silence) to move in a straight direction. These experiments revealed that a person can move in a straight line on average for 20 meters only. This number may be taken as the mean free path. As s2 = Lλ, then with u = 2 km h᎑1 (it is rather fast in the forest or in a blizzard!) s is only 0.4 km while L = ut = 8 km! This result, as Gorobetz asserts, shows that a traveler has no chance to reach a goal even after many hours of roaming with such a velocity. So it is wise in such circumstances, adds Gorobetz, to stay put, make a shelter, and wait for help or improvement of weather (the sun may break through the clouds). Dissociation of Iodine The bond strength of I2 molecules is rather weak: only 151 kJ mol᎑1 compared to 436 kJ mol᎑1 for H2 molecules (24). Therefore even at the boiling point dissociation of iodine should be noticeable. It would be interesting to calculate approximately the number of iodine atoms that are in equilibrium with molecular iodine in 1 L of vapor. At its boiling point (183 ⬚C = 456 K) the pressure of iodine is 1 atm. The equilibrium constant for dissociation is K = p(I)2兾p(I2), and p(I) = [Kp(I2)]1兾2 ≈ (K)1兾2 because p(I2) >> p(I). For the reaction I2 → 2I, ∆H ⬚ = 151 kJ mol᎑1, ∆S ⬚ = 100.8 J mol᎑1 K᎑1 (25), and K = exp(᎑∆G兾RT) = exp(∆S兾R − ∆H兾RT) = exp[(100.8兾8.314) − 151000兾(8.314)(456)] = 9.25 × 10᎑13 ≈ 10᎑12. Thus p(I) = (10᎑12)1兾2 = 10᎑6 atm. From the ideal gas equation pV = nRT (here p = 10᎑6 atm, V = 1 L, R = 0.082 L atm mol᎑1 K᎑1) we have n ≈ 2.7 × 10᎑8 mol, that is about 1.6 × 1016 iodine atoms per liter! Of course, this calculation is rather rough because we used standard thermodynamic quantities at 298 K and did not take into account their dependence on temperature. The strict calculation based on translational and vibrational partition functions and electronic factors for atomic and molecular iodine can be found in Glasstone’s textbook (25). Safety Considerations Heating iodine in an evacuated tube far enough from the sealing place is absolutely safe. And what about the tube with air and initial pressure equal to 1 atm? Heating this tube gently up to the melting point of iodine increases the pressure of the iodine vapor to ≈ 100 mm and the pressure of the hot air up to 1.3 atm. The bursting pressures of glass tubes are presented in Shriver’s manual (26). The calculated bursting pressure for the standard wall glass tubing is 7.1 atm (o.d. 10 mm, i.d. 9 mm), 5.6 atm (o.d. 15 mm, i.d. 13.8 mm), and 4.3 atm (o.d. 20 mm, i.d. 18.8 mm). Shriver writes that “some workers routinely use standard wall 10 mm tubing at 10 atm pressure, and the author has been told of instances in which 20 mm tubing was used at this pressure without mishap”. So any experiment with the tube at 1.3 atm pressure should be regarded as safe. Nevertheless, it is reasonable to wear goggles during this experiment. It is reasonable also to make both ends of the ampoule smooth (the ends should be hemispherical and the wall thickness uniform) and evacuate and seal the ampoule through a narrow glass tube (T-seal). This prevents possible cracking while heating both 244
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ends. While blowing the end of an ampoule, iodine crystals at the other end should be cold, and while pumping the ampoule to high vacuum, a cold trap should be in the vacuum line so as to prevent the corrosive iodine vapors from getting into the pump oil. W
Supplemental Material
Photos and movies showing some of the phenomena discussed in the article are available in this issue of JCE Online. Notes 1. When this article had been completed R. W. Ramette published a paper “Colorful Iodine” with marvelous photos (27). He made an “iodine thermometer” in his yard (12 L sealed flask with some iodine) giving a visual indication of the temperature with increasing sublimation pressure. This flask can be also seen on the Journal cover. 2. A very interesting and simple experiment with the counterdiffusion of NH3 and HCl vapors in a long tube at atmospheric pressure as well as Liesegang rings in this system were described by Campbell (ref 2, experiment 46) and by Hawkes (13). 3. The instructor can also discuss the following items: why the root-mean-square velocity of gas molecules is so close to the sound speed in this gas; the collision frequency and the mean free path as a function of molecular diameters of colliding molecules (in accordance with the kinetic theory of gases, the larger this value, the greater the probability that two molecules will collide, and λ is inversely proportional to the mean cross-sectional area of the molecules); the dependence of heat transfer on the λ value; the necessity of the Dewar vessels evacuation to ensure that heat transfer is low enough and so on. 4. In a more strict consideration, one should take into account the mutual diffusion of iodine and air molecules; see, for example, ref 13 and references therein. 5. For the more precise measurements of s and the subsequent calculations of s and Z it is recommended to use a narrow glass tube with a little iodine crystal in the bottom. A narrow tube will prevent iodine vapors from convective movements. This is important in view of “misconceptions” in many experiments with “diffusion”, which are really a convective mixing of gases (19). 6. C. S. Hoyt (3) described “a tube, evacuated to increase the mean free path, [which] contains bits of blue glass resting on a pool of mercury. When the mercury is heated, bringing about vaporization of the liquid, the impact of the large molecules of mercury is sufficient to drive the glass vigorously in chaotic fashion about the interior of the tube. An even better demonstration is provided by a similar tube which uses a pithball to show the molecular collisions. With a suitable rate of heating, the pithball may be supported in space for any period of time”. This experiment with mercury resembles a “rocket” described in this article but it is by far more dangerous. 7. Many years ago witty physicists called the random walk “the drunkard’s walk”. They mean a sailor who leaves a pub late in the evening and moves along the street. The distance between the street-lamps is constant (λ). The man reaches the nearest pole, has a rest and goes further in any direction because he does not remember the direction he has come from. After λ steps he goes s = λ(N )1兾2 meters instead of L = λN meters he would have gone if he had moved in one direction only.
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Literature Cited 1. Andrews, L. J.; Keefer, R. M. Molecular Complexes in Organic Chemistry; Holden-Day: San Francisco, 1964; Chapter 2.1. 2. Campbell, J. A. J. Chem. Educ. 1970, 47, 273–277; experiment 4a. 3. Hoyt, C. S. J. Chem. Educ. 1947, 24, 186–189. 4. Goldsmith, R. H. J. Chem. Educ. 1995, 72, 1132. 5. Handbook of Chemistry and Physics, 73rd ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1992. 6. Calvert, J. G.; Pitts, J. N. Photochemistry; Wiley: New York, 1966; Chapter 3. 7. Lange’s Handbook of Chemistry; 4th ed.; Handbook Publ.: Sandusky, OH, 1944; p 1428. 8. Baron, I.; Knacke, O. Thermochemical Properties of Inorganic Substances; Springer: Berlin, 1973; p 355. 9. Atkins, P. W. General Chemistry; Scientific American Books: New York, 1989; p 152. 10. Levinson, G. S. J. Chem. Educ. 1982, 59, 337–338. 11. Comprehensive Inorganic Chemistry; Pergamon Press: New York, 1975; Vol. 2. 12. Dushman, S. Scientific Foundation of Vacuum Technique, 2nd ed.; revised by Lafferty, J. M.; Wiley: New York, 1962; Chap-
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ter 1, Sections 6, 10, 14, 15. 13. Hawkes, S. J. J. Chem. Educ. 1997, 74, 1069. 14. Miller, L. E. J. Chem. Educ. 1954, 31, 112–124. 15. Feynman, R. P.; Leighton, R. B. The Feynman Lectures on Physics; Addison–Wesley: Reading, MA, 1963; Vol. 1, Chapters 6.3, 43. 16. International Encyclopedia of Heat and Mass Transfer; CRC Press: Boca Raton, FL, 1966; p 304. 17. Brockett, C. P. J. Chem. Educ. 1966, 43, 207–210. 18. Fate, G.; Lynn, D. G. J. Chem. Educ. 1990, 67, 536–538. 19. Davis, L. C. J. Chem. Educ. 1996, 73, 824–825. 20. Cohen, R. D. J. Chem. Educ. 1986, 63, 933–934. 21. Leenson, I. A. J. Chem. Educ. 1998, 75, 998–1003. 22. Kruglak, H. J. Chem. Educ. 1988, 65, 732–734. 23. Gorobetz, B. Nauka i Zhizn’ (Science and Life, in Russian) 1997, 12, 70–73. 24. Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1968; Table V.8. 25. Glasstone, S. Thermodynamics for Chemists; Van Nostrand: New York, 1947; p 311. 26. Shriver, D. F. The Manipulation of Air-Sensitive Compounds; McGraw-Hill: New York, 1969; p 215. 27. Ramette, R. W. J. Chem. Educ. 2003, 80, 878.
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