Neon, atomic volume

The atomic volumes of the alkali metals increase with atomic number, as do those of the inert gases. Notice, however, that the volume occupied by an alkali atom is somewhat larger than that of the adjacent inert gas (with the exception of the lithium and helium—helium is the cause of this anomaly). The sodium atom in sodium metal occupies 30% more volume than does neon. Cesium occupies close to twice the volume of xenon. 

Calculate the ratio of the number of electrons in a neutral xenon atom to the number in a neutral neon atom. Compare this number to the ratio of the atomic volumes of these two elements. On the basis of these two ratios, discuss the effects of electron-electron repulsions and electron-nuclear attractions on atomic size. 

Note Some samples of gases may have equal values for these attributes. Assume the larger containers have a volume twice the volume of the smaller containers and assume the mass of an argon atom is twice the mass of a neon atom. 

Let s start with one neon atom and think through what happens as we add more atoms and open the stopcock (Figure 20.2). One atom has some number of microstates (W) possible for it in the left flask and the same number possible in the right flask. Opening the stopcock increases the volume, which increases the number of possible particle locations and, thus, translational energy levels. As a result, the system has 2, or 2, times as many microstates possible when the atom moves through both flasks (final state, Wfinai) as when it is confined to one flask (initial state, Wi Hiai). 

Figure 3.10 describes an idealized scenario of two possible states and where an elementary measurement is preceded by uncertainty. An experiment, by definition, aims at reducing uncertainty. Given the idealized probability density function (lower panel) allied with the pressure, a single measurement by the chemist avails 1.00 bit of Shannon-type information. The measurement addresses the question Is the neon atom in the left-side compartment The information is less if the compartments differ in any respect volume, wall stickiness, and so forth. 

The following figure shows three 1.00-L bulbs connected by valves. Each bulb contains neon gas with amounts proportional to foe number of atoms pictorially represented in each chamber All three bulbs are maintained at foe same temperature. Unless stated otherwise, assume that foe valves connecting chambers are closed and seal foe gases in their respective chambers. Assume also that foe volume between chambers is negligible. 

The German physicist Lothar Meyer observed a periodicity in the physical properties of the elements at about the same time as Mendeleev was working on their chemical properties. Some of Meyer s observations can be reproduced by examining the molar volume for the solid element as a function of atomic number. Calculate the molar volumes for the elements in Periods 2 and 3 from the densities of the elements found in Appendix 2D and the following solid densities (g-cuU ) nitrogen, 0.88 fluorine, 1.11 neon, 1.21. Plot your results as a function of atomic number and describe any variations that you observe. 

A volume of 2.5 cm3 mol-1 is clearly much smaller than the value we calculated earlier in Worked Example 1.3 with the ideal-gas equation, Equation (1.13). It is also smaller than the volume of solid neon made in a cryostat, suggesting the atoms in a solid are also separated by much empty space, albeit not so widely separated as in a gas. 

In Table XXIII-2, we can interpolate between the monovalent positive and negative ions to get radii for the inert gas atoms. Thus we find approximately the following No 1.1 A, A 1.5 A, Kr 1.7 A, Xe 1.95 A. It is interesting to compute the volumes of the inert gas atoms which we should get in this way, and compare with the volumes which we find for them from the constant b of Van der Waals equation. For neon, for instance, the volume from Table XXIII-2 would be... 

The helium, argon, neon, and hydrogen were supplied by the Air Reduction Co. The methane was supplied by Phillips Petroleum Co. The deuterium was prepared from heavy water provided by Atomic Energy of Canada. The heavy water was reacted with an excess of the liquid alloy of Na and K, by breaking an ampoule of the alloy in the presence of 5 grams of heavy water contained in a closed system of 3-liter volume. 

Thirds I want you to take a look at the units of the quantities shown in the control har. The pressure is measured in the unit atm. This is not a reference to quick cash hut rather an ahhreviation for atmospheres. One atmosphere is a pressure roughly equal to the air pressure at sea level. Volume is measured in liters a unit with which you should he familiar. The third and fourth control bars indicate the number of atoms of helium and neon that are present. The unit is mol which stands for the word mole. For now just think of this number as an indicator—not an exact count—of the number of atoms in either the simulation or the real gas the simulation represents. For example the default value of the number of moles of helium is 1.0. Clearly, there s more than one atom of helium in the simulation. Later on, you 11 find out how many atoms of a real gas this 1.0 represents (a lot ). The temperature is measured in degrees Kelvin, or K. Water freezes at 273.16 degrees Kelvin, which is 0 degrees Celsius or about 32 degrees Fahrenheit. 

To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected. Given the atomic radius of neon, 0.69 A, and knowing that a sphere has a volume of 4Trr /3, calculate the fraction of space that Ne atoms occupy in a sample of neon at STP. 

Apply your knowledge of the kinetic theory of gases to the following situations, (a) Two flasks of volumes V] and V2 (V2 > 1) contain the same number of helium atoms at the same temperature, (i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks, (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers, (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures Ti and T2 T2 > T ). (i) Compare the rms speeds of the atoms in the two flasks, (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers, (c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is 74°C. Comment on the validity of... 

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