Density of the metals

The usual commercial form of the element is powder, but it can be consolidated by pressing and resistance-sintering in a vacuum or hydrogen atmosphere. This process produces a compact shape in excess of 90 percent of the density of the metal. 

This is because the concentrations of solid copper and solid silver are incorporated into the equilibrium constant. The concentration of solid copper is fixed by the density of the metal—it cannot be altered either by the chemist or by the progress of the reaction. The same is true of the concentration of solid silver. Since neither of these concentrations varies, no matter how much solid is added, there is no need to write them each time an equilibrium calculation is made. Equation (21) will suffice. 

A. 13 When a piece of metal of mass 1 12.32 g is dropped into a graduated cylinder containing 23.45 mL of water, the water level rises to 29.27 mL. What is the density of the metal (in grams per cubic centimeter) ... 

The best way to determine the type of unit cell adopted by a metal is x-ray diffraction, which gives a characteristic diffraction pattern for each type of unit cell (see Major Technique 3 following his chapter). However, a simpler procedure that can be used to distinguish between close-packed and other structures is to measure the density of the metal we then calculate the densities of the candidate unit cells and decide which structure accounts for the observed density. Density is an intensive property, which means that it does not depend on the size of the sample (Section A). Therefore, it is the same for a unit cell and a bulk sample. Hexagonal and cubic close packing cannot be distinguished in this way, because they have the same coordination numbers and therefore the same densities (for a given element). 

STRATEGY We calculate the density of the metal by assuming first that its structure is ccp (fee) and then that it is bcc. The structure with the density closer to the experimental value is more likely to be the actual structure. The mass of a unit cell is the sum of the masses of the atoms that it contains. The mass of each atom is equal to the molar mass of the element divided by Avogadro s constant. The volume of a cubic unit cell is the cube of the length of one of its sides. That length is obtained from the radius of the metal atom, the Pythagorean theorem, and the geometry of the cell. 

Increasing atomic mass accounts for both these trends. The volume occupied by an individual atom in the metallic lattice varies slowly within the d block, so the more massive the nucleus, the greater the density of the metal. Toward the end of each row, density decreases for the same reason that melting point decreases. The added electrons occupy antibonding orbitals, and this leads to a looser array of atoms, larger atomic volume, and decreased density. 

Let us describe the solid as having a constant electron density for all energies. Of course, such metals do not exist, but the situation gives us the simplest case. The matrix element Vat has also been assumed to be constant, meaning that A(e) is proportional only to the electron density of the metal. 

Capacitance as a function of charge was calculated.79 The capacitance curves showed a single hump, near qM = 0, and leveled off for qM about 10 /xC/cm2 on either side of the potential of zero charge, due to the dielectric saturation of the dipole system. The limiting values of the capacitance increased with increasing electron density of the metal. The nonideality of the metal was shown to... 

From the surface area S, the mean particle size dvs, is calculated as dvs = 6/Sp where p is the density of the metal. The weight mean diameter dy, = Mid// 23 i nid/ was determined from the degree of X-ray line broadening. 

When the atom comes closer to the metal surface, the electron wave functions of the atom start to feel the charge density of the metal. The result is that the levels 1 and 2 broaden into so-called resonance levels, which have a Lorentzian shape. Strictly speaking, the broadened levels are no longer atomic states, but states of the combined system of atom plus metal, although they retain much of their atomic character. Figure A.9 illustrates the formation of broadened adsorbate... 

Thus, the Drude model predicts that ideal metals are 100 % reflectors for frequencies up to cop and highly transparent for higher frequencies. This result is in rather good agreement with the experimental spectra observed for several metals. In fact, the plasma frequency cop defines the region of transparency of a metal. It is important to realize that, according to Equation (4.20), this frequency only depends on the density of the conduction electrons N, which is equal to the density of the metal atoms multiplied by their valency. This allows us to determine the region of transparency of a metal provided that N is known, as in the next example. 

In closely related experiments it was shown that sp C—H activation takes place reversibly within the coordinahon sphere of the electron-rich Ir(I)-diphosphine complex 58 (Scheme 6.9) to form an alkyl-amino-hydrido derivative 57 reminiscent of the CCM intermediate 24 the solid-state structure of 57 is shown in Figure 6.13 [40]. It appears that C—H activation only takes place after coordination of the amine function to the Ir(I) center (complex 58, NMR characterized). Amine coordination allows to break the chloro bridge of 59 and to augment the electron density of the metal center, thus favoring oxidative addihon of the C—H bond. Most importantly, the microscopic reverse of this C—H activation process (i.e. C—H reductive elimination) models the final step of the CCM cycle (see Scheme 6.1) indeed, the reaction of Scheme 6.10 is cleanly reversible at 373 K. 

Nickel is known to have a face-centered cubic (fee) type of crystal structure. The atomic density of the metal is 9.14 X lO atoms/cm, the atomic weight is 58.73, and the density (p) is 8.91 g/cm. ... 

Gray, heavy, and very hard metal malleable and ductile body-centered cubic lattice structure the density of the metal 16.65 g/cm at 20°C and that of powder 14.40 g/cm melts at 2,996°C vaporizes around 5,458°C electrical resistivity 13.1 microhm-cm at 25°C modulus of elasticity 27x10 psi Poisson s ratio 0.35 magnetic susceptibility 0.849x10 cgs units at 25°C insoluble in water, alcohol and practically all acids soluble in hydrofluoric acid... 

The V=0 stretching frequency is an important characteristic of oxovanadium(IV) complexes, generally observed at 985 50 cm-1.353,355 It is quite sensitive to the nature of the ligands. Donors that increase the electron density of the metal reduce its acceptor properties towards O, the V—O multiple bond character and the stretching frequency. For complexes VOL , v(V=0) falls in the order L = H20 > NCS- > CN- > DMSO F this series bears no obvious relation to the spectrochemical and nephelauxetic series.353... 

A metal object suspended by a very fine wire from the arm of a balance weighs 25.0 g in air, but when it is suspended in water it appears to weigh only 15.0 g (Figure 7-2). Find the density of the metal. 

The weight of a metal sample is measured by finding the increase in weight of a volumetric flask when the metal sample is placed in it. The volume of the metal sample is measured by finding how much less water the volumetric flask holds when it contains the metal sample. Compute the density of the metal sample from the following data, assuming that the density of water is 1.000 g/ml. 

Reduction by hydrogen produces water as reported previously. The increase of CO frequency from 2100 to 2105 cm 1 when water is desorbed at 200°C under vacuum prior to the CO adsorption shows that water is probably coordinately bonded to palladium atoms and slightly increases the electronic density of the metal, as expected for Lewis bases. We observed the same effect on supported platinum (22). 

---