Mass, 9-10 determine from density

The degree of crystallinity can be determined from density measurements and knowledge of the density of a 100% amorphous polymer, p, and 100% crystalline polymer, p,. If constant mass is assumed, p, and p are linked to the density of the specimen by the relationship ... 

Crystallinity can also be determined from density data and calorimetric measurements. Accurate measurements of the density (with a precision of about 0.2 kg m ) are carried out in a density gradient column and the mass crystallinity can be obtained from the equation ... 

Fig. 10. Determination from plot of mass density function.

One characterizes a fractal cluster by its fractal dimension Df which can be determined from the integration of the radius-dependent mass density p r) from the center up to a large radius R as follows ... 

Heavy isotopes endow the compounds in which they appear with slightly greater masses than their unlabeled counterparts. These compounds can be separated and quantitated by mass spectrometry (or density gradient centrifugation, if they are macromolecules). For example, O was used in separate experiments as a tracer of the fate of the oxygen atoms in water and carbon dioxide to determine whether the atmospheric oxygen produced in photosynthesis arose from HgO, COg, or both ... 

The molecular weight (mean relative molecular mass) was obtained by determination of density but, in order to determine that the gas was monatomic and its atomic and molecular weights identical, it was necessary to measure the velocity of sound in the gas and to derive from this the ratio of its specific heats kinetic theory predicts that Cp/C = 1.67 for a monatomic and 1.40 for a diatomic gas. 

The independent variables in these equations are the dimensionless spatial coordinates, x and r. The dependent variables are the dimensionless velocity components (u the axial velocity, v the radial velocity, and w circumferential velocity), temperature , and pressure pm- The viscosity and thermal conductivity are given by p and A, and the mass density by p. Density is determined from the temperature and pressure via an ideal-gas equation of state. The dimen-... 

As ealeulations show, when the density inereases with a distance from the earth s surface the parameter I is smaller than 0.4. On the contrary, with a decrease of the density toward the earth s center we have 7 >0.4. Inasmuch as in reality 7 <0.4, we conclude that there is essential concentration of mass in the central part of the earth. In other words, the density increases with depth and this happens mainly due to compression caused by layers situated above, as well as a concentration of heavy components. In conclusion, it may be appropriate to notice the following a. In the last three sections, we demonstrated that the normal gravitational field of the earth is caused by masses of the ellipsoid of rotation and its flattening can be determined from measurements of the gravitational field. 

The principal experimental method used to measure the density of a solid is determination of the mass of liquid displaced by a known mass of solid. It is essential that the solid have no appreciable solubility in the liquid, that all occluded air be removed from the solid and that the density of the displacement fluid be less than that of the solid lest the solid float. Densities of crystalline solids also can be determined from the dimensions of the unit cell. Davis and Koch discuss other methods for measuring the density of liquids and solids such as hydrostatic weighing of a buoy and flotation methods. 

The constants characterizing the electrode reaction can be found from this type of polarization curve in the following manner. The quantity k"e is determined directly from the half-wave potential value (Eq. 5.4.27) if E0r is known and the mass transfer coefficient kQx is determined from the limiting current density (Eq. 5.4.20). The charge transfer coefficient oc is determined from the slope of the dependence of In [(yd —/)//] on E. 

Example 5-6 Friction Loss in a Sudden Expansion. Figure 5-7 shows the flow in a sudden expansion from a small conduit to a larger one. We assume that the conditions upstream of the expansion (point 1) are known, as well as the areas A and A2. We desire to find the velocity and pressure downstream of the expansion (V2 and P2) and the loss coefficient, Kt. As before, V2 is determined from the mass balance (continuity equation) applied to the system (the fluid in the shaded area). Assuming constant density,... 

Using the numbers quoted above and the derived mass of the Earth gives pc = 5.52 gem-3, which, by comparison with the density of other materials measured in the laboratory, means that the Earth must be made of rock, and heavy rock at that. The mass of the other planets can be determined from their orbital periods and their radii can be measured, for example, from rates of transit in front of the Sun, and so the density of the other planets within the solar system can then be determined (Table 7.1). 

We can estimate densities of solids from the information in Figure 10-1. Radium has Z = 88 and an approximate atomic volume of 40 cm3 /mol. Then we use the molar mass of radium to determine its density ... 

To determine the density of a liquid, the mass in grams of a measured volume of liquid in milliliters is determined. The density is calculated from these measurements. The volume may be measured by a variety of devices, such as a graduated cylinder, pipet, or buret. Very precise determinations of volume are measured with pycnometers. These devices hold a specified volume. A cap or stopper with a capillary overflow tube ensures repeatability in the measurement. See Figure 15.15. 

Computer-controlled motorized syringe-type precision burettes are generally employed nowadays for addition of titrant. The burettes are calibrated by weighing the amounts of distilled water they deliver over various time intervals. The delivery rate in units of volume per unit time is determined from the mass rate delivery using the density of water at the calibration temperature. 

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