Mass equivalents, conversion factors

The factor gc is the conversion factor that relates equivalent force and mass (ML/t2) units in engineering systems. In these systems both force and mass... 

Solution This is a steady-flow process for which Eq. (2.10h) applies. The initial and final velocities of water in the storage tanks are negligible, and the term bu2/2gc may be omitted. The remaining terms are expressed in units of (Btu)(lbnl) 1 through use of appropriate conversion factors. At 200(°F) the density of water is 60.1 (lbm)(ft)-3, and l(ft)3 is equivalent to 7.48(gal) thus the mass flow rate is... 

This set of equations connects Planck s photon energy Ep with Einstein s mass/en-ergy equivalence, with Boltzmann s kinetic energy, with the kinetic energy of a particle and with the kinetic energy of an electron in an electric field of a voltage U of 1 V. The most important conversion factors used in photochemistry and photophysics are collected in Tab. 3-2. 

U and V respectively. Systeme International (SI) units, described in Appendix B, are used extensively but not slavishly. Chemically convenient quantities such as the gram (g), cubic centimeter (cm ), and hter (L = dm =10 cm ) are still used where useful—densities in g cm , concentrations in mol L , molar masses in g. Conversions of such quantities into their SI equivalents is trivially easy. The situation with pressure is not so simple, since the SI pascal is a very awkward unit. Throughout the text, both bar and atmosphere are used. Generally bar = 10 Pa) is used when a precisely measured pressure is involved, and atmosphere = 760 Torr = 1.01325 X 10 Pa) is used to describe casually the ambient air pressure, which is usually closer to 1 atm than to 1 bar. Standard states for all chemical substances are officially defined at a pressure of 1 bar normal boiling points for liquids are still understood to refer to 1-atm values. The conversion factors given inside the front cover will help in coping with non-SI pressures. 

If the molecular weight of a substance is M, then there are M kg/kmol, M g/mol, and M Ibm/lb-mole of this substance. The molecular weight may thus be used as a conversion factor that relates the mass and the number of moles of a quantity of the substance. For example. 34 kg of ammonia (NH3 M = 17) is equivalent to... 

Now, suppose that while working in chemistry lab, you need 3.00 moles of manganese (Mn) for a chemical reaction. How can you measure that amount Like the 5 dozen jellybeans, the number of moles of manganese can be converted to an equivalent mass and measured on a balance. To calculate mass from the number of moles, you need to multiply the number of moles of manganese required in the reaction (3.00 moles of Mn) by a conversion factor that relates mass and moles of manganese. That conversion factor is the molar mass of manganese (54.9 g/mol). 

The conversion factor between atomic mass units and grams is numerically equal to the inverse of Avogadro s number Na, and the mass of a single atom in atomic mass units is numerically equal to the mass of one mole of atoms in grams. Thus, one atom of has a mass of 1.007825 u because 1 mol of has a mass of 1.007825 g. The dalton is a mass unit that is equivalent to the atomic mass unit and is used frequently in biochemistry. 

Conversion factors can also be linked together to make a series of unit changes. Converting 25 kg to the equivalent mass in centigrams can be done using two conversion factors. 

The molar mass, which expresses the equivalent relationship between 1 mole of a substance and its mass in grams, can be used as a conversion factor. We multiply by the molar mass of an element or compound (Jt, in g/mol) to convert a given amount (in moles) to mass (in grams) ... 

The average mass of nitrogen is 14.01 amu. The appropriate equivalence statement is 1 N atom = 14.01 amu, which yields the conversion factor we need ... 

Einstein theory for mass-energy equivalence n. The equivalence of a quantity of mass m and a quantity of energy E by the formula E = mc. The conversion factor is the square of the velocity of light. Serway RA, Faugh JS, Bennett CV (2005) College physics. Thomas, New York. 

A good laboratory balance can measure mass routinely to within 10 kg, and use of a microbalance with considerable precautions can lead to mass measurements to within 10 kg or so (Section 2.3). This is stiU three orders of magnitude larger than the mass changes equivalent to heats of reaction, so the physicists argument is valid from this point of view. (Note that the above calculation of Am exemplifies an important property of the SI, its coherence, by which we mean that if all quantities in a formula are expressed in SI units without prefixes the result of the calculation is also expressed in the appropriate SI unit, with no need for conversion factors). 

This energy can be expressed as TNT equivalent mass by using the adequate energy conversion factor (approximately 1,120 cal per gram of TNT),... 

As you saw earlier, you can use molarity as a conversion factor, and in this way you can calculate the volume of solution that is equivalent to a given mass of solute (see Example 4.10). This means that you can replace mass measurements in solution reactions by volume measurements. In the next example, we look at the volumes of solutions involved in a given reaction. 

All of the solution concentration units introduced in this chapter are direct proportionalities. Percentage concentration by mass is a direct proportionality between mass of solute and mass of solution molarity, between moles of solute and liters of solution molality, between moles of solute and kilograms of solvent and normality, between equivalents of solute and liters of solution. These proportional relationships allow you to think of solution concentration units as conversion factors between the two units in the fraction. Do you know mass of solution and need mass of solute Use percentage concentration. Do you know volume of solution and need moles of solute Use molarity. Thinking about solution concentration units in this way allows you to become more skilled at solving quantitative problems. 

There are two ways to calculate the number of equivalents (eq) in a sample of a substance. If you know the mass of the substance and its equivalent mass, use equivalent mass as a conversion factor to get equivalents, as in Example 16.10. If the sample is a solution and you know its volume and normality, multiply one by the other. V X N = eq, according to Equation 16.10. 

Note Some mass spectrometrists use the unit thomson [Th] (to honor J. J. Thomson) instead of the dimensionless quantity nr/z. Although the thomson is widely accepted (or tolerated), it is not an SI unit. The thomson is equivalent to m/z in that there is no conversion factor between these units. 

To count atoms by weighing them, we need one other conversion factor—the mass of 1 mol of atoms. For the isotope carbon-12, we know that the mass of 1 mol of atoms is exactly 12 grams, which is numerically equivalent to carbon-12 s atomic mass in atomic mass units. Since the masses of all other elements are defined relative to carbon-12, the same relationship holds for all elements. 

The expression above is equivalent to equation (4.3), but equation (4.4) emphasizes that the molarity, c, is a conversion factor for converting from liters of solution to moles of solute. In Example 4-8, we use molarity as a conversion factor in a calculation to determine the mass of solute needed to produce the solution in Figure 4-5. 

Commercial broilers had the highest population, about 7 billion, and they produced the second largest amount of manure cattle, which had a population of about 100 million, produced the largest amount. No differentiation was made in this assessment between dairy and beef cattle. The daily production rate per head of dry manure solids used was the arithmetic average of dairy cattle and beef cattle, since the dairy-to-beef cattle ratio of the reported manure production rates is about 1.45 (Stanford Research Institute, 1976). Some assessments indicate that the ratio of productivities is 3.1 (Jaycor, 1990). The effects of daily manure production per animal are evident as shown in Table 5.2. When published waste production factors are used for conversion of the animal populations to human equivalents in terms of solid waste generation as shown in the table, the total human population equivalent of these animals is estimated at almost 3 billion people. This is approximately 12 times the U.S. population in the mid-1990s, a ratio considerably less than reported in 1968, when it was estimated to be 20 times that of the human population (American Chemical Society, 1969). But the latter ratio included liquid wastes as well. The ratio of total animal excreta to total municipal biosolids generation calculated here, both of which exclude liquid wastes, is about 36 on a mass basis (307.1 dry t/8.6 million dry t). 

The product of the Reynolds and Schmidt numbers, which counts as one dimensionless number, is equivalent to the Peclet number for mass transfer, PeMx- The Peclet number represents the ratio of the convective mass transfer rate process to the diffusion rate process of component, and it appears on the left-hand side of the dimensionless mass transfer equation for component i. The remaining r dimensionless transport numbers can be treated simultaneously because they represent ratios of scaling factors for the reactant-product conversion rate due to the jth independent chemical reaction relative to the rate of diffusion of component I. Hence,... 

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