Mass-relation calculations

The approach followed in Chapter 3 to calculate mole-mass relations in reactions is readily applied to solution reactions represented by net ionic equations. 

In order to use Eqs. (3) and (4) or the data given in Fig. 1, for the calculation of maximum turbulent fluctuation velocity the maximum energy dissipation e , must be known. With fully developed turbulence and defined reactor geometry, this is a fixed value and directly proportional to the mean mass-related power input = P/pV, so that the ratio ,/ can be described as an exclusive function of reactor geometry. In the following, therefore details will be provided on the calculation of power P and where available the geometric function ,/ . 

The ideal gas equation can be combined with the mole-mass relation to find the molar mass of an unknown gas PV = nRT (ideal gas equation) and n — (mole-mass relation) if we know the pressure, volume, and temperature of a gas sample, we can use this information to calculate how many moles are... 

In the Delaware and Chesapeake estuaries (USA), uranium shows distinctly nonconservative behavior at salinities <5 (Sarin and Church 1994 Church et al. 1996). This was suggested to be due to sedimentary redox processes in the extensive salt marshes in the Delaware and Chesapeake bays. From mass balance calculations it was concluded that almost two-thirds of the uranium in the tidal waters were retained in the sediments. It was also suggested that, extrapolated globally, uranium removal in salt marshes and marine wetlands, including mangroves, are important sinks for U that may responsible for up to 50% of the total marine removal (Church et al. 1996). Removal of U is also observed within the Baltic Sea, related to the association of U with colloids (see Section 2.5). 

The problems relating to mass transfer may be elucidated out by two clear-cut yet different methods one using the concept of equilibrium stages, and the other built on diffusional rate processes. The selection of a method depends on the type of device in which the operation is performed. Distillation (and sometimes also liquid extraction) are carried out in equipment such as mixer settler trains, diffusion batteries, or plate towers which contain a series of discrete processing units, and problems in these spheres are usually solved by equilibrium-stage calculation. Gas absorption and other operations which are performed in packed towers and similar devices are usually dealt with utilizing the concept of a diffusional process. All mass transfer calculations, however, involve a knowledge of the equilibrium relationships between phases. 

In the special case of an ideal single catalyst pore, we have to take into account that diffusion is quicker than in a porous particle, where the tortuous nature of the pores has to be considered. Hence, the tortuosity r has to be regarded. Furthermore, the mass-related surface area AmBEX is used to calculate the surface-related rate constant based on the experimentally determined mass-related rate constant. Finally, the gas phase concentrations of the kinetic approach (Equation 12.14) were replaced by the liquid phase concentrations via the Henry coefficient. This yields the following differential equation ... 

Typically, application of science involves prediction of function such as determining at what rate a well must be pumped to create a suitable capture zone. What period of time will be required to biodegrade a mass of contaminant within a plume How much activated carbon will be required to treat the discharged vapor What will be the cost of electricity to power the remediation system Engineers are more likely capable of designing a balanced remediation system that has flow rates matched to reaction times or water-air contact rates. Tank sizes, power consumption, and similar rate-time-related calculations also fall within the specialty of the engineer. 

The gassed condition is important in mass transfer calculations. In general, the ungassed- and gassed-power are related by the equation PG = P. The value of P is calculated from the power correlation for Rushton turbines [16]. The correction factor, y, is calculated from the following equations ... 

Related Calculations. In this example, it was stated at the outset that mass-transfer effects were not limiting the process rate. In the general case, however, it is important to calculate the effect of mass-transfer resistance on the reaction rate. 

Related Calculations. For a batch reactor, the material balance is Rate of accumulation of species A = rate of generation of species A, or dNA/dt = rA, where N is number of moles at time t and r is rate of reaction (which can be, for example, per unit of catalyst mass in the reactor, in which case it must be multiplied by the number of such units present). The rate at any given time can be found by plotting Na against residence time and measuring the slope, but this technique can lead to large errors. A better approach is to use the Taylor-series interpolation formula (see mathematics handbooks for details). 

Related Calculations. Use this procedure for any pipe in which there is laminar flow of liquid. Table 6.1 gives a quick summary of various ways in which the Reynolds number can be expressed. The symbols in Table 6.1, in the order of their appearance, are D = inside diameter of pipe, ft v = liquid velocity, ft/s p = liquid density, lb/ft3 p. = absolute viscosity of liquid, lb mass/fts d = inside diameter of pipe, in. From a table of pipe properties, d = 22.626 in. Also, k = z/S liquid flow rate, lb/h B = liquid flow rate, bbl/h k = kinematic viscosity of the liquid, Cst q = liquid flow rate, ft3/s Q = liquid flow rate, ft3/min. Use Table 6.1 to find the Reynolds number for any liquid flowing through a pipe. 

Related Calculations. This procedure can be used to calculate average sizes, moments, surface area, and mass of solids per volume of slurry for any known particle size distribution. The method can also be used for dry-solids distributions, say, from grinding operations. See Example 10.7 for an example of a situation in which the size distribution is based on an experimental sample rather than on a known size-distribution function. 

Related Calculations. The average concentration of solute in the cake consists of mass of solute remaining divided by void volume. These values appear as the final column in Table 14.5. 

Related Calculations. Apart from the rule of thumb concerning superficial velocity (see step 1), be aware of similar guidelines that pertain to mass flow rate through the absorption tower. For plastic packing, the liquid and gas flow rates are both typically around 1500 to 2000 lb/h per square foot of tower cross-sectional area for ceramic packing, the corresponding range is about 500 to 1000 lb/h. 

Related Calculations. Where in-line equalization basins are used, additional damping of the BOD mass-loading rate can be obtained by increasing the volume of the basins. Although the flow to a treatment plant was equalized in this example, flow equalization would be used, more realistically, in locations with high infiltration or inflow or peak stormwater flows. 

Related Calculations. For calculation of the liquid-phase mass transfer coefficient, ki, the following formula can be used [Ref. 14], where N c is the Schmidt number and subscript c refers to the liquid phase ... 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

Imagine that the experiment you are doing in the laboratory produces 5.55 g of a compound. How many moles is this To find out, you calculate the molar mass of the compound and determine it to be 185.0 g/mol. The molar mass relates grams and moles, but this time you need the inverse of the molar mass as the conversion factor. 

The empirical formula of a compound can be simply related to the mass percentage of its constituent elements using the mole concept. For example, the empirical formula for ethylene (molecular formula C2H4) is CH2. Its composition by mass is calculated from the masses of carbon and hydrogen in 1 mol of CH2 formula units ... 

Nielen et al. (2001) focused on a related facet of the illegal use of growth promoters in cattle, namely the detection of anabolic steroids in illegal cocktails. They presented a Q-TOF LC-MS-MS method with the aim of measuring accurate mass and calculating elemental composition for identification purposes. 

There have been few experimental tests of the theoretical predictions of turbulent coagulation under controlled conditions. Delichaisios and Probstein (1975) measured rates of coagulation of 0.6-mm latex particles suspended in an aqueous solution in turbulent pipe flow. The Reynolds numbers ranged from 17,000 to 51,000 for flow through a 1-in. (l.D.) smooth-walled pipe. For the core of the pipe flow, the turbulence was approximately isotropic. The energy dissipation per unit mass was calculated from the relation... 

The fraction f was calculated by comparing the original amount of initiator with the amount of unconsumed initiator, which was obtained from its area under the GPC trace and its area-to-mass relation. The fraction f and kp/kl were 0.86 and 4.6 respectively. 

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