Mass density concentration

When trying to understand and to manipulate matter and materials, chemistry does not start by looking at the natural world in all its complexity. Rather, it seeks to establish what have been termed exemplar phenomena ideal or simplified examples that are capable of investigation with the tools available at the time (Gilbert, Borrlter, Elmer, 2000). This level consists of representatiorrs of the empirical properties of solids, liquids (taken to include solutions, especially aqueous solutiorts), colloids, gases and aerosols. These properties are perceptible in chemistry laboratories and in everyday life and are therefore able to be meastrred. Examples of such properties are mass, density, concentration, pH, temperatrrre and osmotic presstrre. 

A bottle of commercial concentrated aqueous ammonia is labeled 29.89% NH3 by mass density = 0.8960 g/mL. ... 

For an ideal gas, the total molar concentration Cj is constant at a given total pressure P and temperature T. This approximation holds quite well for real gases and vapours, except at high pressures. For a liquid however, CT may show considerable variations as the concentrations of the components change and, in practice, the total mass concentration (density p of the mixture) is much more nearly constant. Thus for a mixture of ethanol and water for example, the mass density will range from about 790 to 1000 kg/m3 whereas the molar density will range from about 17 to 56 kmol/m3. For this reason the diffusion equations are frequently written in the form of a mass flux JA (mass/area x time) and the concentration gradients in terms of mass concentrations, such as cA. 

Equations (4.1) or (4.2) are a set of N simultaneous equations in iV+1 unknowns, the unknowns being the N outlet concentrations aout,bout, , and the one volumetric flow rate Qout- Note that Qom is evaluated at the conditions within the reactor. If the mass density of the fluid is constant, as is approximately true for liquid systems, then Qout=Qm- This allows Equations (4.1) to be solved for the outlet compositions. If Qout is unknown, then the component balances must be supplemented by an equation of state for the system. Perhaps surprisingly, the algebraic equations governing the steady-state performance of a CSTR are usually more difficult to solve than the sets of simultaneous, first-order ODEs encountered in Chapters 2 and 3. We start with an example that is easy but important. 

Shown in Figure 3 is the model fitting of the sorption data for the HA and its esters. The mass densities of the materials (Table 5) have been used to convert the concentration to volume fraction. As shown, the model is able to satisfactorily interpolate the experimental data. The estimated parameters of the model are reported in Table 6. 

At the macroscopic level, matter is described in terms of fields such as the velocity, the mass density, the temperature, and the chemical concentrations of the different molecular species composing the system. These fields evolve in time according to partial differential equations of hydrodynamics and chemical kinetics. 

Similar considerations concern the irreversible processes of diffusion and reaction in mixtures [5]. A system of M different molecular species is described by the three components of velocity, the mass density, the temperature, and (M — 1) chemical concentrations and is ruled by M + 4 partial differential equations. The M — 1 extra equations govern the mutual diffusions and the possible chemical reactions... 

Solvent Relative molecular mass Density g / cm (20 °C) Melting point °C Boiling point °C Maximum admissible concentration (MAC) cm / m ... 

The mathematical translation of the plane-source problem is as follows. Initially, there is a finite amount of mass M but very high concentration at a = 0, i.e., the density or concentration at a = 0 is defined to be infinite (which is unrealistic but merely an abstraction for the case in which initially the mass is concentrated in a very small region around a = 0). The initial condition is not consistent with that required for Boltzmann transformation. Hence, other methods must be used to solve the case of plane-source diffusion. Because this is the classical random walk problem, the solution can be found by statistical treatment as the following Gaussian distribution ... 

The extended source can be viewed as a summation (or integral) of point plane sources. The mass density at each plane e ( 8,8) is Cod. At position x, which is distance x - away from this plane, according to Equation 3-45a, the concentration due to this plane source is... 

Salt Solubility/ mass% Density kg m-3 Mass of water in 1 dm3 of solution/g Mass of salt in 1 dm3 of solution/g Molar concentration of sa/Mnol dm 3... 

In these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

There are numerous ways of expressing concentration in diffusion problems, the most important for our purposes being mass density, molar density, mass fraction, and mole fraction. The chemical engineer and the chemist are familiar with the relationships between these quantities. Table I is given for the sake of summarizing the notation used here. 

When a series of stirred-tanks is used as a chemical reactor, and the reactants are fed at a constant rate, eventually the system reaches a steady state such that the concentrations in the individual tanks, although different, do not vary with time. When the general material balance of equation 1.19 is applied, the accumulation term is therefore zero. Considering first of all the most general case in which the mass density of the mixture is not necessarily constant, the material balance on the reactant A is made on the basis of FA moles of A per unit time fed to the first tank. Then a material balance for the rth tank of volume V (Fig. 1.17) is, in the steady state ... 

A simple theory of the concentration dependence of viscosity has recently been developed by using the mode coupling theory expression of viscosity [197]. The slow variables chosen are the center of mass density and the charge density. The final expressions have essentially the same form as discussed in Section X the structure factors now involve the intermolecular correlations among the polyelectrolyte rods. Numerical calculation shows that the theory can explain the plateau in the concentration dependence of the viscosity, if one takes into account the anisotropy in the motion of the rod-like polymers. The problem, however, is far from complete. We are also not aware of any study of the frequency-dependent properties. Work on this problem is under progress [198]. 

In equations 5-8, the variables and symbols are defined as follows p0 is reference mass density, v is dimensional velocity field vector, p is dimensional pressure field vector, x is Newtonian viscosity of the melt, g is acceleration due to gravity, T is dimensional temperature, tT is the reference temperature, c is dimensional concentration, c0 is far-field level of concentration, e, is a unit vector in the direction of the z axis, Fb is a dimensional applied body force field, V is the gradient operator, v(x, t) is the velocity vector field, p(x, t) is the pressure field, jl is the fluid viscosity, am is the thermal diffiisivity of the melt, and D is the solute diffiisivity in the melt. The vector Fb is a body force imposed on the melt in addition to gravity. The body force caused by an imposed magnetic field B(x, t) is the Lorentz force, Fb = ac(v X v X B). The effect of this field on convection and segregation is discussed in a later section. 

To appreciate an eventual effect of crosslink density on mass density, we have to compare networks having the same hydrogen bond concentration. This is possible, for instance, in the series B of Table 10.4 (Morel et al., 1989). 

The state of a system is defined by its properties. Extensive properties are proportional to the size of the system. Examples include volume, mass, internal energy, Gibbs energy, enthalpy, and entropy. Intensive properties, on the other hand, are independent of the size of the system. Examples include density (mass/volume), concentration (mass/volume), specific volume (volume/mass), temperature, and pressure. 

The process will be described with all apparatus, machines and product streams. The latter are identified by specification numbers and listed in a table together with properties such as mass flow, concentration, liquid/gas phase, density. If already known, also process parameters such as pressure and temperature are listed. A list of utilities covering heating fluids, cooling agents, pressurized air and nitrogen and the electrical power supply will be delivered. 

Liquid-solid mass transport (liquid reactant) Amount of catalyst Catalyst particle size Concentration of reactant in liquid phase Temperature Agitation rate Reactor design Viscosity Relative densities Concentration of gas-phase reactant Concentration of active components on catalyst... 

This simple model is schematically represented for single flighted screws in Fig. 10.28. The model is based on the overall balances for enthalpy, mass, and concentration that can be derived for each individual chamber moving through the extruder. Assuming constant density, the preceding equation reduces to... 

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