Mass balance equation conservation

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

General Material Balances. According to the law of conservation of mass, the total mass of an isolated system is invariant, even in the presence of chemical reactions. Thus, an overall material balance refers to a mass balance performed on the entire material (or contents) of the system. Instead, if a mass balance is made on any component (chemical compound or atomic species) involved in the process, it is termed a component (or species) material balance. The general mass balance equation has the following form, and it can be applied on any material in any process. 

When the system has been defined, an equation can be written to state the law of conservation of mass. Such a total mass balance equation can be given in verbal form as... 

The mass balance equations express conservation of mass in terms of the components in the basis. The mass of each chemical component is distributed among the species and minerals that make up the system. The water component, for example, is present in free water molecules of the solvent and as the water required to make... 

The governing equations are composed of two parts mass balance equations that require mass to be conserved, and mass action equations that prescribe chemical equilibrium among species and minerals. Water Aw, a set of species, 4/, the min-... 

The mass conservation equation only relates concentration variation with flux, and hence cannot be used to solve for the concentration. To describe how the concentrations evolve with time in a nonuniform system, in addition to the mass balance equations, another equation describing how the flux is related to concentration is necessary. This equation is called the constitutive equation. In a binary system, if the phase (diffusion medium) is stable and isotropic, the diffusion equation is based on the constitutive equation of Pick s law ... 

Replacing ds/dt by the entropy balance equation, du/dt by the energy conservation equation, and dpkidt by the mass balance equation, we have... 

We begin the derivation of the conservation of mass by simply inserting into Eq. 2.3-2, P = M and p = 1, yielding directly the macroscopic mass balance equation ... 

One of the key elements of the assessment phase of a pollution prevention program involves mass balance equations. These calculations are often referred to as material balances the calculations are performed via the conservation law for mass. The details of this often-used law are described below. 

In the next sections, the design equations for the three ideal reactor t)q>es will be derived for isothermal conditions. In practice, the heat effects associated with chemical reactions usually result in non-isothermal conditions. The application of the law of conservation of energy leads to the so-called energy balance equation. This derivation is analogous to the derivation of the mass balance equations, and will not be treated here (see for instance, [4,5]). However, it should be noted that under non-isothermal conditions, the energy balance equation should always be solved simultaneously with the corresponding mass balance equation, since the reaction rate depends not only on composition but also on temperature. 

All mathematical models of chromatography consist of a differential mass balance equation for each component involved and the equation expresses mass conservation in the process [13, 109], In the ED model the mass balance equation for a single component is expressed as follows ... 

Not all of the balance equations are independent of one another, thus the set of equation used to solve particular problems is not solely a matter of convenience. In chemical reactor modeling it is important to recall that all chemical species mass balance equations or all chemical element conservation equations are not independent of the total mass conservation equation. In a similar manner, the angular momentum and linear momentum constraints are not independent for flow of a simple fluid . 

Additional sets of equations that describe additional processes can be coupled and solved together. For example, the conservation of thermal energy and groundwater flow equations are coupled to the ADR equation and chemical mass balance equations in the work of Raffensperger (1995). 

Conservation Equations. Mass balance equations for the gaseous and aqueous phases are written in standard reservoir simulator form 10, 93). For the nonwetting foam or gas phase in a one-dimensional medium,... 

The numerical integration of the mass conservation equations consists basically in a time-iterative method with two sequential steps for each increment of time. In the first one, the transport of ions between each cell is calculated, yielding transient concentrations that are used in the second one, where the chemical equilibria and charge and mass balance equations are solved within each volume element. The first corresponds to the transport phenomena term in the differential conservation equation of each species, and the second corresponds to the rates of production of ions in those same equations. In this way, the model obtains new values that are used to perform the integration forward in time. 

The depth of reactions allows composing the mass balance equation for each chemical reaction j according to the law of conservation of matter at any stage of its evolution ... 

The second equation is usually based on conservation of mass of a common element or compound across the chemical reactions that are occurring. There are two possible mass balance equations in this experiment, for example, the pair based on the mass of Mg. Thus, the mass of Mg in the components of the mixture, MgO and Mg3N2, equals either the initial mass of Mg or the final mass of Mg in dried total MgO. 

Setting up the mass balance equation in either the sections of the Loschmidt s tube, we obtain the following equation for the conservation of mass... 

Figure 3.38. Derivation of mass balance equations in the case of an ideal tube reactor. Here, differential mass conservation dV = A dz for s and x for a tubular reactor with recycle, leading to Equ. 3.85 at steady state.

In fluid dynamics fluids are in motion. Generally, they are moved from place to place by means of mechanical devices such as pumps or blowers, by gravity head, or by pressure, and flow through systems of piping and/or process equipment. The first step in the solution of flow problems is generally to apply the principles of the conservation of mass to the whole system or to any part of the system. First, we will consider an elementary balance on a simple geometry, and later we shall derive the general mass-balance equation. 

This is in the same form as the general mass-balance equation (2.6-3), with the sum of the forces as the generation rate term. Hence, momentum is not conserved, since it is generated by external forces on the system. If external forces are absent, momentum is conserved. 

The mass balance equation, also referred to as the equation of continuity, is simply a formulation of the principles of the conservation of mass. The principle states that the rate of mass accumulation in a control volume equals the mass flow rate into the control volume minus the mass flow rate out of the control volume. In Cartesian coordinates (x, y, z), the mass balance equation for a pure fluid can be written as ... 

The goal of DFT modeling is to understand the chain of elementary reaction events in the electrochemical conversion and to calculate the rate constants for these steps. The reaction mechanism and the rate constants, obtained from DFT, are then used to establish and parameterize time-dependent mass balance equations for the adsorbed/desorbed species. The steady-state solution of the surface coverage equations provides the conversion function, which can be used in the simplified current conservation equation in the CL model. The solution of the CL performance model yields the CL polarization curve, which can be used in the fuel cell or stack model. The chain of information transfer looks schematically like... 

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