Conservation total mass

When we assume a steady-state constant-density reactor, we obtain the simple form of this equation (V. pu = 0 or pu constant), which is just total mass conservation as required from stoichiometry. 

We first derive a relation for total mass conservation. Consider an arbitrary volume V enclosed in a surface Q. The mass inside the volume is JpdV, where p is density (in kg/m ) and dt is an infinitesimal volume in the volume V. The time derivative of the mass in the volume (i.e., the rate of the variation of the mass with time) is... 

For the total mass conservation of a single-phase fluid, / represents the fluid density p. jr represents the diffusional flux of total mass, which is zero. For flow systems without chemical reactions, d> = 0. Therefore, from Eq. (5.12), we have the continuity equation as... 

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 . 

At p = 0, we obtain dmo/dt = 0, which leads to the obvious condition of total mass conservation for a dissolved substance. From the equation for the first moment one obtains dmi/tfe 0 at r —> 00. It means that at r 00, the center of mass of dissolved substance moves with the average flow velocity U. The second moment at r 00 tends to... 

With (4.2.2) thus the total mass conservation in the node... 

Also Section 4.4 remains formally unaltered. In the Remark, we have the result (4.4.5) from where again the total mass conservation, now in the form (4.7.5), as a formal algebraic consequence. 

Thus we have the total mass conservation law as follows dM... 

Reactive scattering or a chemical reaction is characterized by a rearrangement of the component particles within the collision system, thereby resulting in a change of the physical and chemical identity of the original collision reactants A + B into different collision products C + D. Total mass is conserved. The reaction is exothemiic when rel(CD) > (AB) and is endothermic when rel(CD) < (AB). A threshold energy is required for the endothemiic reaction. 

The easiest principle to appreciate is conservation of mass. Except for nuclear reactions, an element s total mass at the end of a reaction must be the same as that present at the beginning of the reaction thus, an element serves as the most fundamental reaction unit. Consider, for example, the combustion of butane to produce CO2 and H2O, for which the unbalanced reaction is... 

The above criteria are a guide for detecting potential problems with gas letdown systems and apply for the first 90 m of piping downstream of the pressure reducer under concern. Systems with only liquid flow are not considered potential problems and need not be investigated. For systems with two phase flow, use the conservative assumption of the total mass flow rate as gas. Any system exceeding these criteria should be further evaluated. 

This relationship, of course, only gives the total mass of solids formed. To reveal how that solid matter is distributed across a crystal population, the other conservation equation considered in Chapter 2 viz. the population balance must be invoked. Firstly, however, the crystal yield is considered a little further. 

A numerical study of the MMEP kinetics, as described by the system of nonlinear differential equations (26), subject to mass conservation (Eq. (27)), has been carried out [64] for a total number of 1000 monomers and different initial MWDs. As expected, and in contrast to the case of wormlike micelles, it has been found that during relaxation to a new equilibrium state the temporal MWD does not preserve its exponential form. 

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. 

We first derive the so-called continuity equation, which is a direct consequence of the conservation of mass. If p is the density, or mass per unit volume, then the total mass of a fluid contained in F is equal to M = fj p dF. Letting dS — fi dS be an element of the surface, with n a unit vector perpendicular to the surface, the mass flow per unit time through the surface element is pv dS. The total fluid flow out of the volume F is then given by... 

To summarize reactions quantitatively, we note that atoms are neither created nor destroyed in a chemical reaction they simply change their partners. The principal evidence for this conclusion is that there is no overall change in mass when a reaction takes place in a sealed container. The observation that the total mass is constant during a chemical reaction is called the law of conservation of mass. 

Because each chemical element is conserved, the masses of the products are equal to the masses of the elements contained in the original compound. This lets us complete the elemental analysis of the compound. The 5.00-g sample contained 4.63 g mercury and 0.37 g oxygen. The percent composition is found by dividing each elemental mass by the total mass and multiplying by 100 ... 

Are these masses reasonable First, it is reasonable that none of the final amounts is negative. Second, we can check to see if total mass is conserved. We started with 125 g ammonia and 256 g oxygen, a total of 381 g. The masses present at the end total 381 g, too, indicating that the calculations are consistent, and the results are reasonable. 

To summarize, the equation for a nuclear reaction is balanced when the total charge and total mass number of the products equals the total charge and total mass number of the reactants. This conservation requirement is one reason why the symbol for any nuclide includes its charge number (Z) as a subscript and its mass number as a superscript. These features provide a convenient way to keep track of charge and mass balances. Notice that in the equation for neutron decay, the sum of the subscripts for reactants equals the sum of the subscripts for products. Likewise, the sum of the superscripts for reactants equals the sum of the superscripts for products. We demonstrate how to balance equations for other reactions as they are introduced. 

The previous discussion has been in terms of the total mass of the system, but most process streams, encountered in practice, contain more than one chemical species. Provided no chemical change occurs, the generalised dynamic equation for the conservation of mass can also be applied to each chemical component of the system. Thus for any particular component... 

Verify that the total mass of solute is conserved. 

The conservation of energy, however, differs from that of mass in that energy can be generated (or consumed) in a chemical process. Material can change form, new molecular species can be formed by chemical reaction, but the total mass flow into a process unit must be equal to the flow out at the steady state. The same is not true of energy. The total enthalpy of the outlet streams will not equal that of the inlet streams if energy is generated or consumed in the processes such as that due to heat of reaction. 

The theories that have been developed to describe mass transfer arise from the law of conservation of mass, which states that mass can be neither created nor destroyed. According to this law, the total mass in a particular region in space can increase only by the addition of mass from the surroundings and can decrease only by the loss of mass back to them. Processes such as radioisotope decay and nuclear fission are exceptions to this law, since they involve the interconversion of matter and energy. In the absence of nuclear decay, however, the law of conservation of mass holds and is broadly applicable to mass transfer problems. 

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 total mass of the ash plus the carbon dioxide plus the water vapor is equal to the total mass of the log plus the oxygen. As always, the law of conservation of matter is obeyed as precisely as chemists can measure. The law of conservation of mass is fundamental to the understanding of chemical reactions. Other laws related to the behavior of matter are equally important, and learning how to apply these laws correctly is a necessary goal of the study of chemistry. 

When a nuclear event takes place, some rest mass is converted to extra mass of the product particles because of their high speed or to the mass of photons of light. While the total mass is conserved in the process, some rest mass (that is, some matter) is converted to energy. 

By working in terms of total mass, the reaction term disappears because the principle of conservation of mass must be satisfied. 

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