Equations mass balance

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- ... 

Counting unknowns, we find four ([HE], [E-], [H3O4], and [OH-]). To solve this problem, therefore, we need to write two additional equations involving these unknowns. These equations are a mass balance equation... 

How does the result of this calculation change if we require our assumptions to have an error of less than 1%. In this case we can no longer assume that [HF] >> [F ]. Solving the mass balance equation (6.37) for [HF]... 

From the ladder diagram it appears that we may safely assume that the concentrations of H2L+ and L are significantly smaller than that for HL, allowing us to simplify the mass balance equation to... 

Note that in writing this mass balance equation, the concentration of Ag(NH3)2i" must be multiplied by 2 since two moles of NH3 occurs per mole of Ag(NH3)2i". The second additional equation is a mass balance on iodide and silver. Since Agl is the only source of N and Ag+, every iodide in solution must have an associated silver ion thus... 

The remaining three equations are given by mass balance equations on HA and Na+... 

Write charge balance and mass balance equations for the following solutions... 

This is an old, familiar analysis that applies to any continuous culture with a single growth-limiting nutrient that meets the assumptions of perfect mixing and constant volume. The fundamental mass balance equations are used with the Monod equation, which has no time dependency and should be apphed with caution to transient states where there may be a time lag as [L responds to changing S. At steady state, the rates of change become zero, and [L = D. Substituting ... 

Prey-predator or host-parasite systems can oe analyzed by mass balance equations ... 

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 consei vation law for mass. The details of this ofien-used law are described below. 

From the mass balance equation for a batch reactor... 

The first order reaction is represented by (-r ) = kC, and applying the mass balance Equation 6-120 and the heat balance Equation 6-121, respectively, gives the fractional conversion in terms of the mass balance equation ... 

Applying tlie generalized form of tlie mass balance Equation 11-56, at constant density, dV/dt = 0. 

The Right-Hand Side of the Mass Balance Equation... 

The airflow rate infiltrating and exfiltrating through each air leakage pass, Q , due to the combined effect of wind, stack, and mechanical ventilation system perfotmance can be calculated ftom the mass balance equation... 

The mass balance equation for the airflow through the gate can be described as... 

Using simulation software (essentially solving the mass balance equation in the transitory regime), one can show that the internal profiles of the products in the system are given by the profiles presented in Figure 10.6. Samples were taken between columns at half periods. 

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. 

It must be kept in mind that the reaction term will not occur in the overall mass balance equations of reactive systems because S(R- = 0, i.e., there is no net mass gain or loss as a result of chemical reactions. 

Identification of the input and output streams used in the overall mass balance equation. 

The requirement for oxygen and carbon source for cell biosynthesis are calculated using nitrogen-limited mass balance equations for growth during exopolysaccharide production 01 res (nitrogen-limited cultures). These balances are derived from experimentally determined values of ... 

The mechanism involved the overall conversion of [5] to [P], The reverse reaction is insignificant because only the initial velocity in one of the forward direction is concerned. The mass balance equation expressing the distribution of the total enzyme is ... 

It may be noted that the energy and mass balance equations assume that the fluid is continuous. This is so in the case of a liquid, provided that the pressure does not fall to such a low value that boiling, or the evolution of dissolved gases, takes place. For water... 

If a concentration gradient exists within a fluid flowing over a surface, mass transfer will take place, and the whole of the resistance to transfer can be regarded as lying within a diffusion boundary layer in the vicinity of the surface. If the concentration gradients, and hence the mass transfer rates, are small, variations in physical properties may be neglected and it can be shown that the velocity and thermal boundary layers are unaffected 55. For low concentrations of the diffusing component, the effects of bulk flow will be small and the mass balance equation for component A is ... 

This mass balance equation shows that material that is initially at radial position rin will move to radial position r for some downstream location, >0. A worked example of radial velocities and curved streamlines is given in Chapter 13, Example 13.10. 

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