Balanced equations information

In Chapter 2 we developed models based on analyses of systems that had simple inputs. The right-hand side was either a constant or it was simple function of time. In those systems we did not consider the cause of the mass flow—that was literally external to both the control volume and the problem. The case of the flow was left implicit. The pump or driving device was upstream from the control volume, and all we needed to know were the magnitude of the flow the device caused and its time dependence. Given that information we could replace the right-hand side of the balance equation and integrate to the functional description of the system. 

Fig. 8.4 Information contained in a balanced equation (from M. S. Silberberg, Chemistry The molecular nature of matter and change, 4th ed., McGraw Hill, 2006, p. 106, reproduced with permission of The McGraw-Hill Companies)...

There are only two possible values for concentration in a CSTR. The inlet stream has concentration and everywhere else has concentration The reaction rate will be the same throughout the vessel and is evaluated at the outlet concentration, SIa = A(ctout,bout, ) For the single reactions considered in this chapter, continues to be related to by the stoichiometric coefficient and Equation (1.13). With SS a known, the integral component balance, Equation (1.6), now gives useful information. For component A,... 

According to the balanced equation, the synthesis of 2.0 moles of ammonia requires 3.0 moles of hydrogen and f.O mole of nitrogen. However, the balanced equation does not give us any direct information about the masses involved in the synthesis. One gram of N2 plus three grams of H2 does not make two grams of NH3. Remember the most important lesson from Chapter 3 ... 

The steady-state approach, however, provides no information on the initial transient conditions, whereby the extractor achieves eventual steady state or on its dynamic response to disturbances. For this it is necessary to derive the dynamic balance equations for the system. 

If equilibrium between the two phases is assumed, the above balance equation can be solved in conjunction with the equilibrium relationship, as shown by Franks (1967) and as indicated in the information flow diagram. Fig. 3.35. 

Under normal circumstances, the use of a characteristic velocity equation of the type shown above can cause difficulties in computation, owing to the existence of an implicit algebraic loop, which must be solved, at every integration step length. In this the appropriate value of L or G satisfying the value of h generated in the differential mass balance equation, must be found as shown in the information flow diagram of Fig. 3.54. 

The block shown in Figure 4.6 represents any unit in an information flow diagram, and shows the nomenclature that will be used in setting up the material balance equations. 

It is becoming common practice, in today s chemical plants, to incorporate some kind of technique to rectify or reconcile the plant data. These techniques allow adjustment of the measurement values so that the corrected measurements are consistent with the corresponding balance equations. In this way, the simulation, optimization, and control tasks are based on reliable information. Figure 3 shows schematically a typical interconnection between the previous mentioned activities (Simulation Sciences Inc., 1989). 

To classify the variables, one must first establish what information each equation is to supply, that is, to obtain an output set assignment for the balance equations. 

We will assume that there is no a priori information and that we also need to assign the weights corresponding to the balance equations. They represent the expected degree of satisfaction of the constraints. Assuming as a first approximation Ri = I, the estimate of the process variables is given by the formula... 

A considerable improvement over purely graph-based approaches is the analysis of metabolic networks in terms of their stoichiometric matrix. Stoichiometric analysis has a long history in chemical and biochemical sciences [59 62], considerably pre-dating the recent interest in the topology of large-scale cellular networks. In particular, the stoichiometry of a metabolic network is often available, even when detailed information about kinetic parameters or rate equations is lacking. Exploiting the flux balance equation, stoichiometric analysis makes explicit use of the specific structural properties of metabolic networks and allows us to put constraints on the functional capabilities of metabolic networks [61,63 69]. 

This quick test does not, however, tell us that there will be only one stable limit cycle, or give any information about how the oscillatory solutions are born and grow, nor whether there can be oscillations under conditions where the stationary state is stable. We must also be careful in applying this theorem. If we consider the simplified version of our model, with no uncatalysed step, then we know that there is a unique unstable stationary state for all reactant concentrations such that /i < 1. However, if we integrate the mass-balance equations with /i = 0.9, say, we do not find limit cycle behaviour. Instead the concentration of B tends to zero and that for A become infinitely large (growing linearly with time). In fact for all values of fi less than 0.90032, the concentration of A becomes unbounded and so the Poincare-Bendixson theorem does not apply. 

The enthalpy of combustion of 1.00 mol CH3OH(l) is —726 kj. (a) Write a balanced equation for the combustion of 1 mol CH3OH(l). (b) What mass of methanol must be burned to heat 209 g of water in a 50.0-g Pyrex beaker from 20°C to 100°C For additional information, see Table 6.1. (c) Using the enthalpy of combustion and the enthalpies of formation of the products of the combustion reaction, calculate the enthalpy of formation of methanol. 

The chemical equation for an elementary reaction is a description of an individual molecular event that involves breaking and/or making chemical bonds. By contrast, the balanced equation for an overall reaction describes only the stoichiometry of the overall process, but provides no information about how the reaction occurs. The equation for the reaction of N02 with CO, for example, does not tell us that the reaction occurs by direct transfer of an oxygen atom from an N02 molecule to a CO molecule. 

Using the information on pp. 138-140, predict the properties of the element francium related to its melting point, density and softness. Predict how francium would react with water and write a balanced equation for the reaction. 

There are many tricks and shortcuts to this process. For example, rather than compiling all of the transformation rate equations (or conducting the actual kinetic experiments yourself), there are many sources of typical chemical half-lives based on pseudo-first-order rate expressions. It is usually prudent to begin with these best estimates of half-lives in air, water, soil, and sediment and perform a sensitivity analysis with the model to determine which processes are most important. One can return to the most important processes to assess whether more detailed rate expressions are necessary. An illustration of this mass balance approach is given in Figure 27.5 for benzol a Ipyrene. This approach allows a first-order evaluation of how chemicals enter the environment, what happens to them in the environment, and what the exposure concentrations will be in various environmental media. Thus the chemical mass balance provides information relevant to toxicant exposure to both humans and wildlife. 

Some additional information that can be conveyed in a balanced chemical equation (s) = solid, (g) = gas, (aq) = aqueous, and (1) = liquid. The following equation shows the proper use of these symbols S(s) + 6HN03(aq) —> H2S04(aq) + 6N02(g) + 2H20(1). It should be noted that [aq] means aqueous solution and [1] means in the liquid phase of a pure substance. Use phase-indicating symbols in your balanced equation in no. 3 above. 

The equilibrium problem matrix. The information concerning components, stoichiometry and formation constants can be written in the form of a table which for the purposes of this chapter will be referred to as the equilibrium problem matrix (EPM). An example of an EPM table for the monomeric A1 species is shown in Table 5.6. The EPM is a logical and compact format for summarising all the information required for solving equilibrium problems. Reading across the rows of the table the information needed to formulate the mass action expressions is contained. Down each component column are the coefficients with which the concentration of each species should be multiplied to formulate the mass balance equation (MBE). Therefore, once given the chemical problem in an EPM format the nature of the mass action equations, formation constants and mass balances considered can all be deduced. 

Proportion Method This method applies the information established by the balanced equation directly. The best part of this method is that the information is presented in a logical manner that practically solves the problem for you. The trick is to write the information given by the balanced equation (Eq. Info.) above the equation and the information provided by the problem (Prob. Info.) below the equation. Write the information above and below the participant identified in the equation by the problem, ignoring those participants not required for the solution of the problem. Place a symbol representing the unknown value as needed in Prob. Info. (W reminds us that the answer should come out in weight—grams.)... 

We use the information associated with the balanced equation to set up the ratio and proportion. Again, we need to watch to see if the desired unit appears in the solution. 

Using the same procedure as in Problem 4.7, the first action is to run the test to see if there is a limiting reactant. We set up the balanced equation with the information we were given and test to see if there is sufficient K3PO4 to use up all of the CaCl2. 

Since 6.37g K3PO4 are required to use up all of the calcium chloride and we were given 8.00g K3PO4, the limiting reactant is the CaCl2. We are now able to set up the balanced equation with the equation information and the... 

Before passing on to the analysis of gas-phase oxidation with hydrogen peroxide, we must first obtain information about its dissociation. Hydrogen peroxide easily dissociates to water and molecular oxygen, which is the typical feature, very useful in some cases and unwanted in another. H202 can dissociate in different ways, but all of them are described by the general material balance equation as follows ... 

The process model can be obtained by different forms, and in bioprocesses mass balance equations canprovide much information. However, in order to have efficient process models and software sensors, a previous adjustment of the model is necessary using on-line data collected from a plant under different operational conditions. This databank is important to guarantee that the model remains calibrated and represents the plant adequately. Some requisites are indispensable for the experimental implementation of models in software sensors response speed to disturbances in the system and appropriate inference of primary variables of interest during key points of the process. 

Applying these concepts to the remainder of the balanced equation yields information that confirms that the equation is balanced—the atom counts for both sides of the equation are the same. 

In an adiabatic operation, Q = 0, and as such there is no attempt to heat or cool the contents in the reactor. The temperature T in the reactor rises in an exothermic reaction and falls in an endothermic reaction. It is essential to control T so that it is neither too high nor too low. To assess the design of both the reactor and the heat exchanger required to control T, the material and energy balance equations must be used together with information on rate of reaction and rate of heat transfer because there is an interaction between T and XA. 

Additional information on the plug flow fixed bed reactors and on the heat and mass balance equations can be found in the Handbook of Heterogeneous Catalysis[15] and in the classical books devoted to chemical engineering kinetics.113,141... 

We have examined the nature of LIFS in some detail. The response of an atomic or molecular system is described in terms of appropriate rate (or balance) equations whose individual terms represent the rate at which individual quantum states are populated and depopulated by radiative and collisional processes. Given the response of a system to laser excitation, one may use the rate equations to recover information about total number density, temperature and collision parameters. 

Without further chemical or electrochemical information (a) Sketch the cell and the processes occurring in it. (b) What is the purpose of aerating the anolyte (c) What type of membrane (cationic or anionic) is required (d) Write the balanced equations that describe the process at the anode, the anolyte, and the cathode, (e) Write the balanced global equation. (Ibanez)... 

Where, x and y are the measured and unmeasured parameters respectively, and A and A2 are compatibles matrices. The topology of the balance equations is represented by the structure of these matrices. In order to classify the parameters one must first establish what information each equation is to supply, that is, to obtain the output set assignment for the balance equations. With the output set assignment we assign to any unmeasured... 

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