Molar balances

Rate-of-change mass balance molar basis... 

Equimolar Counterdiffusion. Just as unidirectional diffusion through stagnant films represents the situation in an ideally simple gas absorption process, equimolar counterdiffusion prevails as another special case in ideal distillation columns. In this case, the total molar flows and are constant, and the mass balance is given by equation 35. As shown eadier, noj/g factors have to be included in the derivation and the height of the packing is... 

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

Because PEA is such an important fragrance material this simple, essentially one-step process has been exhaustively studied to optimize reaction conditions and purification procedures. Because of the high reactivity of the iatermediates and the tendency toward polymer formation, critical factors such as throughput, temperature, molar ratios of reactants, addition rates, reactor materials and design, and agitation rate must be carefully balanced to provide an economical product with acceptable odor properties. 

The second term in brackets in equation 36 is the separative work produced per unit time, called the separative capacity of the cascade. It is a function only of the rates and concentrations of the separation task being performed, and its value can be calculated quite easily from a value balance about the cascade. The separative capacity, sometimes called the separative power, is a defined mathematical quantity. Its usefulness arises from the fact that it is directly proportional to the total flow in the cascade and, therefore, directly proportional to the amount of equipment required for the cascade, the power requirement of the cascade, and the cost of the cascade. The separative capacity can be calculated using either molar flows and mol fractions or mass flows and weight fractions. The common unit for measuring separative work is the separative work unit (SWU) which is obtained when the flows are measured in kilograms of uranium and the concentrations in weight fractions. 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

To make the necessary thermodynamic calculations, plausible reaction equations are written and balanced for production of the stated molar flows of all reactor products. Given the heat of reaction for each applicable reaction, the overall heat of reaction can be determined and compared to that claimed. However, often the individual heats of reaction are not all readily available. Those that are not available can be determined from heats of combustion by combining combustion equations in such a way as to obtain the desired reaction equations by difference. It is a worthwhile exercise to verify this basic part of the process. 

Processes involving chemical reactions must be approached differently. It is best to express the compositions of flow streams entering the process or unit operation in terms of molar concentrations. Balances are developed in terms of the largest components that remain unchanged by the reactions. 

We will consider flow through a solid element. Introducing the notations for molar flow density, partial density, and the reaction rate gives an equation for the mass balance ... 

For the mass balance of component A, diffusion velocity and the corresponding diffusion factor are defined with regard to the mean molar velocity V, defined by the equation... 

It is often experimentally convenient to use an analytical method that provides an instrumental signal that is proportional to concentration, rather than providing an absolute concentration, and such methods readily yield the ratio clc°. Solution absorbance, fluorescence intensity, and conductance are examples of this type of instrument response. The requirements are that the reactants and products both give a signal that is directly proportional to their concentrations and that there be an experimentally usable change in the observed property as the reactants are transformed into the products. We take absorption spectroscopy as an example, so that Beer s law is the functional relationship between absorbance and concentration. Let A be the reactant and Z the product. We then require that Ea ez, where e signifies a molar absorptivity. As initial conditions (t = 0) we set Ca = ca and cz = 0. The mass balance relationship Eq. (2-47) relates Ca and cz, where c is the product concentration at infinity time, that is, when the reaction is essentially complete. 

Vmin = Minimum fresh air flow based on slope of operating line, L/V, on x-y diagram V = Vapor flowrate, mols/hr or molar volume W = Bottoms product, or still bottoms, or ketde bottoms, mols also see B or mols/hr bottoms product or mols of residue or bottoms/unit time (Ponchon heat balance)... 

Stoichiometry in Reactive Systems. The use of molar units is preferred in chemical process calculations since the stoichiometry of a chemical reaction is always interpreted in terms of the number of molecules or number of moles. A stoichiometric equation is a balanced representation that indicates the relative proportions in which the reactants and products partake in a given reaction. For example, the following stoichiometric equation represents the combustion of propane in oxygen ... 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

For a nonreactive system, the material balance may be done either on a mass or on a molar basis. 

Strategy (1) Start by calculating the number of moles of Fe2+. Then (2) use the coefficients of the balanced equation to find the number of moles of Mn04. Finally, (3), use molarity as a conversion factor to find the volume of KMn04 solution. 

Deviation of methane gas from ideal gas behavior. Below about 350 atm, attractive forces between methane (CH4) molecules cause the observed molar volume at 25°C to be less than that calculated from the ideal gas law. At 350 atm, the effect of the attractive forces is just balanced by that of the finite volume of CH4 molecules, and the gas appears to behave ideally. Above 350 atm, the effect of finite molecular volume predominates and V, > 1C... 

Example 12.4 illustrates a principle that you will find very useful in solving equilibrium problems throughout this (and later) chapters. As a system approaches equilibrium, changes in partial pressures of reactants and products—like changes in molar amounts—are related to one another through the coefficients of the balanced equation. 

In taking these sums, the standard molar entropies are multiplied by the number of moles specified in the balanced chemical equation. 

The substrate balance in a batch culture for component i in the culture volume of VR and change of molar concentration of C, is equal to the rate of formation of product ... 

The production rate of acetic acid was 2kg-h 1, where the maximum acetic acid concentration was 12%. Air was pumped into the fermenter with a molar flow rate of 200 moMi-. The chemical reaction is presented in (E. 1.1) and flow diagram in Figure 9.5. Determine the minimum amount of ethanol intake and identify the required mass balance for the given flow sheet. The ethanol biochemical oxidation reaction using A. aceti is ... 

P, with the remainder oxygen. The mass spectrum of compound B yields a molar mass of 97.99 g-mol. Write the molecular formula of compound B. (c) Compound B reacts with an aqueous solution of calcium hydroxide to form compound C, a white precipitate. Write balanced chemical equations for the reactions in parts (a), (b), and (c). 

Step 1 Write the balanced chemical equation for the equilibrium and the corresponding expression for the equilibrium constant. Then set up an equilibrium table as shown here, with columns labeled by the species taking part in the reaction. In the first row, show the initial composition (molar concentration or partial pressure) of each species... 

Because 1 mol AgCI — 1 mol Cl, the molar solubility of AgCl is given by the equation s = [Cl ]. From the balanced overall equation, we see that [Cl-] = [Ag(NH )2+l in the saturated solution. The equilibrium table, with all concentrations in moles per liter, is... 

In a steady-state ocean the sediment deposition rate of a nutrient like phosphorus ought to be balanced by riverbome influx to the oceans 1.5. 0Tg P are transported to the oceans by rivers (Richey, 1983). Assuming a C/P molar... 

See Figure 1.2. A component balance can be expressed in mass units, and this is done for materials such as polymers that have ill-defined molecular weights. Usually, however, component A will be a distinct molecular species, and it is more convenient to use molar units ... 

The component balance will be based on the molar flow rate ... 

Unlike Qp, Na is not a conserved quantity and varies down the length of the tube. Consider a differential element of length and volume h.zAc. The molar flow entering the element is IV (z) and that leaving the element is lV (z+Az), the difference being due to reaction within the volume element. A balance on component A gives... 

The outlet flow rate is required. The easiest way to obtain this is by a molar balance on the inerts ... 

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