Mole balances liquid phase

Generally, these concentrations are expressed in terms of moles of solute per mole of pure solvent (liquid phase) and moles of solute per mole of inert gas (gas phase), thus making the material balance calculations easier. 

P, yj and fw designate the total pressure, the mole fraction of component i in vapor phase and the fugacity of pure water). The mass balance in the liquid phase results in four additional equations ... 

The remaining equations are phase equilibria for ammonia (eq. K4) and water (eq. K5), mass balances for ammonia (eq. XV) and hydrogen sulfide (eq. XVII), the condition of bulk electroneutrality (eq. XIX), the mole balance in the vapor phase (eq. XX), and the assumption that, for the ammonia-rich systems considered exclusively, in the mass balance for the liquid hydrogen sulfide may be neglected. The system of eight equations can easily be solved ... 

Equilibrium vapor condensate was analyzed by means of density measurement at 25.00° 0.02°C. An Ostwald pycnometer (capacity ca. 5 cm3) was used. Liquid phase composition was calculated by taking a material balance. In this case, the three moles of water present in trihydrous lithium perchlorate were considered water component. The accuracies of both compositions were 0.001 mole fraction. 

In the case of the flash calculations, different algorithms and schemes can be adopted the case of an isothermal, or PT flash will be considered. This term normally refers to any calculation of the amounts and compositions of the vapour and the liquid phase (V, L, y,-, xh respectively) making up a two-phase system in equilibrium at known T, P, and overall composition. In this case, one needs to satisfy relation for the equality of fugacities (eq. 2.3-1) and also the mass balance equations (based on 1 mole feed with N components of mole fraction z,) ... 

Assume that two streams leave the process a liquid water stream at rate ndotUq and a vapor stream at rate ndotvap. Apply mole balances around the cooler to calculate the exit composition of the vapor phase. 

Batch Reactor. In a batch reactor there are no inlet or outlet streams In = Out = 0. The total feed is charged into the reactor at the beginning and no withdrawal is made until the desired conversion level has been reached. Hence a reaction process occurring in a batch reactor is an unsteady one. All variables change with time. In addition, we assume that it is a perfectly mixed batch reactor, so that the concentrations of the reaction components, reactants or products are the same over the whole reactor volume. This assumption allows us to consider applying the mole balance equation across the whole reactor. With the term reactor we mean the space where the reaction(s) take place. For liquid phase reactions the reactor volume is smaller than the size of the physical reactor. It is the volume of the liquid phase, where the reaction ) take(s) place. 

To get the dynamic model of the movement of the front, the column is separated into two parts by cutting off below the thirtieth stage (Figure 6). It is assumed that the total amount of isopropanol leaves the liquid phase within the region of the temperature front. Furthermore, the vapour flow rates are supposed to be the same along the column Vk = V, k=l,...,K. It is to be emphasized that the mole fractions of isopropanol remain almost uneffected in the upper part. As a result the reflux R consists of pure isopropanol and hence the overall mass balance equations of the upper part are... 

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

The objective in analyzing these units is to calculate the temperature, the conqjosition, and the flow rates of the vapor and hquid exit streams, given the properties of the entering streams. First, write the mole balances. For two components, we write two component balances and a mole fraction summation for each unknown stream as given by Equations 3.3.1 to 3.3.4 in Table 3.3.1. There are two phases in equilibriiun leaving the valve, condenser and vaporizer, although the phases have not, as yet, been separated. A phase separator will separate the phases. For a vaporizer, both component and phase separation occur in the same process unit. As stated before, the first numerical subscript is the line number and the second the component number. We also identify the phases by an additional subscript, V for vapor and L for liquid. Because we are assuming equilibrium between the vapor and liquid for each component downstream of the valve, we can... 

The composition of the liquid phase can be obtained from a material balance on the initial moles of NO2 and NO admitted to the equilibration vessel by means of the equation,... 

Generally, when analyzing laboratory experiments it is best to process the data in terms of the measured variable, Since concentration is the measured variable for most liquid-phase reactions, the general mole balance equation applied to reactions in which there is no volume change becomes... 

There are a number of instances when it is much more convenient to work in terms of the number of moles (iV, N-g) or molar flow rates (Fj, Fg, etc.) rather than conversion. Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates rather than conversion are preferred. In Section 3.4 we de.scribed how we can express concentrations in terms of the molar flow rates of the reacting species rather than conversion, We will develop our algorithm using concentrations (liquids) and molar flow rates (gas) as our dependent variables. The main difference is that when conversion is used as our variable to relate one species concentration to that of another species concentration, we needed to write a mole balance on only one species, our basis of calculation. When molar flow rates and concentrations are used as our variables, we must write a mole balance on each species and then relate the mole balances to one another through the relative rates of reaction for... 

Because this reaction is liquid phase, the mole balance can be put in the fob lowing form ... 

To obtain a plot of heat generated, G(T), as a function of temperature, we must solve for X as a function of T using the CSTR mole balance, the rate law, and stoichiometry. For example, for a first-order liquid-phase reaction, the CSTR mole balance becomes... 

Liquid Phase. For liquid-phase reactions in which there is no volume change, concentration is the preferred variable. The mole balances are shown in Table 4-5 in terms of concentration for the four reactor types we have been discussing. We see from Table 4-5 that we have only to specify the parameter values for the system (CAo,Uo,etc.) and for the rate law (i.e., ifcyv. .3) to solve the coupled ordiaaiy differential equations for either PFR, PBR, or batch reactors or to solve the coupled algebraic equations for a CSTR. 

TAS2.E 4-5. Mole Balances for Liquid-Phase Reactions... 

Conversion does not have any meaning in startup because one cannot separate the moles reacted from the moles accumulated in the CSTR. Consequently, we must use concentration rather thtm conversion as our variable in the balance equation. For liquid-phase (o == Uq) reactions with constant overflow (V = Vj). using t = y,)/Vq we can transform Equation (4-43) to... 

Note that equations analogous to Equation (8-71) for G(T) can be derived for other reaction orders and for reversible reactions simply by solving the CSTR mole balance for X. For example, for the second-order liquid-phase reaction... 

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