Volumetric concentrations, calculation

The molarity of the EDTA solution, MEDTA in Equation (5.52), can be known directly through its preparation with the use of an analytical balance and a volumetric flask. That is, one can purchase pure disodium dihydrogen EDTA and use it as a primary standard. In that case, the solution is prepared and the concentration calculated according to the discussion in Chapter 4 (see Section 4.3, especially Example 4.2, and Section 4.4.1). 

Devolatilization of Residual Toluene Residual toluene is continuously removed from a polymer melt stream of 454 kg/h at 230°C and 0.006 weight fraction of toluene, at a vacuum of 20 torr. The density of the polymer is 0.98 g/cm3, and the Florry-Huggins interaction parameter is yl2 = 0.43. (a) Calculate the equilibrium concentration, we- (b) If equilibrium is reached, that is, Wf = we, where uy is the final concentration, calculate the separation efficiency Fs = (wo — Wf)/wQ. (c) If the final concentration wy = 2we, calculate Fs- (d) Calculate for (c) the volumetric flow rate of the vacuum pump removing the volatiles. 

Volumetric analysis - calculating the concentration of a test substance... 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

Lee [86] examined earlier studies on cylinders in turbulent flow fields, and found in turbulent flow that the wake would decrease with increasing turbulence intensity, and then disappear, and the mean flow would behave in the same manner as for Stokes flow. He therefore proposed, and showed, that the drag on a particle in turbulent flow could be determined from a Stokes law with the molecular viscosity replaced by an effective viscosity calculated from the volumetric concentration of particles, the flow Reynolds number, the density ratio, and the Proude number. The Proude number, determining the ratio between the initial- and gravity forces, is defined as ... 

To predict the size distribution of a uniform aerosol coagulating in a chamber without deposition on the walls, the following procedure can be adopted The volumetric concentration of aerosol is assumed constant and equal to its (known) initial value. The change in the number concentration with time is calculated from (7.75). The size distribution at any time can then be determined for each value of u — < r /Woo front the relation n = (JV /0) (tj). using the tabulated values. The calculation is carried out for a range of values of t). 

In a qua.si-steudy State situation, the concentration of suspended matericil changes slowly with time. The sedimentation flux then represents the rate of loss of material from the volume of the chamber above unit area of floor. The results of the calculation of the volumetric concentration comptu-e well with the numerical computations of Lindauer and Castieman (1971) for long times. 

Figure 7.18. Dependence at 2(fC of calculated values of the average parameter on molar-volumetric concentration of dimethacrylate in bulk [Mq].

Volumes may be proportionally adjusted to smaller or larger volumetric flasks as required. Further dilution to prepare the intermediate solution is required. For the example preparation shown in Equation 23.1, a second dilution into another clean 250-mL PP, PMP, or PFA volumetric flask is required. Example volume and concentration calculations are shown in Equation 23.2 ... 

The calculated volumetric concentration of SA cosolvent in the RA vapor is quite low so that NVR after rinsing should be quite low. 

The balance of incoming and outgoing sohds to maintain a steady volume fluidized bed is readily calculated from the volumetric concentrations of the incoming suspension and the fluidized bed. Sohds are removed by withdrawing excess fluidized bed material (e.g. floe blanket) over a slimy weir or into a concentrator cone at the surface of the fluidized bed (zone of separation into the clear liquid zone). In the examples calculated above ... 

Establish wash-water requirement from volumetric balance calculations and make sure that each underflow has enough liquid to carry the solids, with the highest sohds concentration at the end of the train ... 

To summarize the model calculation, the concentrations of each species (reactant and products) in the bed are calculated using Eqs. (20) and (21). Equation (23) is used to calculate the concentration profiles of each species in the upper dilute region. The total gas flow rate can be calculated by addition of the molar flows of each species at any given axial location within the bed. The total flow rate can be converted to the volumetric gas flow rate, and the superficial gas velocity may be determined using Eqs. (24) and (25). The values for hydrodynamic parameters are then calculated for the obtained gas velocity and the set of equations is solved numerically. Figure 27 shows the axial profiles of butane and maleic anhydride concentrations calculated based on the model equations. The effects of fine particle (<7p < 45 pm) contents on butane conversion are also predicted as shown in Fig. 28. As surmised from the figure, the content of fine particles affects fluidization properties and reactor conversion. 

Calculate the fall velocity for the single particle and the fall velocity if the volumetric concentration of particles is increased to 20%. 

Consider a 20" OD pipe with a wall thickness of 0.375", rubber lined with a rubber thickness of 14". The internal diameter of the pipe would be Dj= [20 - 2(0.375+0.25)] = 18.75" or 477 mm. The cross-sectional area of the pipe would be 0.178 m and the average flow speed of the slurry would be calculated as E= 0.453/0.178 = 2.55 m/s. Applying the Thomas-Einstein equation to the volumetric concentration of 8.7% gives an... 

For bimodal mixtures (mixtures of fine and coarse particles), the Saskatchewan Research Council (SRC) (2000) suggested that the effects of the fines on the viscosity of the carrier liquid should be used to calculate the apparent viscosity jjuj, However, the actual density of the liquid should be used without corrections for volumetric concentration of fines. 

Fig. 19. Experimental and calculated extinction velocity gradients versus volumetric concentration of CH in methane-air mixtures (without additives and doped with 0.12% TMP) the solid curves are extrapolations of the experimental data, and the dashed curves are extrapolations of the calculation data...

Fig. 20. Experimental and calculated upper and lower flammability concentration limits of methane-air mixtures versus volumetric concentration of TMP.

The calculated kinetic curves were obtained at integration the presented system of differential Eqs. (l)-(4) by the Runge-Kutta4th order method using mathematical program package Mathcad 2000 Professional. For convenience of calculation, we have converted molar-volumetric concentrations of components to relative current concentrations X.=... 

Volumetric Concentration of Oxygenates—If the volumetric concentration of each oxygenate is desired, calculate the volumetric concentration according to Eq 14 ... 

Suppose each of the following solutions is diluted to a final volume of 1.00 L in a volumetric flask. Calculate the new concentration of each solution. 

Freshly opened bottles of these reagents are generally of the concentrations indicated in the table. This may not be true of bottles long opened and this is especially true of ammonium hydroxide, which rapidly loses its strength. In preparing volumetric solutions, it is well to be on the safe side and take a little more than the calculated volume of the concentrated reagent, since it is much easier to dilute a concentrated solution than to strengthen one that is too weak. 

Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mF of water measured with a graduated cylinder. This solution is quantitatively transferred to a 250-mF volumetric flask and diluted to volume. Calculate the concentration of this second solution to the correct number of significant figures. 

A standard solution of Mn + was prepared by dissolving 0.250 g of Mn in 10 ml of concentrated HNO3 (measured with a graduated cylinder). The resulting solution was quantitatively transferred to a 100-mL volumetric flask and diluted to volume with distilled water. A 10-mL aliquot of the solution was pipeted into a 500-mL volumetric flask and diluted to volume, (a) Express the concentration of Mn in parts per million, and estimate uncertainty by a propagation of uncertainty calculation, (b) Would the uncertainty in the solution s concentration be improved... 

The vitamin B12 content of a multivitamin tablet is determined by dissolving ten tablets in water. The dissolved tablets are transferred to a 100-mL volumetric flask and diluted to volume. A 50.00-mL portion is removed and treated with 0.500 mg of radioactive vitamin B12 having an activity of 572 cpm. After homogenization, the vitamin B12 in the sample is isolated and purified, producing 18.6 mg with an activity of 361 cpm. Calculate the average concentration of vitamin B12 in the tablet (in milligrams per tablet). 

Fuel economy is measured usiag a carbon balance method calculation. The carbon content of the exhaust is calculated by adding up the carbon monoxide (qv), carbon dioxide (qv), and unbumed hydrocarbons (qv) concentrations. Then usiag the percent carbon ia the fuel, a volumetric fuel economy is calculated. If the heating value of the fuel is known, an energy specific fuel economy ia units such as km/MJ can be calculated as well. 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

This program helps calculate the rate of methanol formation in mol/m s at any specified temperature, and at different hydrogen, carbon monoxide and methanol concentrations. This simulates the working of a perfectly mixed CSTR specified at discharge condition, which is the same as these conditions are inside the reactor at steady-state operation. Corresponding feed compositions and volumetric rates can be calculated from simple material balances. 

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