Volume-Based Concentration Units

Based on these ideas, the intrinsic viscosity (in 0 concentration units) has been evaluated for ellipsoids of revolution. Figure 9.3 shows [77] versus a/b for oblate and prolate ellipsoids according to the Simha theory. Note that the intrinsic viscosity of serum albumin from Example 9.1-3.7(1.34) = 4.96 in volume fraction units-is also consistent with, say, a nonsolvated oblate ellipsoid of axial ratio about 5. 

Note that the flux and the area A are based on unit reactor volume. This permits direct comparison between resistances during the course of a reaction because it remains constant. Propylene concentration is expressed in gmol per liter of gas, a number which is kinetically significant. The activity of the propylene contacting the catalyst surface is assumed to be proportional to its concentration at the surface, Cg. 

This assumes that the concentration at any value of x is not a function of radius. Ca is the concentration of reacting species A, u the mean convective velocity, which is assumed to be neither a function of axial or radial position, and Ta is the reaction rate of A based on unit volume. If nth-order power law kinetics pertain, i.e. 

Volume of first and second vessels Liquid volume Enzyme velocity constant Maximum enzyme velocity constant in unprotonated form Initial enzyme velocity constant Enzyme velocity constant based on unit volume of immobilised biocatalyst Maximum rate of reaction involving substance S Maximum rate of reaction involving substance P Specific rate of generation of biomass fraction Biomass concentration Initial or feed biomass concentration Average biomass concentration Concentration of prey Concentration of predator Biomass concentration at optimum dilution rate... 

As a first approximation a convective term in the film region has been negleted, u is the superficial gas velocity and u f denotes the gas velocity at minimum fluidization conditions. Tne specific mass transfer area a(h) is based on unit volume of the expanded fluidized bed and e OO is the bubble gas hold-up at a height h above the bottom plate. Mathematical expressions for these two latter quantities may be found in detail in (20). The concentrations of the reactants in the bubble phase and in film and bulk of the suspension phase are denoted by c, c and c, respectively. The rate constant for the first order heterogeneous catalytic reaction of the component i to component j is denoted... 

As a strong acid mixes with a strong base (i.e., titration), the pH of the solution changes with increasing amounts of a strong acid added to an initial volume of a strong base. The units for the mass balance equation should be moles, not moles/liter (i.e., concentration unit). Suppose a volume Vb of NaOH with concentration Cb is titrated with a volume Va of HC1 with concentration Ca. Then,... 

The correct answer is (D). Choices (A), (B), and (C) are all based on weights, which do not change with changes in temperature. Molarity, on the other hand, is a concentration unit comparing mass per unit of volume. Because volume is affected by changes in temperature, molarity will be affected by temperature increase. 

Hie concentration unit consistent with the conventional SI units for R is mol m-3. In that regard, the derivation of the Van t Hoff relation (Eq. 2.10) uses the volume of water, not the volume of the solution, so technically a unit based on molality is implied. However, the Van t Hoff relation is only an approximate representation of the osmotic pressure appropriate for dilute solutions, for which the numerical difference between molality and molarity is usually minor, as indicated in the text. Thus, molarity of osmotically active particles (= osmolarity) is suitable for most calculations and is generally more convenient (note that concentration in moles per m3 is numerically equal to ihm). 

Galai CIS-1000 is an on-line particle size analyzer. A bypass from the process line feeds the sample into the sensor unit where it is sized and either drained off or fed back to the line. Full compatibility with the laboratory instrument is maintained since it uses the identical combination of laser-based time-of-transit particle sizing using the 1001 sensor and dynamic shape analysis using the 1002 sensor. The size range covered is from 2 pm to 3600 pm with measurement of size, area, volume, shape, concentration and estimated surface area with a cycling time of 300 s. 

When the interfacial area is not known, mass transfer rates may be based on a unit volume rather than a unit of interfacial area. The resulting coefficients are the products of ka and /cl, as previously defined, and a, the interfacial area per unit volume. When concentration driving forces are used in defining fco and /cl, the products and ki a have the dimension sec. Some typical mass transfer data are shown in Table III. 

Because the extraction factor is a dimensionless variable, its value should be independent of the units used in Eq. (15-11), as long as they are consistently applied. Engineering calculations often are carried out by using mole fraction, mass fraction, or mass ratio units (Bancroft coordinates). The flow rates S and F then need to be expressed in terms of total molar flow rates, total mass flow rates, or solute-free mass flow rates, respectively. In the design of extraction equipment, volume-based units often are used. Then the appropriate concentration units are mass or mole per unit volume, and flow rates are expressed in terms of the volumetric flow rate of each phase. 

Percent concentration is the simplest concentration unit. The amount of solute is compared to the amount of solution in order to measure concentration. This concentration unit is generally used for concentrated solutions of acids and bases. The percentage of solute can be expressed by mass or volume. 

Penicillin G amidase was immobilized on pre-fabricated carriers or insolubUized as crosslinked crystals. Eupergit-related value for R (mean particle radius of swelled carrier) was 80 pm [87]. V , (assuming maximum intrinsic activity per accessible catalyst volume, based on active enzyme molecules 1 unit=l pmol min at 28°C) was 90 and 170 U cm for Eupergit C and 250L, respectively [87]. D ff (effective diffusion coefficient) was taken from literature [87] or calculated as shown in the text. Km (intrinsic Michaelis constant) was uniformly taken as 13 mM [87] and S = 268 mM corresponds to the substrate concentration at catalyst surface of a 10 % solution of penicillin G salt, q was calculated according to Atkinson et al. for spherical particles [85]. For simplification, surface and pore related indices have been omitted. 

The SI unit for concentration is moles per cubic meter (mol/m3). Mole (mol) is the base SI unit for the amount of substance. Cubic meter (m3) is a derived unit for volume. The use of regularly formed multiples such as cubic centimeter and cubic decimeter is also allowed. The special name liter (51) has been approved for use instead of cubic decimeter, but its use is restricted to the measurement of liquids and gases. 

The density of the solution is often needed for mass balance, flow rate, and product yield calculations. Density is also needed to convert from concentration units based on solution volume to units of concentration based on mass or moles of the solution. Density is defined as the mass per unit volume and is commonly reported in g/cm, however, other units such as pounds mass (Ibm)/ft and kg/m are often used. When dealing with solutions, density refers to a homogeneous solution (not including any crystal present). Specific volume is the volume per unit mass and is equal to 1/p. 

For example, if you dissolve 0.500 mol of Na2C03 in enough water to form 0.250 L of solution, the molarity of Na2C03 in the solution is (0.500 mol)/(0.250 L) = 2.00 M. Molarity is especially usefiil for relating the volume of a solution to the quantity of solute contained in that volume, as we saw in our discussions of titrations. — (Section 4.6) The molality of a solution, denoted m, is a concentration unit that is also based on moles of solute. Molality equals the number of moles of solute per kilogram of solvent ... 

Hence, the mass transfer equation (eq. 7.9-5a), when written in terms of the concentration based on unit solid volume, is given by ... 

Based on the demonstration, the concentrate accounts for 20% by volume of the contaminated groundwater influent stream to the filtration unit. The volume of concentrate generated each day and the range of costs for the three different flow rates are shown below for the bioremediation system and conventional disposal ... 

The choice of a concentration unit is based on the purpose of the experiment. The advantage of molarity is that it is generally easier to measure the volume of a solution, using precisely calibrated volumetric flasks, than to weigh the solvent, as we saw in Section 4.5. For this reason, molarity is often preferred over molality. On the other hand, molahty is independent of temperature, because the concentration is expressed in munber of moles of solute and mass of solvent. The volume of a solution typically increases with increasing temperature, so that a solution that is 1.0 M at 25°C may become 0.97 M at 45°C because of the increase in volume. This concentration dependence on temperature can significantly affect the accuracy of an experiment. Therefore, it is sometimes preferable to use molality instead of molarity. 

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