Mass- and Volume-Based Concentration Units

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

In the above equalitms, Kl is the overall mass transfer coefficient (based on phase L), a is the specific interfacial area for mass transfer related to unit column volume, X and Y are the phase solute concentrations, X is the... 

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... 

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. 

It is obvious that a consistent system for the description of concentrations in the gas phase is necessary. Usually, fractional or percentage concentrations are used. Mixing ratios of low concentrated volatile compounds and gases are based on the parts per... unit system. This unit is obsolete but is still used in the current literature. It cannot be utihzed for particle concentrations. Therefore, the WHO (1999) has adopted a mass per volume system with concentrations [C] in mgm . Other units frequently employed to express the concentration of gases include moles per volume or molecules per volume (vanLoon and Duffy, 2000, Kurzweil, 1999). 

Consider an analytical method involving the titration of hydrochloric acid with anhydrous sodium carbonate to determine the concentration of the acid. The measurements made are mass (weighing out a chemical to make up a solution of known concentration) and volume (dispensing liquids with pipettes and burettes). The reaction between the two chemicals is based on amount of substance - one mole of sodium carbonate reacts with two moles of hydrochloric acid - and the mass of a mole is known (e.g. the formula weight in grams of one mole of sodium carbonate is 105.99). All the measurements are based on either length or mass and are traceable to SI units, so the method is a primary method. 

Now, invent a parameter a that defines the area of interfacial area per unit bulk volume of the mass transfer destination medium and form the expression K a [x ] - [x]). The dimension of A a([x ] - [x]) is now mass per unit time per unit volume or M/t L, where M is the dimension of mass, t is the dimension of time, and L is the dimension of length. From this expression, the dimension of K a is per unit time or 1/t. It will be shown later in this section on absorption towers, however, that the dimensions of K/i will not be Ht if mole fraction units are used for the concentrations. Both and K/i are also called overall mass transfer coefficients based on the liquid side. The corresponding overall mass transfer coefficients based on the gas side are Ky and KyO, respectively. 

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. 

The total mass of particulate matter per unit volume of air is perhaps the simplest integral property, and it is on this quantity that U.S. federal standards for particulate pollution have been based. Until recently there was a single primary (health related) standard of 50 g/m (annual geometric mean) and 150 /rg/m- (maximum 24-hr concentration not to be exceeded more than once per year), with an upper cutoff in panicle size of 10 /ttm (PMio). However, epidemiological studies indicate an association between adverse health effects, including enhanced mortality, and submicron aerosol concentrations in many U.S. cities (Pope cl al.. 1995). This has led to the establishment of an additional mass ba.sed standard for particles smaller than 2.5 /im (PMj.j) (U.S. EPA, 1996). There is also a separate health-based standard for lead, one component of the atmospheric aerosol. 

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. 

Primes or subscripts could be used to identify rate constants based on a unit mass of catalyst or on a unit volume of catalyst and those based on partial pressure or on concentration of reactant, but this notation would be cumbersome and perhaps confusing. In most cases, a simple k denotes the kinetic constant, but the units must be carefully checked for consistency. In the Thiele modulus, k must be expressed in sec, [Eq. (4.23)] but once 4> and r] are evaluated, other definitions of k can be used, as in Eq. (4.33). 

From a health and policy perspective, a mass metric does not adequately describe exposure to UFP. The number or surface area of particles per unit volume may be a better metric. However, at this time, only limited exposure data based on number concentration exists and no number concentration based ambient standards have been established. Further, there is no consensus yet as to whether size, chemical composition, or some combination thereof provides the best measure of UFP toxicity. 

The two base quantities (and their associated SI units) that are most important for quantitative chemical analysis are amount of substance (mole) and mass (kilogram), although length (meter) is also important via its derived quantity volume in view of the convenience inirodnced by our common use of volume concentrations for liquid solutions. (Note, however, that the latter will in principle vary with temperature as a result of expansion or contraction of the liquid). 

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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