Concentration units used expression

The conversion between concentration units and the expression of the units themselves can be confusing. We will now review the typical concentration units used in various environmental media. Concentration in water is usually given as mass per unit volume or moles per unit volume. The conversion between them is a straightforward application of molecular weights. For example, we have 2.0 g/m of CO2 dissolved in water. The molecular weight of carbon dioxide is 44 g/mole. Then the concentration in moles/m is... 

The value of the partition coefficient in this derivation, AT, is the ratio of the concentration of solute in the coating to the concentration of solute in the ambient (vapor) phase, with all concentrations being expressed in units of mass of solute per unit volume. Alternative expressions for the partition coefficient can be derived for concentration units of (moles of solute/coating volume) or (mass of solute/coating mass), or on a mole fraction basis. The value of K will be dependent on the concentration units used. For our purposes in the remainder of discussion, will refer specifically to the partition coefficient using the concentration units of mass per unit volume as described above. 

Let us first derive the units of the overall mass transfer coefficients when the concentration units used are in mole fractions. Let the overall mass transfer coefficient for the gas side be Kyf and that for the liquid side be K. Gd Y is mole of solute flowing per unit time. Mass transfer is a process where mass crosses an area perpendicular to the direction of motion of the solute particles. This area is the contact area for mass transfer. Let the differential area be designated as dA. Thus, in terms of mass transfer, Gd[Y] is equal to j,/([y/] - y )dA. From this expression, the dimensions of Kyf are mole per unit time per unit mole fraction per unit square area or MItImole fraction-1. In an analogous manner, Ld X is equal to ] -... 

Because of the inconvenient nature of the standard state defined above, the concentration units used to describe the concentration dependence of the chemical potential are usually different. More convenient choices for concentration are molality and molarity. When the solution is dilute the relationship between mole fraction and molality is quite simple (see equation (1.2.3)). In terms of molality, the expression for the concentration dependence of the chemical potential of component B becomes... 

Before leaving this section, one comment about the concentration units used should bp made. Molality, which we have used here. and indicated by.the symbol M, is concentration expressed as moles of solute per kilogram of solvent. Molarity, defined as the number of moles of solute per liter of solution, is also a commonly used concentration unit. However, because the volume of a solution varies with composition and with temperature, molarity can be more difficult to deal with than molality, which is... 

The quantity that changes most in example 1 is Ac neither S nor soluble substances considerable changes can occur in all expressions of supersaturation depending on the concentration units used, as seen in example 2 where [Pg.126]

Since the Debye-Hiickel method is limited to very dilute solutions, experimental methods must be invoked to find F for m > 10 molal. The derivations are largely patterned after Section 2.8. The use of emf methods for the same purpose is briefly dealt with below Eq. (4.7.2). Once again, the choice of P = 1 bar serves as the standard pressure in this case the activity coefficient F, introduced in Section 3.3 is appropriate. When molalities are used as concentration units the expression f serves the purpose. 

Transport of mass or diffusion of mass takes place in a fluid mixture of two or more species whenever there is a spatial gradient in the proportion of the mixture, that is, a concentration gradient. Consider a two-component or binary system, for example, a glass of water into which a drop of colored dye is injected. As is known from experience, the dye will diffuse outward from the point of injection where the concentration is highest compared to the other portions of the water where there is no dye. The transport of dye molecules is equal and opposite to the transport of the water molecules, and after a sufficient time, an equilibrium state is achieved with a uniform mixture of dye and water. In a solution or mixture, there are a variety of ways of defining concentration. The two basic concentration units used are mass concentration and molar concentration. Let a solution be made up of i number of species. The concentration parameters can be expressed in a variety of ways as follows ... 

In the older literature, C is the concentration in equivalents per liter. The volume of the solution in cubic centimeters per equivalent is equal to 1000/C, and A = 1000 k/C, the units employed in Table 8.32 cm equiv ]. The formula unit used in expressing the concentration must be specified ... 

The Henry s law constant for the solubility of radon in water at 30°C is 9.57 X 10-6 Mlmm Hg. Radon is present with other gases in a sample taken from an aquifer at 30°C. Radon has a mole fraction of 2.7 X 10-6 in the gaseous mixture. The gaseous mixture is shaken with water at a total pressure of 28 atm. Calculate the concentration of radon in the water. Express your answers using the following concentration units. 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

Equilibrium constants are dimensionless numbers, yet the concentrations used in an equilibrium constant expression have units. To understand this, we need to explore the reaction quotient Q, introduced in Chapter 14. In Section 16-1 we explore in detail the link between Q and Keq. Here we use Q to address the issue of concentration units and the equilibrium constant. 

In the preceding solvent extraction models, it was assumed that the phase flow rates L and G remained constant, which is consistent with a low degree of solute transfer relative to the total phase flow rate. For the case of gas absorption, normally the liquid flow is fairly constant and Lq is approximately equal to Li but often the gas flow can change quite substantially, such that Gq no longer equals Gj. For highly concentrated gas phase systems, it is therefore often preferable to define flow rates, L and G, on a solute-free mass basis and to express concentrations X and Y as mass ratio concentrations. This system of concentration units is used in the simulation example AMMONAB. 

Equation (88) is the expression used commonly for solutions of synthetic polymers, but, where the nature of adsorption and binding is of critical interest, alternative forms exist. These differ mainly in the modes of expressing concentration (e.g. activity, molality, molarity, mass/unit volume). Interrelations among the units and expressions have been presented very clearly by Timasheff and Townend15. ... 

There are many ways of expressing the relative amounts of solute(s) and solvent in a solution. The terms saturated, unsaturated, and supersaturated give a qualitative measure, as do the terms dilute and concentrated. The term dilute refers to a solution that has a relatively small amount of solute in comparison to the amount of solvent. Concentrated, on the other hand, refers to a solution that has a relatively large amount of solute in comparison to the solvent. However, these terms are very subjective. If you dissolve 0.1 g of sucrose per liter of water, that solution would probably be considered dilute 100 g of sucrose per liter would probably be considered concentrated. But what about 25 g per liter—dilute or concentrated In order to communicate effectively, chemists use quantitative ways of expressing the concentration of solutions. Several concentration units are useful, including percentage, molarity, and molality. 

Literature values of SPMD-water partition coefficients (iifswS) should be used with caution. Different units of Ks are generated when the concentrations in SPMD and water are expressed on a mass basis (e.g., ng g ) or a volume basis (e.g., ng mL ). Depending on the choice of concentration units, values will have units of g g mL mL or mL g or Ksv, values are given as dimensionless numbers in the former two cases. Care should be taken to distinguish between the different versions of Ksv,. Preferably, mL mL units should be used, because most of the equations for SPMD uptake kinetics use the volume of an SPMD rather than its mass. The two most frequently used versions of Ks are interrelated by... 

A = latm. The units of are (mL gas)/(LSWatm), giving [A(aq)] units of (mL gas)/G. SW). In this concentration unit, the gas abundance is expressed as the volume it would occupy if extracted from the seawater and subjected to STE Under these conditions, the gas s molar volume is 22,414 mL (assuming ideal gas behavior). Thus, gas concentrations expressed in units of can be converted to molarity and molinity (mol/kg) using the following ... 

The commonly used units of expression are explained in Table, 6-2. Expressing concentration data in micrograms per cubic meter facilitates relating ambient concentrations to emission. This practice is generally accepted as standard by the Environmental Protection Agency (epa) in the United States and similar agencies in other countries. 

The general population can be exposed to chemical substances in indoor as well as in outdoor (ambient) air via inhalation of vapors, aerosols, and dusts in the air. The term inhalation exposure is defined as the concentration of a substance in inhaled air at the boundary of the body, and is expressed as an average concentration per unit time (e.g., mg/m per day). In order to estimate a daily dose of a substance from the exposure concentration of the substance in the air, the inhalation rate is used. According to US-EPA (1997), the average daily dose (ADD) can be estimated from the exposure concentration by using the following equation ... 

The catalytic action of an enzyme, its activity, is measured by determining the increase in the reaction rate under precisely defined conditions—i.e., the difference between the turnover (violet) of the catalyzed reaction (orange) and uncatalyzed reaction (yellow) in a specific time interval. Normally, reaction rates are expressed as the change in concentration per unit of time (mol 1 s see p. 22). Since the catalytic activity of an enzyme is independent of the volume, the unit used for enzymes is usually turnover per unit time, expressed in katal (kat, mol s ). However, the international unit U is still more commonly used (pmol turnover min 1 U = 16.7 nkat). 

Concentration is the most common means for describing the composition of a solution in biochemistry. Enzyme kinetic expressions are typically expressed in these concentration units. Unless otherwise noted, this is the method used throughout this text. Nevertheless, other methods for describing compositions are utilized. For example, mole fractions are often used in Job plots. Gases in solution are commonly measured in terms of partial pressures. Below is a brief description of a few of these other conventions or methods. 

Of course, the equilibrium constant Km the latter equation does not have the same value as the ATin the equilibrium equation for ammonia. The numerical value of ATdepends on the particular reaction, the temperature, and the units used to describe concentration. For liquid solutions, the concentrations are usually expressed as molarity. For a mixture of gases, the concentration of each molecular species is commonly given either as molarity or as pressure in atmospheres. 

The amount of solute and solvent in a solution can be quantitatively expressed using numerous concentration units. The choice of a particular concentration unit depends largely on practice and convenience. We have probably all made solutions using recipes or directions that tell us to add so much water to a substance. In the field of chemistry, the most common concentration units are molarity, molality, percent by mass, and parts per. Each of these is defined here ... 

Concentrations of gaseous pollutants are often expressed in terms of parts per million (ppm) by volume, and time is expressed in minutes. Use of these concentration units must be reflected in the units used for the rate constants as well for example, second-order rate constants are in units of ppnt-1 min-1. Occasionally, gas concentrations are given in units of mol L-1 or in units of pressure such as Torr, atmospheres, or Pascals these can be converted to the more conventional units... 

In physical chemistry it is convenient to express concentrations as molalities and to use molality units to express the activity of the components. This is the convention we follow in this section. Accordingly, the standard state for a component consists of a solution in which that component has an activity of 1.0 mole (kg solvent) ... 

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