Units, of concentration

In addition to the definitions concerning states of matter that find daily usage in the vocabulary of the IH, other terms used to describe degree of exposure include the following  

Before we consider topics such as the design of an assay, calculation of drug purity, and so on, it is useful to revise the units and terms chemists use for amount of substance and concentration. The fundamental unit of quantity or amount of substance used in chemistry is the mole. The mole is the amount of a substance (either elements or compounds) that contains the same number of atoms or molecules as there are in 12.0000 g of carbon-12. This number is known as the Avogadro number (after Amedeo Avogadro, an Italian chemist) or Avogadro s constant, and has the value 6.02 X 1023. When this amount of substance is dissolved in solvent (usually water) and made up to 1 litre, a 1 molar (1 m) solution is produced. In a similar way, if one mole of substance were made up to 2 litres of solvent, a 0.5 m solution would result, and so on. The litre is not the SI unit of volume but, along with the millilitre (mL), is still used in the British Pharmacopoeia. 

In pharmaceutical analysis laboratories, concentration is usually expressed as (for example) 1 m (1.026) or 0.5 m (0.998). The nominal concentration is given as molarity, while the number in brackets refers to the factor (f) of the solution. The factor of a volumetric solution tells you by how much the given solution differs from the nominal, or desired strength. 

The first solution, above, is slightly stronger than 1 m, since the factor is greater than 1.000. The second solution is slightly weaker than half molar, as the factor is less than 1.000. It follows that a solution with a factor of 1.000 is of precisely the stated molarity 

If the absolute molarity of the solution is required, it can easily be found by multiplying the factor and the nominal molarity. For instance, in the examples above, the first solution has an absolute molarity of 1m X 1.026 = 1.026 M, which as predicted above is slightly stronger than 1 m. Similarly, the second solution has an absolute molarity of 0.499 m (i.e. 0.5 m X 0.998). It follows from this that the factor of a solution is simply the ratio 

Factors are used in volumetric analysis because they simplify calculations (a laudable aim, in any subject). Consider the first solution above the strength of the solution is 1 m (1.026). If 10 mL of this solution were removed, by pipette, transferred to a 100 mL volumetric flask, and made up to volume with water, the resulting solution would have a concentration of 0.1 M (1.026). The original solution has been diluted tenfold, but the factor of the new solution remains as 1.026. This illustrates an important principle, namely, that once a factor has been determined for a volumetric solution, subsequent dilution or reaction will not affect it (although see later for an exception to this). 

---

Although the terms solute and solution are often associated with liquid samples, they can be extended to gas-phase and solid-phase samples as well. The actual units for reporting concentration depend on how the amounts of solute and solution are measured. Table 2.4 lists the most common units of concentration. 

Normality is an older unit of concentration that, although once commonly used, is frequently ignored in today s laboratories. Normality is still used in some handbooks of analytical methods, and, for this reason, it is helpful to understand its meaning. For example, normality is the concentration unit used in Standard Methods for the Examination of Water and Wastewaterf a commonly used source of analytical methods for environmental laboratories. 

Molality is used in thermodynamic calculations where a temperature independent unit of concentration is needed. Molarity, formality and normality are based on the volume of solution in which the solute is dissolved. Since density is a temperature dependent property a solution s volume, and thus its molar, formal and normal concentrations, will change as a function of its temperature. By using the solvent s mass in place of its volume, the resulting concentration becomes independent of temperature. 

The units of concentration most frequently encountered in analytical chemistry are molarity, weight percent, volume percent, weight-to-volume percent, parts per million, and parts per billion. By recognizing the general definition of concentration given in equation 2.1, it is easy to convert between concentration units. 

In the polymer literature each of the five quantities listed above is encountered frequently. Complicating things still further is the fact that a variety of concentration units are used in actual practice. In addition, lUPAC terminology is different from the common names listed above. By way of summary, Table 9.1 lists the common and lUPAC names for these quantities and their definitions. Note that when

[Pg.593]

Concentration. The basis unit of concentration in chemistry is the mole which is the amount of substance that contains as many entities, eg, atoms, molecules, ions, electrons, protons, etc, as there are atoms in 12 g of ie, Avogadro s number = 6.0221367 x 10. Solution concentrations are expressed on either a weight or volume basis. MolaUty is the concentration of a solution in terms of the number of moles of solute per kilogram of solvent. Molarity is the concentration of a solution in terms of the number of moles of solute per Hter of solution. 

The H in solubility tables (2-121 to 2-144) is the proportionahty constant for the expression of Henry s law, p = Hx, mere x = mole fraction of the solute in the liqiiid phase p = partial pressure of the solute in the gas phase, expressed in atmospheres and H = a. proportionality constant expressed in units of atmospheres of solute pressure in the gas phase per unit concentration of the solute in the hquid phase. (The unit of concentration of the solute in the liquid phase is moles solute per mole solution.)... 

Conversion Factors between Volume and Mass Units of Concentration (25°C, 760 mm Hg)... 

Finally, the fundamental unit of concentration obtained by RBS is in atoms/cm or concentration in the sample-versus-bachscattering energy loss. To convert the profile of a backscattering peak into a depth profile it is necessary to assume a density for the material being profiled. For single-element films, such as Si, Ti, and W, an elemental density can be assumed for the film and an accurate thickness is obtained. In the case of multi-elemental films with an unknown density, a density for the film is calculated by summing the density of each element, normalized to its concentration. The accuracy of this assumption is usually within 25%, but for some cases the actual density of the film may vary by as much as 50%— 100% from the assumed density. It is useful to note that ... 

To design an air recirculation system it is necessary to know the performances of fans, air cleaners, and exhaust hoods included in the current system. The equations described here include the source generation rate and the total airflow rate through the room, which could be difficult to measure. The ratio between source rate and flow rate has the unit of concentration and should in fact be equal to the concentration without recirculation. The equations could thus be transformed to include the contaminant concentration without recirculation instead of this ratio. In this way a direct comparison between concentration without and with recirculation is possible. By using the described equations it is then possible to design an air recirculation system to result in the demanded concentration in a workroom. 

The rate is proportional to the concentrations of both A and B. Because it is proportional to the product of two concentration terms, the reaction is second-order overall, first-order with respect to A and first-order with respect to B. (Were the elementary reaction 2A P + Q, the rate law would be = A[A] second-order overall and second-order with respect to A.) Second-order rate constants have the units of (concentration) time) as in M sec. ... 

Notice that reaction rate has the units of concentration divided by time. We will always express concentration in moles per liter. Time, on the other hand, can be expressed in seconds, minutes, hours.A rate of 0.10 mol/L - min corresponds to... 

Dissociation constant, the ratio of the rate of offset of ligand away from a receptor divided by the rate of onset of the ligand approaching the receptor. It has the units of concentration and specifically is the concentration of ligand that occupies 50% of the total number of sites available for ligand binding at equilibrium (see Affinity). 

Where the molecular weight of a substance is not definitely known, it is obviously not possible to write down the molecular absorption coefficient, and in such cases it is usual to write the unit of concentration as a superscript, and the unit of length as a subscript. Thus... 

The form using molality [equation (7.34)] as the unit of concentration is the one most commonly encountered. It is often written as / (instead of /m). 

Although many industrial reactions are carried out in flow reactors, this procedure is not often used in mechanistic work. Most experiments in the liquid phase that are carried out for that purpose use a constant-volume batch reactor. Thus, we shall not consider the kinetics of reactions in flow reactors, which only complicate the algebraic treatments. Because the reaction volume in solution reactions is very nearly constant, the rate is expressed as the change in the concentration of a reactant or product per unit time. Reaction rates and derived constants are preferably expressed with the second as the unit of time, even when the working unit in the laboratory is an hour or a microsecond. Molarity (mol L-1 or mol dm"3, sometimes abbreviated M) is the preferred unit of concentration. Therefore, the reaction rate, or velocity, symbolized in this book as v, has the units mol L-1 s-1. 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

By custom, the units of concentration are always included in the units of rate constants but are customarily omitted for equilibrium constants. Problem 7-15 provides further insights. 

Some of the most important information about a mechanism comes from experiments that determine how fast a chemical reaction occurs under various conditions. In chemical reactions, amounts of reactants and products change, so reaction rates are given in units of amount per unit time for example, molecules per second. Amounts also can be expressed as concentrations, so rates can be measured in units of concentration per unit time for example, molar per minute. 

Rates of reaction have units of (concentration) (time)". Because time does not appear in any other term on the right-hand side of the rate law, the units of k must always include time in the denominator. The concentration... 

C17-0032. Draw a molecular picture of the carbonic acid solution of Example, with one molecule for each 0.01 M unit of concentration, showing how the solution looks after the addition of three hydroxide ions. 

Several terms have been used to define LOD and LOQ. Before we proceed to develop a uniform definition, it would be useful to define each of these terms. The most commonly used terms are limit of detection (LOD) and limit of quantification (LOQ). The 1975 International Union of Pure and Applied Chemistry (lUPAC) definition for LQD can be stated as, A number expressed in units of concentration (or amount) that describes the lowest concentration level (or amount) of the element that an analyst can determine to be statistically different from an analytical blank 1 This term, although appearing to be straightforward, is overly simplified. If leaves several questions unanswered, such as, what does the term statistically different mean, and what factors has the analyst considered in defining the blank Leaving these to the analyst s discretion may result in values varying between analysts to such an extent that the numbers would be meaningless for comparison purposes. 

Because for now we are concerned only with equilibrium conditions and not with the rate at which equilibrium is reached, we can combine k and k x to form a new constant, KA = MM which has the unit of concentration. KA is a dissociation equilibrium constant (see Appendix 1.2A [Section 1.2.4.1]), though this is often abbreviated to either equilibrium constant or dissociation constant. Replacing k and k gives ... 

Both molarity (Chap. 10) and normality (Chap. 15) are defined in terms of a volume. Since the volume is temperature-dependent, so are the molarity and normality of the solution. Two units of concentration that are independent of temperature are introduced in this chapter. Molality is defined as the number of moles of solute per kilogram of solvent in a solution. The symbol for molality is m. Note the differences between molality and molarity ... 

Solubilities may be expressed in any appropriate units of concentration, such as the quantity of the solute dissolved (weight or number of moles) divided by the... 

Material, Units of Concentration, and Other Variables Concentration9 Referenceb... 

---