Expressing Concentration

Several different methods of expressing concentration are commonly used in various branches of water chemistry and it is appropriate to present these here. This discussion will also provide definitions and methods of calculation that will be useful in the later chapters of this book, 

There are two basic ways to express the mass concentration of dissolved species (solutes) in solution. The first is to state concentration in units of mass of solute in a unit volume of solution—the so-called w/v (weight/ volume) basis, The second is a w/w basis, that is, weight of solute in a given weight of solution. Both of these methods of expressing concentration are widely used in water chemistry. For example, the units mg/liter and ppm (parts per million) are, respectively, the w/v and w/w units most often used to express the concentration of various materials in waters and wastewaters. They can be interconverted if the density of the solution is known. 

If the density of the solution is unity, these two methods of concentration expression are identical, that is, 

For waste waters and mgs ngtu gl o s (with the exception of seawater and brines), we ononol the as iryg n thoH  

In both types of concentration expression the mass component of the concentration term can take a variety of forms. The simplest form is when specific components of a solution are expressed in terms of the specific components themselves, for example, if we were to analyze a solution of ammonium nitrate (NH4NO3) for ammonium ion (NH4 ) and for nitrate ion (NOs ) and find that 100 ml of solution contained 36 mg NH4 and 124 mg NO3 , we could compute that the solution contains  

---

Both molarity and formality express concentration as moles of solute per liter of solution. There is, however, a subtle difference between molarity and formality. Molarity is the concentration of a particular chemical species in solution. Formality, on the other hand, is a substance s total concentration in solution without regard to its specific chemical form. There is no difference between a substance s molarity and formality if it dissolves without dissociating into ions. The molar concentration of a solution of glucose, for example, is the same as its formality. 

The relative amount of a constituent in a sample is expressed as its concentration. There are many ways to express concentration, the most common of which are molarity, weight percent, volume percent, weight-to-volume percent, parts per million, and parts per billion. Concentrations also can be expressed using p-functions. 

Whereas there is sometimes confusion in how concentrations of aqueous solutions of hydrazine ate expressed, concentrations of wt % N2H4 ate used herein. In many parts of the wodd, however, concentrations ate often expressed in terms of wt % hydrazine hydrate, N2H4 -H2 O. Hydrazine hydrate is 64 wt % N2H, 36% H2O. The correlation between the two systems is therefore ... 

The differential rate equations of a complex reaetion, expressing rates as functions of concentrations, are usually simpler in form than are the corresponding integrated equations, whieh express concentrations as funetions of time moreover, it is always possible to write down the differential rate equations for a postulated kinetie seheme, whereas it may be difficult or impossible to integrate them. Of course, we usually measure concentration as a funetion of time. If, however, we can measure rates, we may use the differential equations directly. 

To avoid the cumbersome use of negative exponents to express concentrations that range over 14 orders of magnitude, S0rensen, a Danish biochemist, devised... 

Note There are many different tests and different versions of the same test for water analysis. If there is any doubt as to method or interpretation consult a reputable water-treatment supplier. The letters ND in the table indicate not detectable. Parts per million (ppm) are also commonly used to express concentration and are essentially identical to mg/l. 

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... 

To indicate the composition of a particular solution we must show the relative amounts as well as the kind of components. These relative amounts chemists call concentrations. Chemists use different ways of expressing concentration... 

For many purposes, especially when dealing with small concentrations, it is cumbersome to express concentrations of hydrogen and hydroxyl ions in terms of moles per litre. A very convenient method was proposed by S. P. L. Sorensen (1909). He introduced the hydrogen ion exponent pH defined by the relationships ... 

For expressing concentrations of reagents, the molar system is universally applicable, i.e. the number of moles of solute present in 1 L of solution. Concentrations may also be expressed in terms of normality if no ambiguity is likely to arise (see Appendix 17). 

If one phase is a gas, as in gas absorption for example, it is often more convenient to express concentrations as partial pressures in which case ... 

The composition of a solution can vaiy, so we must specify the concentrations of solutes as well as their identities. There are several ways to express concentration, each having advantages as well as limitations. Any concentration value is a ratio of amounts. The amount of one component, usually a solute, appears in the numerator, and some other amount, describing either the solvent or the total solution, appears in the denominator. 

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. 

We remember that neither solids, such as Ca5(P04)30H(s), nor liquids, such as H20(1), appear in the equilibrium constant expression. Concentrations of products appear in the... 

The table includes most of the methods of expressing concentration that are in current... 

Some analysts prefer to work with equivalents rather than moles. In that case, the normality method of expressing concentration is used and the equivalent weight is needed, rather than the formula weight. The equivalent weight of one substance reacts with the equivalent weight of the other substance. In other words, the reaction is always one-to-one one equivalent of one substance always reacts with one equivalent of the other. Thus, we can write the following as a true statement at the equivalence point of the titration ... 

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. ... 

Remember from Chapter I that the electrochemist often expresses concentration in units of mol cm rather than mol dm. ... 

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. 

Where C is a matrix of component concentrations or sample properties, S is a matrix of basis vectors (pure component spectra, or spectral profiles reflecting a pure sample property), and E and Ec are model residuals. The direct model expresses the analyzer responses (X) as a function of concentrations, whereas the inverse model expresses concentrations as a function of the analyzer responses. Because the former is more in line with the Beer-Lambert Law (absorbance = concentration x absorptivity), it is given the label direct . 

Ct - A means of expressing concentration as a convenient mechanism for establishing an exposure mechanism. Specifically, it is the product of airborne concentration of aerosolized diesel fuel (mg/m ) and duration of exposure (hours). 

It is quite common practice to express concentrations as a ratio, using the parts per method of describing the ratio. Thus, in soil the ratio is simple, 1 ng/g, or (10 9 g/g), is a ppb, or one part per billion5. In water or air, the issue is a bit more complex since it is necessary to reconcile the units of mass per unit volume to units of mass per unit mass. We make this reconciliation by dividing by the density of the fluid. For water this is, for purposes of this book, taken as... 

Molality a way to express concentration of a solution, moles of solute per kilogram of solvent... 

Parent in a nuclear reaction the original substance that emits some form of radiation Partial Pressure pressure exerted by an individual gas in a mixture of gases Parts Per MUlion way to express concentration by giving the number of units of mass or volume out of one million units of mass or volume... 

Finally, it is important to remember that the number of molecules, or volumes, of a given gaseous species forms the basis of units in atmospheric chemistry in water chemistry, mass rather than volume is used as the basis for expressing concentrations in ppm, and so on. 

Percent solution is another common way to express concentration. The precise units of percent solution typically depend on the phase of each component. For solids dissolved in liquids, mass percent is usually used ... 

You can use the dilution equation with any units of concentration, provided you use the Scime units throughout the calculation. Because molarity is such a common way to express concentration, the dilution equation is sometimes expressed in the following way, where Mj and refer to the initial and final molarity, respectively ... 

There are numerous ways of expressing concentration in diffusion problems, the most important for our purposes being mass density, molar density, mass fraction, and mole fraction. The chemical engineer and the chemist are familiar with the relationships between these quantities. Table I is given for the sake of summarizing the notation used here. 

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) ... 

Now let us turn our attention to the osmotic pressure generated by the macroion in this system. Since we have already restricted ourselves to dilute solutions, it is adequate for our purposes to use Equation (35), making allowance for the fact that we have been expressing concentrations as molality in this section. The volume of 1 kg of solvent equals 1000 Vx°/Mx, so Equation (35) becomes... 

---