Quantitative Ways of Expressing Concentration

Concentration is the proportion of a substance in a mixture, so it is an intensive property, one that does not depend on the quantity of mixture present 1.0 L of 

---

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. 

LeChatelier s Principle is fundamental to understanding these relationships. A reaction is favored if the concentration of reactants is high and the concentration of products is low. The free energy relationships shown in this section are a quantitative way of expressing this qualitative observation. 

The concentration of a solution can be expressed either qualitatively or quantitatively. The terms dilute and concentrated are used to describe a solution qualitatively. A solution with a relatively small concentration of solute is said to be dilute one with a large concentration is said to be concentrated. Chemists use various ways to express concentration quantitatively, and we examine several of these next. 

A simple way of expressing the concentration dependence of the diffusion coefficient has been given above in eq. V -119. A more quantitative approach is based on the free volume theory. 

Freezing-point lowering is a colligative property. Colligative properties of solutions are properties that depend on the concentration of solute molecules or ions in solution but not on the chemical identity of the solute (whether it is ethylene glycol or urea, for instance). In the next sections, we will discuss several colligative properties, which are expressed quantitatively in terms of various concentration units. We will first look into ways of expressing the concentration of a solution. 

The role that acid and base catalysts play can be quantitatively studied by kinetic techniques. It is possible to recognize several distinct types of catalysis by acids and bases. The term specie acid catalysis is used when the reaction rate is dependent on the equilibrium for protonation of the reactant. This type of catalysis is independent of the concentration and specific structure of the various proton donors present in solution. Specific acid catalysis is governed by the hydrogen-ion concentration (pH) of the solution. For example, for a series of reactions in an aqueous buffer system, flie rate of flie reaction would be a fimetion of the pH, but not of the concentration or identity of the acidic and basic components of the buffer. The kinetic expression for any such reaction will include a term for hydrogen-ion concentration, [H+]. The term general acid catalysis is used when the nature and concentration of proton donors present in solution affect the reaction rate. The kinetic expression for such a reaction will include a term for each of the potential proton donors that acts as a catalyst. The terms specific base catalysis and general base catalysis apply in the same way to base-catalyzed reactions. 

You can describe the acidity of an aqueous solution quantitatively by stating the concentration of the hydronium ions that are present. [HsO" ] is often, however, a very small number. The pH scale was devised by a Danish biochemist named Spren Sorensen as a convenient way to represent acidity (and, by extension, basicity). The scale is logarithmic, based on 10. Think of the letter p as a mathematical operation representing -log. The pH of a solution is the exponential power of hydrogen (or hydroni-um) ions, in moles per litre. It can therefore be expressed as follows ... 

Intensity, or chroma, refers to the saturation of a color. A color is saturated when it reaches its maximum intensity. An artist lessens the intensity of a color by adding gray to dull it or by adding the complementary color on the color wheel. The artist is changing the concentration of colored particles in a solution. A chemist knows that a solution is saturated when no more solute can dissolve in a particular volume of a solvent. The chemist expresses solution concentration in a quantitative way. One way for a chemist to express the concentration of a saturated solution is grams of solute per 100 ml of solution. Another way to express the concentration is in moles of solute per liter of solution. In a colored saturated solution, the color is at maximum intensity. If the solution is not saturated, the color is less intense because there are fewer colored particles to bring to the eye the wavelengths that are colored. 

Before we begin considering shifts in an equilibrium system, we need a quantitative way to describe the state of the system at any time, whether it has established equilibrium or not. In Chapter 13, you learned about the reaction quotient, Q, which was used to describe equilibrium systems. In solubility equilibria, we re not really dealing with a quotient—-just a product. Because the expression is the product of the concentrations of two different ions, the equilibrium expression that describes solubility equilibria is known as the ion product. Q is calculated in the same way as K, except it does not necessarily describe a system at equilibrium. Referring to our initial example, for the equilibrium shown below... 

A possible way to increase the accuracy of this immersion approach is to use the slurry method and to analyse a weighed sample of the slurry in the bottom of the test-tube, instead of analysing the supernatant (Nunn etal., 1981). One then simply makes use of Equation (5.49), the operational expression of the relative surface excess of the solute with respect to the solvent. Here n1 and n2 are the total amounts of solute and solvent in the sample of slurry (either adsorbed or in solution) and c[ and c their concentrations in the solution. If one uses a liquid-solid ratio large enough to avoid any measurable change in concentration on adsorption, then c and c are simply the concentrations in the starting solution. The measurement is accurate provided the quantitative analysis of the slurry, which involves measuring the total amounts of 2 and 1... 

In the quantitative treatment of ion-exchange processes, several authors used the law of mass action. The main difference among these approaches is how the activities and surface concentration of the ions are treated. The first such approach was the Kerr equation, which uses the concentration of the ions on the solid and liquid as well but totally neglected the activity coefficients (Kerr 1928). The Vanselow (1932) equation applied activities in the solution and expressed the concentration of the ions on the solid phase in mole fraction, and in this way, it defined the selectivity coefficient (Equation 1.79). 

Risk characterization provides for both qualitative and quantitative descriptions of risk. The step involves integrating the results of the hazard identification, dose-response assessment, and exposure assessment to characterize risk. Often, a direct comparison between exposure criteria developed in the first two steps and the results of the exposure assessment (concentration in the environmental media or the estimated dose, as appropriate) provide a basis for determining whether risks are acceptable. Typically, if criteria are exceeded, the risk is not acceptable. What is defined as acceptable, as well as the way risk is expressed, is often a... 

Three ways of quantitatively expressing the concentration of a solution will be presented here Mass/mass percent, %(m/m), mass/volume percent, %(m/v), and molarity, M. A fourth, molality, will appear later in this chapter. You should know an interesting fact about concentrations. No matter what size sample of a solution you have, be it a teaspoonful or a bucketful, the concentration is the same for both. This is because concentrations are stated in terms of the amount of solute in a fixed amount of solvent 100 g, 100 mL, or 1.00 L. It s like density. The density of mercury is 13.6 g/mL. If I have 100 mL or three drops of mercury, the density of mercury is still 13.6 g/mL. Neither density nor concentration depends on the size of the sample. 

Air is ma.de up primarily of N2, O2, and Ar, which comprise 99.9% of dry air. There is a variable amount of water vapor, and many minor and trace gaseous components, as well as aerosol and particulate species. Table 26.1 lists some atmospheric gaseous components of environmental interest, along with representative concentrations in the troposphere. Typically, gaseous concentrations are expressed as mixing ratios, that is, volume/volume concentrations. A 1-ppm concentration represents 1 volume in 10 volumes of air. Such mixing ratios are independent of temperature and pressure. Environmental effects, though, may be quantitatively related to mass concentrations, and concentrations may be reported as mass per unit volume, usually mg/m of air, under specific conditions of temperature and pressure. Aerosols and particulates are reported in this way. 

Although the quantitative kinetic expressions for each of the three types of gel are different, they respond qualitatively in a similar way to most important variables. For all types or gels, gel times become shorter at higher temperatures, at higher concentrations, and in the presence of increasing concentrations of neutral salts. 

One can discuss this in a quantitative way by inserting appropriate expressions defining (f> - and Consider, for instance, the situation obtained with a noninteracting (l,l)-electrolyte of a concentration that is smaller than the bound-charge density. Then Eq. (34) simplifies to... 

In many cases in the Hterature, when experimental data are reported for the influence of the reaction rate or TOP on the cluster size the impact of mass transfer, internal diffosion is not discussed in particular. Intuitively, it can be anticipated that when the experimental observations are influenced by mass transfer, the reaction kinetics and thus cluster-size dependence should be less prominent. For the two-step sequence it is, however, worth to consider such dependence in a quantitative way. As discussed in the previous section, for the case of Langmuir adsorption and subsequent transformation of the adsorbed species, the plots for the catalyst effectiveness factor dependence of the Thiele modulus are available when the rate expression is given by v = kKC/ + KC) and the Thiele modulus rp is rp = L kKCs/ D 1 + KQ)), where Dg is the effective diffosion coefficient, Q is the concentration on the surface and L is the grain characteristic length (ratio of volume to surface area). When 3, the effectiveness factor is inversely proportional to the Thiele modulus and thus to the particle size. 

Alternatively, since r is the reciprocal of the sum of rate constants for all the processes undergone by the excited state, the reaction rate constant may be estimated if the others (e.g. for phosphorescence and intersystem crossing in the case of a triplet) are known from other studies. The most convenient way, however, of measuring t for a reaction that can be quenched is to carry out a quantitative quenching study at different quencher concentrations. In the most straightforward systems the results can be fitted to a straight-line plot expressed as < 1.16, where is the quantum yield in the absence of quencher, < > is the measured quantum yield at quencher concentration [Q], and is the rate constant for quenching. 

---