Concentration unit

Concentrations of dissolved solutes are expressed based on volume or by weight. The most common method is to express on volume basis. 

Molarity (M). Number of moles of solute per liter of solution (1,000 mL) 

Normality (N). Number of equivalents of solutes per liter of solution Equivalents of solute. Weight (g) of solute/equivalent weight (EW) of the solute, where EW = MW/n n = number of H+ (for acids) and OH (for bases) per molecule of oxidation-reduction reactions, number of electrons gained per molecule. 

Mole fraction is defined as the ratio of the number of moles of a compound to the total number of moles of all compounds. 

The concentration of ions dissolved in water is expressed in a variety of ways  

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Weight per volume. The units most commonly used are milligram per liter (mg/1), for major ions, and microgram per liter (pg/1), for trace elements. For example, data for groundwater from the Uriya 3 well are given in Table 5.2 in weight per volume units. 

Ionic equivalence units. The number of anions in solution always equals the number of dissolved cations. Interactions of aqueous solutions with rocks always end up in ionically balanced solutions. Thus for the discussion of chemical processes it is most meaningful to express chemical data in ionic equivalence units, or equivalents  

The data needed to calculate the equivalents of common ions are given in Table 5.1. Equivalent units are too large for convenient use for common waters, and therefore the milliequivalent (meq) unit is used lmeq of Na+ = 23 mg, and 1 meq of SO4- = 48 mg. Milliequivalent units are applied per volume units, as in meq/1, or per weight units, as in meq/g. 

A wide range of units is commonly used to express solution concentration, and confusion often arises in the interconversion of one set of units to another. Wherever possible throughout this book we have used the SI system of units. Although this is the currently recommended system of units in Great Britain, other more traditional systems are still widely used and these will be also described in this section. 

Consider the simple example of a solution of acetonitrile in water formed by mixing 10 g of acetonitrile with 90 g of water. The concentration of acetonitrile can be simply stated as 10% by weight. Another way of expressing the concentration is in terms of the relative number of moles of these molecules. Given that the molecular mass of acetonitrile is 41.04g, the number of moles of acetonitrile Hg used to form the solution is 10.000/41.04 = 0.2437. The corresponding number of moles of water is 90.000/18.02 = 4.9945 where 18.02 is its molecular mass. Thus, one may express the concentration as the mole fraction, xg, of acetonitrile where 

Another commonly used concentration unit in physical chemistry is molality. It is defined as the number of moles of component B per 1000 g of pure component A, which is regarded here as the solvent. In the present case, the molality is 

2437 X 1000/90 = 2.708 m. This is still a weight/weight ratio but has units of 

For example, a 0.02 m solution of acetonitrile in water corresponds to a mole fraction xb equal to 3.6 x 10 .  

The concentration unit used for analysis is molarity, that is, the number of moles of solute per liter of solution. It should be noted that the molarity involves a weight/volume ratio, and that the volume involved is that of the total solution. In order to determine the molarity of the system being considered here, one must know the density of the solution. In general, this property cannot be determined from the densities of the individual components but must be found in an independent experiment. The density of acetonitrile-water solutions as a function of the weight fraction of acetonitrile is shown in fig. 1.1. From these data one finds that the density of the solution made of 10 g acetonitrile and 90 g water is 0.979 g mL at 25°C. Thus, the volume of the same solution is 102.15 mL and the corresponding molarity, 0.2437/0.10215 = 2.386 M. The relationship between the molarity cb and mole fraction xb is 

We learned in Chapter 4 that chemists often express concentration of solutions in units of molarity. Recall that molarity, M, is defined as the number of moles of solute divided by the number of liters of solution [M4 Section 4.5], 

In this section, we will learn about molality and percent by mass, two additional ways to express the concentration of a mixture component. How a chemist expresses concentration depends on the type of problem being solved. 

Molality (m) is the number of moles of solute dissolved in 1 kg (1000 g) of solvent  

For example, to prepare a 1 molal (1 m) aqueous sodium sulfate solution, we must dissolve 1 mole (142.0 g) of Na2S04 in 1 kg of water. 

The major goal of this chapter is to help you master the concepts associated with solutions—concentration units, solubility, and especially colligative properties. We will also examine the properties of colloids. If you are still unsure about calculations and the mole concept, review Chapters 1,3, and 4. And again, the only way to master these concepts is to Practice, Practice, Practice. 

A solution is a homogeneous mixture composed of solvent and one or more solutes. The solvent is normally the substance present in the greatest amount. The solute is the substance that is present in the smaller amount. If water is the solvent, it is an aqueous solution. You may have more than one solute in a solution. 

Some substances will dissolve in a particular solvent and others will not. There is a general rule in chemistry that states like dissolves like. Polar substances (such as alcohols) will dissolve in polar solvents like water. Nonpolar solutes (such as iodine) will dissolve in nonpolar solvents such as carbon tetrachloride. The mass of solute per 100 mL of solvent (g/100 mL) is a common alternative to expressing the solubility as molarity. It is necessary to specify the temperature because the solubility of a substance will vary with the temperature. The solubility of a solid dissolving in a liquid normally increases with increasing temperature. The reverse is true for a gas dissolving in a liquid. 

A solution containing the maximum amount of solute per given amount of solvent at a given temperature is a saturated solution. An unsaturated solution has less than that maximum amount of solute dissolved. Sometimes, there may be more that that maximum amount of solute, resulting in a supersaturated solution. Supersaturated solutions are unstable and eventually expel the excess solute, forming a saturated solution. 

There are many ways of expressing the relative amounts of solute(s) and solvent in a particular solution. The terms saturated, unsaturated, and supersaturated discussed above give a qualitative measure of solubility, as do the terms dilute and concentrated. Dilute refers to a solution that has a relatively small amount of solute in comparison to the amount of solvent. Concentrated refers to a solution that has a relatively large amount of solute in comparison to the solvent. These terms are very subjective and chemists prefer to use quantitative 

If you follow the dimensional analysis techniques you learned in Chapter 1, you can convert between concentration units, as shown in Sample Exercise 13.5. To convert between molality and molarity, the density of the solution will be needed, as in Sample Exercise 13.6. 

An aqueous solution of hydrochloric acid contains 36% HCl by mass, (a) Calculate the mole fraction of HCl in the solution, (b) Calculate the molality of HCl in the solution. 

Ana lyze We are asked to calculate the concentration of the solute, HCl, in two related concentration units, given only the percentage by mass of the solute in the solution. 

Plan In converting concentration units based on the mass or moles of solute and solvent (mass percentage, mole fraction, and molality), it is useful to assume a certain total mass of solution. Let s assume that there is exactly 100 g of solution. Because the solution is 36% HCl, it contains 36 g of HCl and (100 — 36) g = 64gof H2O. 

We must convert grams of solute (HCl) to moles to calculate either mole fraction or molality. We must convert grams of solvent (H2O) to moles to calculate mole fractions and to kilograms to calculate molality. 

Several different methods are used to express relative amounts of solute and solvent in a solution. Two concentration units, molarity and mole fraction, were referred to in previous chapters. Two others, mass percent and molality, are considered for the first time. 

In Chapter 4, molarity was the concentration unit of choice in deahng with solution stoichiometry. You will recall that molarity is defined as 

In both solutions, n can be found by multiplying the molarity, M, by the volume in liters, V. Hence 

It s easier to dilute a concentrated solution than to start from scratch.  

Copper sulfate is widely used as a dietary supplement for animal feed. A lab technician prepares a stock solution of CUSO4 by adding 79.80 g of CUSO4 to enough water to make 500.0 mb of solution. An experiment requires a 0.1000 M solution of CUSO4. 

Several different methods are used to express relative amounts of solute and solvent in a solu- CENGAGENOW 

Ksoime (concentrated solution) = soiute (dilute solution) 

Practice Exercise Is iodine (I2) more soluble in water or in carbon disulfide (CS2)  

Quantitative study of a solution requires that we know its concentration, that is, the amount of solute present in a given amount of solution. Chemists use several different concentration units, each of which has advantages as well as limitations. Let us examine the three most common luiits of concentration percent by mass, molarity, and molahty. 

The percent by mass (also called the percent by weight or the weight percent) is defined as 

The percent by mass has no imits because it is a ratio of two similar quantities. 

The molarity unit was defined in Section 4.5 as the munber of moles of solute in For calculations involving mohrity, see 

Practice Problem A Predict whether vitamin Bg, also known as pyridoxine, is water soluble or fat soluble. 

1 Which compounds do you expect to be more soluble in benzene than in water (Select aU that apply.) 

2 Which vitamins (see the given structures) do you expect to be water soluble (Select all that apply.) 

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The elements ay are absorptivities (or are proportional to absorptivities, depending on the concentration units and cell dimensions), x= ( ) is the unknown concentration vector, and y = ( () is the absorbance vector, observed at wavelengths Li and X2. 

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. 

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. 

Preparing a solution of known concentration is perhaps the most common activity in any analytical lab. The method for measuring out the solute and solvent depend on the desired concentration units, and how exact the solution s concentration needs to be known. Pipets and volumetric flasks are used when a solution s concentration must be exact graduated cylinders, beakers, and reagent bottles suffice when concentrations need only be approximate. Two methods for preparing solutions are described in this section. 

A stock solution is prepared by weighing out an appropriate portion of a pure solid or by measuring out an appropriate volume of a pure liquid and diluting to a known volume. Exactly how this is done depends on the required concentration units. For example, to prepare a solution with a desired molarity you would weigh out an appropriate mass of the reagent, dissolve it in a portion of solvent, and bring to the desired volume. To prepare a solution where the solute s concentration is given as a volume percent, you would measure out an appropriate volume of solute and add sufficient solvent to obtain the desired total volume. 

MacCarthy, P. A Novel Classification of Concentration Units, /. Chem. Educ. 1983, 60, 187-189. 

These mass per volume concentration units can be written as... 

The ratio n/c2 is called the reduced osmotic pressure-and can be plotted with or without the RT-and the zero-intercept value (subscript 0) is the limiting value of the reduced osmotic pressure. Quite an assortment of different pressure units are used in the literature in reporting n values, and the units of R in Eq. (8.88) must be reconciled with these pressure (as well as concentration) units. 

It is conventional to use molality—moles of solute per kilogram of solvent (symbol m)—as the concentration unit in electrolyte thermodynamics. Accordingly, we shall represent the concentrations of both the indifferent electrolyte and the polymer in these units in this section m3 and m2, respectively. In the same dilute (with respect to polymer) approximation that we have used elsewhere in this chapter, m2 is related to the mass volume system of units C2 by... 

The wolume fraction emerges from the Einstein derivation at the natural concentration unit to describe viscosity. This parallels the way volume fraction arises as a natural thermodynamic concentration unit in the Flory-Huggins theory as seen in Sec. 8.3. 

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

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The units of [77] reveal the concentration units in this experiment to be grams of protein per cubic centimer of solution. Dividing this concentration unit by the density of the unsolvated protein converts these concentration units to volume fractions ... 

Based on these ideas, the intrinsic viscosity (in 0 concentration units) has been evaluated for ellipsoids of revolution. Figure 9.3 shows [77] versus a/b for oblate and prolate ellipsoids according to the Simha theory. Note that the intrinsic viscosity of serum albumin from Example 9.1-3.7(1.34) = 4.96 in volume fraction units-is also consistent with, say, a nonsolvated oblate ellipsoid of axial ratio about 5. 

The first term reflects the fact that, in practice, volume fraction is not the concentration unit ordinarily used. Even for nonsolvated spheres, some factors will modify the Einstein 2.5 term merely as a result of reconciling practical concentration units with

[Pg.597]

The urea solution stream is then fed to the vacuum concentrator unit which operates at 17.3 kPa (130 mm Hg abs) and produces 88.7 wt % urea. It then goes to either two-stage evaporators if prills are made, or a single-stage unit for granule production. 

The solubihty coefficient must have units that are consistent with equation 3. In the hterature S has units cc(STP)/(cm atm), where cc(STP) is a molar unit for absorbed permeant (nominally cubic centimeters of gas at standard temperature and pressure) and cm is a volume of polymer. When these units are multiphed by an equihbrium pressure of permeant, concentration units result. In preferred SI units, S has units of nmol /(m GPa). 

Mass concentration units for ambient measurements are mass (/xg) per unit volume (m ). Size classification involves the use of specially designed inlet configurations, e.g., PMjq sampling. To determine mass concentration, all the particles are removed from a known volume of air and their total mass is measured. This removal is accomplished by two techniques, filtration and impaction, described in Chapter 13. Mass measurements are made by pre-and postweighing of filters or impaction surfaces. To account for the absorption of water vapor, the filters are generally equilibrated at standard conditions T = 20°C and 50% relative humidity). 

In solution k metics we commonly work with systems at constant volume, and we find it convenient to employ molar concentration units. Dividing both sides of Eq. (1-9) by volume V gives... 

To analyze the rate constant problem we start with Eq. (5-43), k = (kT/h)K. The term (kT/h) has the unit second", so consistency is achieved if the concentration units of k and are identical. As before, we pass to pure numbers, writing (for a second-order rate constant)... 

A first-order rate constant has the dimension time, but all other rate constants include a concentration unit. It follows that a change of concentration scale results in a change in the magnitude of such a rate constant. From the equilibrium assumption of transition state theory we developed these equations in Chapter 5 ... 

Cancer risk of pollutant = (Annual Average Concentration)(Unit Risk)... 

Removing more heat from the pumparound returns, either by generating steam or adding coolers. This can decouple the fractionator from the reboilers in the gas concentration unit. 

Removing external streams. If gas comes from another unit or vents from a column in the gas concentration unit, consider routing it to the interstage rather than the suction. The refinery needs to evaluate if external streams are worth recovering or whether they can be routed elsewhere. 

To carry out these calculations for solution reactions, you need to be familiar with a concentration unit called molarity, which tells you how many moles of a species are in a given volume of solution. ... 

Molality and molarity are concentration units morality is something else. 

It is frequently necessary to convert from one concentration unit to another This problem arises, for example, in making up solutions of hydrochloric acid. Typically, the analysis or assay that appears on the label (Figure 10.2, p. 263) does not give the molarity or molality of the add. Instead, it lists the mass percent of solute and the density of the solution. 

Conversions between concentration units are relatively straightforward provided you first decide on a fixed amount of solution. The amount chosen depends on the unit in which concentration is originally expressed. Some suggested starting quantities are listed below. 

Again using the definition for the concentration unit M - (mol solute)/(L of solution), we arrive at the number of moles solute ... 

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. 

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