CONCENTRATIONS OF SOLUTIONS

The mixture of the two solutions provides a medium or space in which the Ag and Cl ions can react. (See Chapter 15 for further discussion of ionic reactions.) 

Solutions also function as diluting agents in reactions in which the undiluted reactants would combine with each other too violently. Moreover, a solution of known concentration provides a convenient method for delivering a specific amount of reactant. 

The concentration of a solution expresses the amount of solute dissolved in a given quantity of solvent or solution. Because reactions are often conducted in solution, it s important to understand the methods of expressing concentration and to know how to prepare solutions of particular concentrations. The concentration of a solution may be expressed qualitatively or quantitatively. Let s begin with a look at the qualitative methods of expressing concentration. 

The mass percent method expresses the concentration of the solution as the percent of solute in a given mass of solution. It says that for a given mass of solution, a certain percent of that mass is solute. Suppose we take a bottle from the reagent shelf that reads sodium hydroxide, NaOH, 10%. This statement means that for every 100 g of this solution, 10 g will be NaOH and 90 g will be water. (Note that this amount of solution is 100 g, not 100 mL.) We could also make this same concentration of solution by dissolving 2.0 g of NaOH in 18 g of water. Mass percent concentrations are most generally used for solids dissolved in liquids  

As instrumentation advances are made in chemistry, our ability to measure the concentration of dilute solutions is increasing as well. In addition to mass percent, chemists now commonly use parts per million (ppm)  

Predict whether a solid might form in each of the following mixtnres of solntions. If so, write the net ionic equation for the reaction. 

LEARNING GOAL Define solubility distinguish between an unsaturated and a saturated solution. Identify a salt as soluble or insoluble. 

15 State whether each of the following refers to a saturated or an unsaturated solution  

17 Using the previous table, determine whether each of the following solutions will be saturated or unsaturated at 20 °C  

To study solution stoichiometry, we must know how much of the reactants are present in a solntion and also how to control the amounts of reactants used to bring about 

The concentration of a solution is the amount of solute present in a given quantity of solution. (For this discussion, we will assume the solute is a liquid or a solid and the solvent is a liquid.) The concentration of a solution can be expressed in many different ways, as we will see in Chapter 12. Here we will consider one of the most commonly used units in chemistry, molarity (M), or molar concentration, which is the number of moles of solute per liter of solution. Molarity is defined as 

Of course, we do not always work with solution volumes of exactly 1 L. This is not a problem as long as we remember to convert the volume of the solution to liters. Thus, a 500-mL solution containing 0.730 mole of C6H12O6 also has a concentration of 1.46 M  

As you can see, the unit of molarity is moles per liter, so a 500-mL solution containing 0.730 mole of C6H12O6 is equivalent to 1.46 mol/L or 1.46 M. Note that concentration, like density, is an intensive property, so its value does not depend on how much of the solution is present. 

Preparing a solution of known molarity, (a) A known amount of a solid solute is transferred into the volumetric flask then water is added through a funnel. (b) The solid is slowly dissolved by gently swirling the flask, (c) After the solid has completely dissolved, more water is added to bring the level of solution to the mark. Knowing the volume of the solution and the amount of solute dissolved in it, we can calculate the molarity of the prepared solution. 

The qualitative terms concentrated and dilute are relative terms, like expensive and cheap 

Molarity can equally well be defined as millimoles per milliliter (mmol/mL), which can simplify some calculations. 

Students sometimes have difficulty seeing how units cancel in these equations. It may help to write M as mol/L until you become completely comfortable with these equations. 

Molarity, or molar concentration, symbolized M, is defined as the number of moles of solute per liter of solution. Thus, 1 L of a 1.5 molar solution of glucose (C6H12O6), written as 1.5 MC6H12O6, contains 1.5 moles of dissolved glucose. Half a liter of the same solution would contain 0.75 mole of dissolved glucose, a milliliter of the solution would contain 1.5 X 10 mole of dissolved gluco.se. and so on. 

In order to calculate the molarity of a solution, we divide the number of moles of solute by the volume of the solution in liters. 

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The surface tension of an aqueous solution varies with the concentration of solute according to the equation y = 72 - 350C (provided that C is less than 0.05Af). Calculate the value of the constant k for the variation of surface excess of solute with concentration, where k is defined by the equation V = kC. The temperature is 25°C. 

In principle, the effects of the concentration of ions can be removed by dividing A2.4.31 by the concentration. Taking Avagadro s constant as L and assuming a concentration of solute c mol m, then from the electroneutrality principle we have = A = z cL and clearly... 

Concentration of solute in mobile phase Cm Diffusion coefficient, liquid film Dt... 

Table 11.4 Solutions for Maintaining Constant Humidity Table 11.5 Concentration of Solutions of H2SO4, NaOH, and CaCi2 Giving Specified Vapor Pressures and Percent Humidities at 25°C Table 11.6 Relative Humidity from Wet and Dry Bulb Thermometer Readings Table 11.7 Relative Humidity from Dew Point Readings...

TABLE 11.5 Concentrations of Solutions of H2SO4, NaOH, and CaCl2 Giving Specified Vapor Pressures and Percent Humidities at 25°C... 

A ratio expressing the total concentration of solute in one phase relative to a second phase all forms of the solute are considered in defining the distribution ratio (D). 

Nonideal asymmetrical chromatographic bands showing (a) fronting and (b) tailing. Also depicted are the corresponding sorption isotherms showing the relationship between the concentration of solute in the stationary phase as a function of its concentration in the mobile phase. 

The use of several QA/QC methods is described in this article, including control charts for monitoring the concentration of solutions of thiosulfate that have been prepared and stored with and without proper preservation the use of method blanks and standard samples to determine the presence of determinate error and to establish single-operator characteristics and the use of spiked samples and recoveries to identify the presence of determinate errors associated with collecting and analyzing samples. 

The attitude we adopt in this discussion is that only those chain segments in the middle of the chain possess sufficient regularity to crystallize. Hence we picture crystallization occurring from a mixture in which the concentration of crystallizable units is Xj and the concentration of solute or diluent is Xg. The effect of solute on the freezing (melting) point of a solvent is a well-known result T j, is lowered. Standard thermodynamic analysis yields the relationship... 

Since capillary tubing is involved in osmotic experiments, there are several points pertaining to this feature that should be noted. First, tubes that are carefully matched in diameter should be used so that no correction for surface tension effects need be considered. Next it should be appreciated that an equilibrium osmotic pressure can develop in a capillary tube with a minimum flow of solvent, and therefore the measured value of II applies to the solution as prepared. The pressure, of course, is independent of the cross-sectional area of the liquid column, but if too much solvent transfer were involved, then the effects of dilution would also have to be considered. Now let us examine the practical units that are used to express the concentration of solutions in these experiments. 

The physical and chemical properties are less well known for transition metals than for the alkaU metal fluoroborates (Table 4). Most transition-metal fluoroborates are strongly hydrated coordination compounds and are difficult to dry without decomposition. Decomposition frequently occurs during the concentration of solutions for crysta11i2ation. The stabiUty of the metal fluorides accentuates this problem. Loss of HF because of hydrolysis makes the reaction proceed even more rapidly. Even with low temperature vacuum drying to partially solve the decomposition, the dry salt readily absorbs water. The crystalline soflds are generally soluble in water, alcohols, and ketones but only poorly soluble in hydrocarbons and halocarbons. 

Variations ia the Hquid-juactioa poteatial may be iacreased whea the standard solutions are replaced by test solutions that do not closely match the standards with respect to the types and concentrations of solutes, or to the composition of the solvent. Under these circumstances, the pH remains a reproducible number, but it may have Httle or no meaning ia terms of the coaveatioaal hydrogea-ioa activity of the medium. The use of experimental pH aumbers as a measure of the exteat of acid—base reactioas or to obtaia thermodynamic equiHbrium coastants is justified only whea the pH of the medium is betweea 2.5 and II.5 and when the mixture is an aqueous solution of simple solutes ia total coaceatratioa of ca <0.2 M. 

Two blue pigments can be prepared in transparent form cyanide iron blue and cobalt aluminum blue. These pigments are used in achieving a blue shade of the metal effect pigments in metallic paints. Transparent cyanide iron blue is prepared by a precipitation reaction similar to the one used for the preparation of the opaque pigment, but considerably lower concentrations of solutions are used. It is produced by Degussa (Germany), Manox (U.K), and Dainichiseika (Japan). 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

As the L/G is decreased, the concentration of solute tends to build up in the upper parts of the absorber, and the point of highest temperature tends to move upward in the tower until finally the maximum temperature develops only on the topmost plate. Of course, the capacity of the hquid phase to absorb solute fafls progressively as the L/G is reduced. 

Foam Production This is important in froth-flotation separations in the manufac ture of cellular elastomers, plastics, and glass and in certain special apphcations (e.g., food products, fire extinguishers). Unwanted foam can occur in process columns, in agitated vessels, and in reactors in which a gaseous product is formed it must be avoided, destroyed, or controlled. Berkman and Egloff (Emulsions and Foams, Reinhold, New York, 1941, pp. 112-152) have mentioned that foam is produced only in systems possessing the proper combination of interfacial tension, viscosity, volatihty, and concentration of solute or suspended solids. From the standpoint of gas comminution, foam production requires the creation of small biibbles in a hquid capable of sustaining foam. 

The difference between the curves for pure water and seawater again illustrates the significance of small concentrations of solute with respecl to bubble behavior. In commercial bubble columns and agitated vessels coalescence and breakup are so rapid and violent that the rise velocity of a single bubble is meaningless. The average rise velocity can, however, be readily calculated from holdup correlations that will be given later. 

Likewise, one knows that Y will be on the equilibrium line with X (see Fig. 15-12). One can therefore calculate a pseudo concentration of solute in the inlet extraction solvent Yf that 011 fall on the operating line [Eq. (15-12)] where=Xr [Eq. (15-20)]. 

Numerical values for solid diffusivities D,j in adsorbents are sparse and disperse. Moreover, they may be strongly dependent on the adsorbed phase concentration of solute. Hence, locally conducted experiments and interpretation must be used to a great extent. Summaries of available data for surface diffusivities in activated carbon and other adsorbent materials and for micropore diffusivities in zeolites are given in Ruthven, Yang, Suzuki, and Karger and Ruthven (gen. refs.). 

Where M is the molecular weight of the solute, Dt is the elevation of boiling point in °C, c is the concentration of solute in grams for lOOOgm of solvent, and K is the Ebullioscopic Constant (molecular elevation of the boiling point) for the solvent. K is a fixed property (constant) for the particular solvent. This has been very useful for the determination of the molecular weights of organic substances in solution. 

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