Solution composition dilution calculations

Here, the solute S is in dilute solution, and tire equation can be used across the enthe composition range of tire A-B binary solvent, when Aa + Ab is close to one. When the concentration of the dilute solute is increased, the more concentrated solution can be calculated from Toop s equation (1965) in the form... 

The equation obtained can be used when the electrode potential can be varied independent of solution composition (i.e., when the electrode is ideally polarizable). For practical calculations we must change from the Galvani potentials, which cannot be determined experimentally, to the values of electrode potential that can be measured E = ( q + const (where the constant depends on the reference electrode chosen and on the diffusion potential between the working solution and the solution of the reference electrode). When a constant reference electrode is used and the working solutions are sufficiently dilute so that the diffusion potential will remain practically constant when their concentration is varied, dE (i(po and... 

Procedure Prepare a series of THI-DNPH Standard Solutions serially diluted from the Stock THI-DNPH Solution. Pipet 1, 2, and 5 mL, respectively, of the Stock THI-DNPH Solution, into separate 10-mL volumetric flasks, and dilute to volume with absolute, carbonyl-free methanol. Prepare a standard curve by injecting 5 p-L of the Stock THI-DNPH Solution, and the serially diluted THI-DNPH Standard Solutions into a 250-mm x 4-mm (id), 10-lm LiChrosorb RP-8 HPLC column (Alltech Associates, Inc., or equivalent) fitted with an ultraviolet detector set at 385 nm. The mobile phase is 50 50 (v/v) methanohO.l M phosphoric acid. Inject 5 pL of sample into the column. Adjustments in the mobile phase composition may be needed as column characteristics vary among manufacturers. At a mobile phase flow rate of 2 mL/ min and column dimensions of 250 x 4.6 mm, elute THI-DNPH at about 6.3 0.1 min. Measure the peak areas. Calculate the amount of THI in the sample from the standard curve. (For THI limits greater than 25 mg/kg, prepare a series of Standard THI-DNPH Solutions in a range encompassing the expected THI concentration in the sample.)... 

Where both the acid and the base are strong electrolytes, the neutralization point will be at pH = 7 and the end point break will be distinct unless the solutions are very dilute (< 10" 3 mol dm"3). The composition of the titrand at any point in the titration may W computed from the total amount of acid and base present. However, when one of the reactants is a weak acid or base the picture is less clear. The incomplete dissociation of the acid or base and the hydrolysis of the salt produced in the reaction must be taken into account when.calculations of end points and solution composition are made. These points have been considered in chapter 3 and are used in the indicator selection procedure outlined in the preceding section of this chapter. 

Because a mixture, unlike a chemical compound, has a variable composition, the relative amounts of substances in a solution must be specified. The qualitative terms dilute (relatively little solute present) and concentrated (relatively large amount of solute) are often used to describe solution content. However, we need to define solution composition more precisely to perform calculations. For example, in dealing with the stoichiometry of solution reactions in Chapter 4, we found it useful to describe solution composition in terms of molarity, or the number of moles of solute per liter of solution. 

The Kirkwood—Buff theory of solution was used to investigate the formation of clusters in aqueous alcohol solutions. The correlation volume (volume in which the composition differs from the bulk one) was calculated for the systems 1-propanol—water and fert-butyl alcohol—water and compared with the sizes of clusters determined by various physical techniques. The calculations indicated that two types of clusters, alcohol- and water-rich clusters, are present in the solutions. Their sizes, which depend on composition in a similar way, exhibit maxima in the water-rich region. The calculated values are in a satisfactory agreement with experiment. The composition inside the clusters (the local composition) was calculated as a function of the correlation volume for dilute aqueous methanol, ethanol, propanols, and terf-butyl alcohol solutions. The results were compared with the local compositions provided by the Wilson and NRTL equations. 

If there is no available salt of constant composition, such as copper(II) sulphate or iron(III), aluminium or chromium alums, it is advisable to prepare first a stock solution of an approximate concentration, slightly higher than required and to determine the concentration by a gravimetric or volumetric method. After suitable calculations the solution is diluted with pure solvent to obtain a solution containing exactly, e.g., 1 mg/ml of the given element. In some cases, standard solutions are obtained by dissolving a precisely weighed amount of the element in its pure form. 

In this chapter (as in Chapter 9) molality, which is number of moles of solute per kilogram of solvent and indicated by the symbol M, will be used. Molarity, defined as the number of motes of solute per liter of solution, is another commonly used concentration unit, but can be somewhat more difficult to deal with since the volume of a solution varies with composition and temperature. However, if the solvent is water and the solution is dilute in solute (so that one liter of solution contains one kilogram of water), as-is generally the case in this chapter, molality and molarity are equal. Therefore, in some of the calculations that follow, especially the titration calculations in this section, we may ignore the distinction between molality (moles of solute per kilogram of water) and molarity (moles of solute, per liter of solution.) -... 

In general we can say that the reference-solvent dilute-solution standard state is easier to use than the solute-free dilute-solution standard state (except, of course, when Y can be assumed to be unity). This is because is completely independent of composition, while depends on the solute-free mole fractions. But more generally, the lesson is that the three kinds of activity coefficients are simply proportional they are aU embedded with the same information, so they aU give the same value for a fugacity. We use the particular standard state that allows us to take advantage of available data and that simplifies calculations. 

The contact of solutions that possess more than one common ion, in particular all contacts of solutions with identical or miscihle solvents, exhibits a more complicated phenomenon. At the initial stage, all exchangeable ions are transferred across the boundary generating a long-living nonequilibrium structure, liquid junction (LJ) , which retains its diffusion potential difference for an extended time, despite the absence of the thermodynamic equilibrium (different compositions) between the interphase and two bulk phases. If the solutions in contact have the same solvent, this potential drop is usually relatively small, mostly within a few dozen mV or less (but it may sometimes reach a much larger value for dilute solutions even in the same solvent). Elaborated procedures for its calculation as a function of the solutions composition exist [12]. For nonidentical solvents, this potential difference may be much larger. 

Figure 12.3 Freezing-point depression and boiling-point elevation of an aqueous solution. Solid curves dependence on temperature of the chemical potential of H2O (A) in pure phases and in an aqueous solution at 1 bar. Dashed curves unstable states. The fiA values have an arbittary zero. The solution curve is calculated for an ideal-dilute solution of composition xa = 0.9.

The value of the equilibrium constant for any reaction can be calculated from the value of AG". Once the equilibrium constant is evaluated, the equilibrium composition can be calculated for any particular case, if information about activity coefficients is available from experimental data or from theoretical estimates. If a solution is dilute... 

Solutions of Electrolytes—Calculating colligative properties of electrolyte solutions is more difficult than for solutions of nonelectrolytes. The solute particles in electrolyte solutions are ions or ions and molecules. Calculations using equations (14.5) and (14.6) must be based on the total number of particles present, and the van t Hoff factor is introduced into these equations to reflect this number. In all but the most dilute solutions, composition must be in terms of activities— effective concentrations that take into accoimt interionic forces. 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

Calculation of Liquid-to-Gas Ratio The minimum possible liquid rate is readily calculated from the composition of the entering gas and the solubility of the solute in the exit liquor, saturation being assumed. It may be necessaiy to estimate the temperature of the exit liquid based on the heat of solution of the solute gas. Values of latent and specific heats and values of heats of solution (at infinite dilution) are given in Sec. 2. 

Prepare a benzene-toluene mixture by placing 0.05 mL of each liquid in a 25 mL graduated flask and making up to the mark with methanol. Take 1.5 mL of this solution, place in a lOmL graduated flask and dilute to the mark with methanol this solution contains benzene at the same concentration as solution 5, and toluene at the same concentration as solution 5. Measure the absorbances of this solution at the two wavelengths selected for the Beer s Law plots of both benzene and toluene. Then use the procedure detailed in Section 17.48 to evaluate the composition of the solution and compare the result with that calculated from the amounts of benzene and toluene taken. 

Take some crude cresol mixture (1 g) and dissolve it in cyclohexane (20 mL). Obtain the infrared spectrum for the mixture if necessary, dilute the solution further with cyclohexane to obtain absorbances which will lie on the calibration graphs. From the selected absorption peaks calculate the absorbances for the three individual isomers and use the calibration graphs to calculate the percentage composition of the cresol mixture. 

In addition, the critical evaluation of enthalpies of dilution and solution, as well as evaluations of heat capacities have been initiated. These evaluations will allow calculations and correlations of activity and osmotic coefficients as a function of temperature and composition. 

MINTEQA2 http //www.epa.gov/ceampubl/mmedia/minteq/index.htm MINTEQA2 is an equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorbed species, and multiple solid phases under a variety of conditions including a gas phase with constant partial pressures. 

---