Concentration solutions

In describing a solution, it is necessary to do so qualitatively, that is, to specify what the solvent is and what the solutes ate. For example, it has just been seen that HCl gas is the solute placed in water to form hydrochloric acid. It is also necessary to know what happens to the material when it dissolves. For instance, one needs to know that hydrogen chloride molecules dissolved in water form H+ ions and Cl ions. In many cases, it is necessary to have quantitative information about a solution, that is, its concentration. The concentration of a solution is the amount of solute material dissolved in a particular amount of solution, or by a particular amount of solvent. Solution concentration may be expressed in a number of different ways. Solutions used in technical applications, such as for cleaning, are often made up of a specified number of grams of solute per 100 mL of solvent added. On the other hand, a person involved in crop spraying may mix the required solution by adding several pounds of pesticide to a specified number of barrels of water. 

The mass of a solute in solution often does not provide full information about its effect. For example, a solution of either NaCl or sodium iodide (Nal) will remove silver from a solution of silver nitrate (AgNOj) when the two solutions ate mixed. The two possible chemical reactions are 

Of course, solutions are not always exactly 1 m in concentration. However, it is easy to perform calculations involving molar concentration using the relationships expressed in the following equation  

Volume solution (L) Molar mass solute X Volume solution (L) 

Example What is the molar concentration of a solution that contains 2.00 mol of HCl in 0.500 L of solution  

The concentration of a solution states the amount of solute (in mass or moles) dissolved in a given amount of solution or solvent. Because many chemical reactions take place in solution, it is important that you understand the most common concentration schemes. 

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. 

Commonly, the unit of mass for solute and solution is gram, but any unit can be used as long as the same unit is used for both. After all, the unit of mass divides out in the calculation. Let s work a few problems involving mass/mass percent. 

Problem 1 55 g of sodium chloride, NaCl, are dissolved in 875 g of water. What is the %(m/m) concentration of NaCl in the final solution How many grams of NaCl are in 200 g of this solution  

The mass of the final solution equals the mass of the NaCl plus the mass of water  

The preferred unit for the concentration of a solution in the SI system is molar concentration (or molarity) which is dehned by 

Number of moles of solute Number of liters of solution 

The units of molarity are mol L (or M for short). For example, a 2.5 M solution contains 2.5 gram moles of solute in every liter of solution. 

Since the volume of a solution changes with temperature, so will the molarity, even though the amount of solute remains the same. If, however, the concentration of a given solution is expressed as moles of solute per kilogram of solvent (called molal concentration or molality), it will be independent of temperature. The units of molality are mol kg (or m, for short). 

The concentration of a particular solute i in a solution can also be expressed as a mole fraction 

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Note that in liquid phase chromatography there are no detectors that are both sensitive and universal, that is, which respond linearly to solute concentration regardless of its chemical nature. In fact, the refractometer detects all solutes but it is not very sensitive its response depends evidently on the difference in refractive indices between solvent and solute whereas absorption and UV fluorescence methods respond only to aromatics, an advantage in numerous applications. Unfortunately, their coefficient of response (in ultraviolet, absorptivity is the term used) is highly variable among individual components. 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

Fig. XI-1. Adsorption kinetics for C g alkanoic acids adsorbing onto alumina for various solution concentrations from Ref. 36. Lines are the fit to Eq. XI-IS.

Referring to Section XI-6B, the effect of the exclusion of coions (ions of like charge to that of the interface) results in an increase in solution concentration from rq to Rq. Since the solution must remain electrically neutral, this means that the counterions (ions of charge opposite to that of the interface) must also increase in concentration from Ro to Rq. Yet Fig. V-1 shows the counterions to be positively adsorbed. Should not their concentration therefore decrease on adding the adsorbent to the solution Explain. 

Apart from tliese mainstream metliods enabling one to gain a comprehensive and detailed stmctural picture of proteins, which may or may not be in tlieir native state, tliere is a wide variety of otlier metliods capable of yielding detailed infonnation on one particular stmctural aspect, or comprehensive but lower resolution infonnation while keeping tlie protein in its native environment. One of tlie earliest of such metliods, which has recently undergone a notable renaissance, is analytical ultracentrifugation [24], which can yield infonnation on molecular mass and hence subunit composition and their association/dissociation equilibria (via sedimentation equilibrium experiments), and on molecular shape (via sedimentation velocity experiments), albeit only at solution concentrations of at least a few tentlis of a gram per litre. 

Industrially. phosphoric(V) acid is manufactured by two processes. In one process phosphorus is burned in air and the phos-phorus(V) oxide produced is dissolved in water. It is also manufactured by the action of dilute sulphuric acid on bone-ash or phosphorite, i.e. calcium tetraoxophosphate(V). Ca3(P04)2 the insoluble calcium sulphate is filtered off and the remaining solution concentrated. In this reaction, the calcium phosphate may be treated to convert it to the more soluble dihydrogenphosphatc. CafHjPOjj. When mixed with the calcium sulphate this is used as a fertiliser under the name "superphosphate . 

Calculate the number of moles of ZnCl2 per kilogram of water in each solution (the molality m). Calculate the volume V of solution containing 1 kg of water at each solute concentration. Plot V vs. m. Use program Mathead, QQLSQ, or TableCurve... 

Study of the solubility behaviour of the compound. A semi-quantitative study of the solubility of the substance in a hmited number of solvents (water, ether, dilute sodium hydroxide solution, dilute hydrochloric acid, sodium bicarbonate solution, concentrated sulphuric and phosphoric acid) will, if intelligently apphed, provide valuable information as to the presence or absence of certain classes of organic compounds. 

The solute concentration should be above 0 2M in dilute solution K increases from 39-7 to about 50. 

Specific rotation is the number of degrees of rotation observed if a 1-dm tube is used and the compound being examined is present to the extent of 1 g per 100 mL. The density for a pure liquid replaces the solution concentration. 

For reasonable quantitative accuracy, peak maxima must be at least 4cr apart. If so, then Rs = 1.0, which corresponds approximately to a 3% overlap of peak areas. A value of Rs = 1.5 (for 6cr) represents essentially complete resolution with only 0.2% overlap of peak areas. These criteria pertain to roughly equal solute concentrations. 

The foregoing equation reveals that essentially the concentration distribution ratio for trace concentrations of an exchanging ion is independent of the respective solution of that ion and that the uptake of each trace ion by the resin is directly proportional to its solution concentration. However, the... 

Parts per million (ppm) and parts per billion (ppb) are mass ratios of grams of solute to one million or one billion grams of sample, respectively. For example, a steel that is 450 ppm in Mn contains 450 pg of Mn for every gram of steel. If we approximate the density of an aqueous solution as 1.00 g/mL, then solution concentrations can be expressed in parts per million or parts per billion using the following relationships. 

Scale of Operation Coulometric methods of analysis can be used to analyze small absolute amounts of analyte. In controlled-current coulometry, for example, the moles of analyte consumed during an exhaustive electrolysis is given by equation 11.32. An electrolysis carried out with a constant current of 100 pA for 100 s, therefore, consumes only 1 X 10 mol of analyte if = 1. For an analyte with a molecular weight of 100 g/mol, 1 X 10 mol corresponds to only 10 pg. The concentration of analyte in the electrochemical cell, however, must be sufficient to allow an accurate determination of the end point. When using visual end points, coulometric titrations require solution concentrations greater than 10 M and, as with conventional titrations, are limited to major and minor analytes. A coulometric titration to a preset potentiometric end point is feasible even with solution concentrations of 10 M, making possible the analysis of trace analytes. 

The final part of a gas chromatograph is the detector. The ideal detector has several desirable features, including low detection limits, a linear response over a wide range of solute concentrations (which makes quantitative work easier), responsiveness to all solutes or selectivity for a specific class of solutes, and an insensitivity to changes in flow rate or temperature. 

The reduced viscosity expresses the specific viscosity per unit of solute concentration. 

In the next section we shall pursue the scattering by fluctuations in density. In the case of solutions of small molecules, it is the fluctuations in the solute concentration that plays the equivalent role, so we shall eventually replace 6p by 6c2. First, however, we must describe the polarizability of a density fluctuation and evaluate 6p itself. 

As noted at the end of the last section, it is fluctuations in concentration 5c2 rather than density which act as the scattering centers of interest for solutions of small molecules. There is nothing in the forgoing theory that prevents us from placing 6p by 6c2, the solute concentration in mass volume" units. Therefore we write for a solution of small molecules... 

Fig. 34. Solubility of chlorine ia water and aqueous HCl and NaCl. Solution concentrations are ia wt %.

The solute concentrations very close to the interface, and are assumed to be in equiUbrium, in the absence of any slow interfacial reaction. According to the linear distribution law, Cg. = thus from equation 14 the mass-transfer flux can be expressed in terms of an overall... 

The sohd can be contacted with the solvent in a number of different ways but traditionally that part of the solvent retained by the sohd is referred to as the underflow or holdup, whereas the sohd-free solute-laden solvent separated from the sohd after extraction is called the overflow. The holdup of bound hquor plays a vital role in the estimation of separation performance. In practice both static and dynamic holdup are measured in a process study, other parameters of importance being the relationship of holdup to drainage time and percolation rate. The results of such studies permit conclusions to be drawn about the feasibihty of extraction by percolation, the holdup of different bed heights of material prepared for extraction, and the relationship between solute content of the hquor and holdup. If the percolation rate is very low (in the case of oilseeds a minimum percolation rate of 3 x 10 m/s is normally required), extraction by immersion may be more effective. Percolation rate measurements and the methods of utilizing the data have been reported (8,9) these indicate that the effect of solute concentration on holdup plays an important part in determining the solute concentration in the hquor leaving the extractor. 

Equipment for food freezing is designed to maximize the rate at which foods are cooled to —18° C to ensure as brief a time as possible in the temperature zone of maximum ice crystal formation (12,13). This rapid cooling favors the formation of small ice crystals which minimize the dismption of ceUs and may reduce the effects of solute concentration damage. Rapid freezing requires equipment that can deHver large temperature differences and/or high heat-transfer rates. 

Another characteristic of the solvent extraction system is the high solute concentration in both aqueous and organic phases, which influences greatly the size of the required installation. Concentrations of rare-earth oxides (REO) higher than 100 g/L are often reached in both phases. The process therefore requires only relatively small equipment. 

HMnO 2H20 [24653-70-1] decomposes at 18°C. Aqueous solutions of permanganic acid below a concentration of 3 wt % are stable over time, whereas in the concentration range of 5—15% HMnO, the decomposition rate increases with increasing initial solution concentration at room temperature (103). 

Concentration. The basis unit of concentration in chemistry is the mole which is the amount of substance that contains as many entities, eg, atoms, molecules, ions, electrons, protons, etc, as there are atoms in 12 g of ie, Avogadro s number = 6.0221367 x 10. Solution concentrations are expressed on either a weight or volume basis. MolaUty is the concentration of a solution in terms of the number of moles of solute per kilogram of solvent. Molarity is the concentration of a solution in terms of the number of moles of solute per Hter of solution. 

The phenomenon of concentration polarization, which is observed frequently in membrane separation processes, can be described in mathematical terms, as shown in Figure 30 (71). The usual model, which is weU founded in fluid hydrodynamics, assumes the bulk solution to be turbulent, but adjacent to the membrane surface there exists a stagnant laminar boundary layer of thickness (5) typically 50—200 p.m, in which there is no turbulent mixing. The concentration of the macromolecules in the bulk solution concentration is c,. and the concentration of macromolecules at the membrane surface is c. 

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