Expressing Concentrations of Solutions

The concentration of a solute in a solution may be expressed in different ways (Table 1-1). In the United States, laboratory data typically are reported in terms of mass of solute per unit volume of solution, usually the deciliter. However, the Systeme International d Unit s (SI) recommends the use of moles of solute per volume of solution for analyte concentrations (substance concentrations), whenever possible, and the use of liter as the reference volume. Although considered incorrect and inappropriate by metrologists, mass concentration also is reported in terms of grams percent or percent. This is typically how concentrations of ethanol in blood are expressed. This terminology indicates an amount of solute per mass of solution (e.g., grams per 100 g) and would be appropriate only if reference materials against which the unknowns were compared were also measured in the same terms. An exception to the general expression of analyte con- 

Mole fraction (or substance fraction) [of a given component]. 

Mole/ratio (or substance ratio) [of a given solute component] 

From The SI for the Health Professions, World Flealth Organization, 1977 

Amount of substance of a solute divided by volume of solution 

---

To evaluate the equilibrium constant in Equation 6-2, we must express concentrations of solutes in mol/L. gases in bars, and omit solids, liquids, and solvents. Explain why. 

Approximately three fourths of the earth s surface is covered with water. The body fluids of all plants and animals are mainly water. Thus we can see that many important chemical reactions occur in aqueous (water) solutions, or in contact with water. In Chapter 3, we introduced solutions and methods of expressing concentrations of solutions. It is useful to know the kinds of substances that are soluble in water, and the forms in which they exist, before we begin our systematic study of chemical reactions. 

In Sections 3-6 through 3-8 we introduced methods for expressing concentrations of solutions and discussed some related calculations. Review of those sections will be helpful as we learn more about acid-base reactions in solutions. 

Why can we describe molarity as a method of convenience for expressing concentrations of solutions ... 

Express concentrations of solutions in terms of molality and mole fractions... 

The units of concentration in Eq. (3) are typically moles per volume. However, in some cases (e.g., with capillary columns), it is more convenient to express concentration of solute in the stationary phase in units of moles per mass of stationary phase, rather than per volume.f ... 

The mole concept is useful in expressing concentrations of solutions, especially in analytical chemistry, where we need to know the volume ratios in which solutions of different materials will react. A one-molar solution is defined as one that contains one mole of substance in each liter of a solution. It is prepared by dissolving one mole of the substance in the solvent and diluting to a final volume of one liter in a volumetric flask or a faction or multiple of the mole may be dissolved and diluted to the corresponding fraction or multiple of a hter (e.g., 0.01 mol in 10 mL). More generally, the molarity of a solution is expressed as moles per liter or as millimoles per milliliter. Molar is abbreviated as M, and we talk of the molarity of a solution when we speak of its concentration. A one-molar solution of silver nitrate and a one-molar solution of sodium chloride will react on an equal-volume basis, since they react in a 1 1 ratio Ag + Cl —> AgCl. We can be more general and calculate the moles of substance in any volume of the solution. 

Calculate the number of calories per gram and calories per ounce in each of these foods. (Use Table 1-4 to convert grams into ounces, remembering that there are 16 ounces in 1 pound.) 1 -26. Even though we need to express concentrations of solutes in mol/L and the concentrations of gases in bars, why do we say that equilibrium constants are dimensionless ... 

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],... 

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). 

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. 

Whereas there is sometimes confusion in how concentrations of aqueous solutions of hydrazine ate expressed, concentrations of wt % N2H4 ate used herein. In many parts of the wodd, however, concentrations ate often expressed in terms of wt % hydrazine hydrate, N2H4 -H2 O. Hydrazine hydrate is 64 wt % N2H, 36% H2O. The correlation between the two systems is therefore ... 

For expressing concentrations of reagents, the molar system is universally applicable, i.e. the number of moles of solute present in 1 L of solution. Concentrations may also be expressed in terms of normality if no ambiguity is likely to arise (see Appendix 17). 

Concentrations of solutions are usually expressed in terms of moles per litre a molar solution (M) has one mole of solute per L. 

Here solute concentration C and Cp (in permeate) are expressed as mass fractions, D is the diffusion coefficient of the solute and y is the distance from the membrane. Rearranging and integrating from C - Cf when y = / the thickness of the film, to C = Cw, the concentration of solute at the membrane wall, when y=0, gives ... 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be governed by Pick s law and the reaction is first order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. Obtain an expression for the mass transfer rate across the gas-liquid interface in terms of the molecular diffusivity, 1), the first order reaction rate constant k. the film thickness L and the concentration Cas of solute in a saturated solution. The reaction is initially carried our at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K7... 

So far, we have seen qualitatively that hydronium ions are always present in water and that, in an aqueous solution of an acid or base, the concentration of H50 + ions depends on the concentration of solute. The time has come for us to express this concentration quantitatively and to see how it depends on the concentration of acid or base in solution. A minor difficulty is that the concentration of H30+ ions can vary over many orders of magnitude in some solutions, it is higher than... 

The composition of a solution can vaiy, so we must specify the concentrations of solutes as well as their identities. There are several ways to express concentration, each having advantages as well as limitations. Any concentration value is a ratio of amounts. The amount of one component, usually a solute, appears in the numerator, and some other amount, describing either the solvent or the total solution, appears in the denominator. 

Like freezing point depression and boiling point elevation, osmotic pressure is proportional to the concentration of solute molecules. Experiments show that osmotic pressure is proportional to both concentration (expressed as... 

A pH around 3 represents an acidic solution, so we expect the hydronium ion concentration to be much larger than the hydroxide ion concentration. Remember that although pH and. w are dimensionless, concentrations of solutes always are expressed In mol/L. Our results have two significant figures because the logarithm has two decimal places. 

The concentration of solution 1 is kept constant while E is measured for different concentrations of solution 2. The expression (2RT/F)lnra2 + E is plotted against m2. The value of the ordinate at point m2 = 0 yields the term (2RT/F) na 1 as lny 2 = 0 at this point. Once the value of a l is known, then Eq. (3.3.10) and the measured E values can be used to calculate the actual mean activity of the electrolyte at an arbitrary concentration. 

Although Equation 10.17 is written in terms of concentration of a specific component, it can also be used if the identity of the solute is unknown. For example, adsorption is used to remove color from liquids. In such cases, the concentration of solute can be measured, for example, by a colorimeter and Equation 10.17 expressed in terms of arbitrary units of color intensity, providing the color scale varies linearly with the concentration of the solute responsible for the color. 

Usually polarimetric measurements are carried out to find out a given optical antipode and the result is reliable, but the sign of rotation, is not always a direct expression of configuration because rotation, as already stated, depends on nature of solvent, concentration of solution and temperature etc. as the following example shows -... 

In this chapter, you learned about solutions and how to use molarity to express the concentration of solutions. You also learned about electrolytes and nonelectrolytes. Using a set of solubility rules allows you to predict whether or not precipitation will occur if two solutions are mixed. You examined the properties of acids and bases and the neutralization reactions that occur between them. You then learned about redox reactions and how to use an activity table to predict redox reactions. You learned about writing net ionic equations. Finally, you learned how to use the technique of titrations to determine the concentration of an acid or base solution. 

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. 

Equation 19.6 is often expressed in an alternative form. If q and c are the concentrations of solute in the stationary and mobile phases, respectively, and K = q/c) is the distribution coefficient of solute between the two phases, then ... 

---