Molal solution, definition

To 5 cc. of IN CuSCh add 10 cc. of a molal solution of tartaric acid then add sodium hydroxide solution, as in (1), and compare the results with those in (1) and (2), but do not attempt to ascribe a definite formula to the complex compound formed. 

To determine the number of moles of solute from the definition of molality, m = (moles solute)/(kg solvent), first find the mass of solvent using its density ... 

The IUPAC definition of pH39 is based upon a 0.05M solution of potassium hydrogenphthalate as the reference value pH standard (RVS). In addition, six further primary standard solutions are also defined which between them cover a range of pH values lying between 3.5 and 10.3 at room temperature, and these are further supplemented by a number of operational standard solutions which extend the pH range covered to 1.5-12.6 at room temperature. The composition of the RVS solution, of three of the primary standard solutions and of two of the operational standard solutions is detailed below, and their pH values at various temperatures are given in Table 15.4. It should be noted that the concentrations are expressed on a molal basis, i.e. moles of solute per kilogram of solution. 

Like mole fraction but unlike molarity, the molality is independent of temperature. The units of molality are moles of solute per kilogram of solvent (mol-kg 1) these units are often denoted m (for example, a 1 m NiS04(aq) solution) and read molal. Note the emphasis on solvent in the definition. To prepare a l m NiS04(aq) solution, we dissolve 1 mol NiS04 in 1 kg of water (Fig. 8.26). 

Now the origin of the scale must be defined, i.e. a pH value must be selected for a standard (as close as possible to the value expected on the basis of definition 1.4.46). A solution of potassium hydrogen phthalate with a molality of 0.05 mol kg-1 has been selected as the reference value pH standard (RVS). 

The molality of the solution, based on the definition of molality, would be ... 

For such solutions, the definition of activity is completed by the requirement that the activity approach the molality ratio in the limit of infinite dilution. That is. 

If followed in experimenrtally accessible dilute solutions, Henry s law would be manifested as a horizontal asymptote in a plot such as Figure 19.3 as the square of the molality ratio goes to zero. We do not observe such an asymptote. Thus, the modified form of Henry s law is not followed over the concentration range that has been examined. However, the ratio of activity to the square of the molality ratio does extrapolate to 1, so that the data does satisfy the definition of activity [Equations (16.1) and (16.2)]. Thus, the activity clearly becomes equal to the square of the molality ratio in the limit of infinite dilution. Henry s law is a limiting law, which is valid precisely at infinite dilution, as expressed in Equation (16.19). No reliable extrapolation of the curve in Figure 19.2 exists to a hypothetical unit molality ratio standard state, but as we have a finite limiting slope at = 0, we can use... 

Equation (19.19) is consistent with the empirical observation that a nonzero initial slope is obtained when the activity of a ternary electrolyte such as BaCl2 is plotted against the cube of m2/m°). As the activity in the standard state is equal to 1, by definition, the standard state of a ternary electrolyte is that hypothetical state of unit molality ratio with an activity one-fourth of the activity obtained by extrapolation of dilute solution behavior to m2/m° equal to 1, as shown in Eigure 19.4. 

From the standpoint of the operational definition of the standard state for the above free energy changes, we must remember that, while mole fractions are strongly recommended composition measures (61 Mil), in practice, both molalities, m, and concentrations, c, are widely used. For dilute aqueous solutions at moderate temperatures the numerical values of m and c are only slightly different. This no longer holds for other solvents. 

NiS04(aq) solution) and read molal. Note the emphasis on solvent in the definition. Therefore, to prepare aim NiS04(aq) solution, we dissolve 1 mol NiS04 in 1 kg of water (Fig. G.13). 

The main feature that distinguishes molality from molarity is its definition in terms of the mass of solvent used to make up the solution the molarity is expressed in terms of the volume of the resulting solution (not the volume of solvent used to make the solution). As a result, the molality is useful when we want to emphasize the relative numbers of molecules of the components of a mixture. That will be required only rarely in this text, so molality will appear much less frequently than molarity (it is used only in Chapter 8). If a concentration given as a molarity needs to be converted into molality, the mass of solvent in the solution must be known. To calculate this mass, the density of the solution is needed. 

The definitions based on molarities, c, are very similar to those based on molalities, and again the solvent must be considered separately from the solutes. (The molarity is defined as the number of moles per liter of solution, and is dependent on the pressure and temperature.) Molarities, like the molalities, are used primarily for solutions for which the concentration ranges are limited. For dilute solutions the molarities of the solutes are approximately proportional to their mole fractions. We thus express the chemical potential of the fcth solute in solution at a given temperature and pressure as... 

The definition is completed by assigning a value to m and (f>c in some reference state. To conform with the definitions made in Sections 8.9 and 8.10, the infinitely dilute solution with respect to all molalities or molarities is usually used as the reference state at all temperatures and pressures, and both m and c are made to approach unity as the sum of the molalities or molarities of the solutes approaches zero. The standard state of the solvent is again the pure solvent, and is identical to its reference state in all of its thermodynamic functions. 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

These equations can be expressed in terms of the chemical potentials of the salts when the usual definition of the chemical potentials of strong electrolytes is used. The transference numbers may be a function of x as well as the molality. Arguments which are not thermodynamic must be used to evaluate the integrals in such cases (see Kirkwood and Oppenheim [33]). One special type of cell to which either Equation (12.112) or Equation (12.113) applies is one in which a strong electrolyte is present in both solutions at concentrations that are large with respect to the concentrations of the other solutes. Such a cell, based on that represented in Equation (12.97), is... 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

Then, from the definition of molality, compute the number of moles solute, n(solute), in the sample. 

The mass of the solvent is 20 g or 0.020 kg, so we calculate the molality of the solution by plugging these values into the definition of molality. 

Molality and molarity are each very useful concentration units, but it is very unfortunate that they sound so similar, are abbreviated so similarly, and have such a subtle but crucial difference in their definitions. Because solutions in the laboratory are usually measured by volume, molarity is very convenient to employ for stoichiometric calculations. However, since molarity is defined as moles of solute per liter of solution, molarity depends on the temperature of the solution. Most things expand when heated, so molar concentration will decrease as the temperature increases. Molality, on the other hand, finds application in physical chemistry, where it is often necessary to consider the quantities of solute and solvent separately, rather than as a mixture. Also, mass does not depend on temperature, so molality is not temperature dependent. However, molality is much less convenient in analysis, because quantities of a solution measured out by volume or mass in the laboratory include both the solute and the solvent. If you need a certain amount of solute, you measure the amount of solution directly, not the amount of solvent. So, when doing stoichiometry, molality requires an additional calculation to take this into account. 

But we can also answer this question by converting molarity to molality. So, what is the molal concentration of a 0.28 molar solution of glucose To convert between molality and molarity, we need to know the density of the solution. The density of a D5W solution is 1.0157 g/mL. We also need to be very careful about the definitions of molarity and molality, and keep in mind whether we are dealing with liters of solutions or kilograms of solvent. 

It is necessary here to digress briefly in order to introduce the term molality which is required for the definition of an ideal dilute solution (section 36.3 below). The molality of a component, i, in a solution, mi, is defined as the amount of the solute, i, in 1 kg (= 1000 g) of solvent. 

When the amount of material present is measured by either concentration, c or molality (= amount of solute/mass of solvent) i the definition of activity differs slightly from the case (equation (39.4)) where a dimensionless measure (like mole fraction, x) is used. Equations for chemical potential, fi, involving mole fractions, x apply quite well when one is examining equilibria in solution. However in other cases concentration, c or molalities, m are often used. Activity will then be defined in relation to a standard concentration, c° ... 

The concept of a chemical potential is germane to a discussion of water activity (aw), which is technologically defined as the ratio of the equilibrium water vapor pressure over a solution or dispersion (p0) and the water vapor pressure over pure water (jb ). Also by definition, the chemical potential of a solvent ( jl0) or a solute (p ) is the rate of change in energy of either with a change only in the molal content of that component in solution. 

Note The key word for the addition of definite amounts of a reactant to a solution is REACTION. The command SELECTED OUTPUT, which has already been mentioned in chapter 2.2.1.4, is very useful here. It directly displays all required data in an extra file in a spreadsheet format, so the user does not have to look through the whole output manually. Under molalities and under totals the species of interest and the total concentration of an element can be issued, respectively. 

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