Molarity converting molality

The molality is the concentration of solute in moles per kilogram of solvent. Its value is independent of the temperature and is directly proportional to the numbers of solute and solvent molecules in the solution. To convert molarity to molality, we note that the former is defined in terms of the volume of the solution, so we convert that overall volume to the mass of solvent present. 

EXAMPLE 8.7 Sample exercise Converting molarity into molality... 

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 main advantage of using molality is that it is temperature-independent because masses don t change when substances are heated or cooled. Thus, it is well suited for calculating certain properties of solutions that we ll discuss later in this chapter. The disadvantages of using molality are that amounts of solution must be measured by mass rather than by volume and that the density of the solution must be known to convert molality into molarity (see Worked Example 11.5). 

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. 

The density of the solution is required to convert molarity to molality or vice versa. 

A plot of the density of sodium hydroxide solutions of varying composition is also shown in fig. 1.1. Electrolyte solutions are considerably more dense than water when they are concentrated. The important point to remember about these systems is that their compositions cannot be varied over the whole range because the solute is normally a solid at room temperature. Thus, the range of the weight fraction scale is determined by the solubility of the solid solute. In order to convert from molality to molarity, the solution density must be determined. Density data for common solutions can be found in data compilations such as the Landolt-Bornstein tables. 

If you follow the dimensional analysis techniques you learned in Chapter 1, you can convert between concentration units, as shown in Sample Exercise 13.5. To convert between molality and molarity, the density of the solution will be needed, as in Sample Exercise 13.6. 

To convert molality to molarity and vice versa, you must know the density of the solution. The calculations are described in the next two examples. As the first example shows, molality and molarity are approximately equal in dilute aqueous solutions. 

Molal units are used predominately by engineers and scientists studying electrolytes because the concentration calculation is independent of density and, hence, temperature. Molal concentration is the number of gm-moles per 1000 gm of solvent. Equations 2-lc and 2-ld show how to convert between molal and molar concentrations. Note that as the acid or base weight fraction approaches one (the grams of solvent approaches zero), the molal concentration approaches infinity. 

Corrections to Be Added to Molar Values to Convert to Molal 2.88... 

It is frequently necessary to convert from one concentration unit to another This problem arises, for example, in making up solutions of hydrochloric acid. Typically, the analysis or assay that appears on the label (Figure 10.2, p. 263) does not give the molarity or molality of the add. Instead, it lists the mass percent of solute and the density of the solution. 

Step 1 Convert the observed osmotic pressure into solute molarity (not molality) by writing Eq. 6 in the form... 

Convert between molality and mole fraction or molarity (Toolbox 8.1 and Examples 8.6 and 8.7). 

We have information about molarity (mol/L) and density (g/mL) and are asked to find molality (mol/kg) and mole fraction (mol/mol). A good way to approach conversions from molarity to another measure is to choose a convenient volume for the solution, determine its mass and the mass of solute, and find the mass of water by difference. Then convert mass of water to kilograms and to moles to complete the calculations. 

What additional information is needed to convert the molality of a 1.00 m Na2S04 solution to the molarity ... 

The phase rule is often used in the form t = c - p + 2 to ascertain the number of degrees of freedom of a system even when the concentration units in the aqueous phase are molal (m) or molar. This is not correct because the phase rule is derived 1n terms of mole fractions (X). Thus, an additional quantity, the total number of moles, is required to convert X into m. This is illustrated by equations below which we shall find useful later on. 

Some pKSH values in non-aqueous solvents and water-organic solvent mixtures are listed in Table 6.6 [18, 19]. They are in molal scale but can easily be converted to molar scale by the relationship ... 

Example Converting Weight Percent into Molarity and Molality... 

Note that it is not possible to convert from molarity to molality or mole fraction unless some information about the density or weight composition of the solution is given. 

To calculate the molality of a solution prepared by dissolving 10.5 g of sodium chloride in 250 g of water, we convert the mass of sodium chloride to moles of NaCl (by dividing the mass by the molar mass) and divide it by the mass of water in kilograms ... 

Molality (m) mol solute kg solvent Temperature-independent useful in special applications Measure by mass must know density to convert to molarity... 

Molar concentration units were converted into molal units using the partial molar volume of the salt. (W e assume that RNA and other buffer components are present in such low concentrations that the density of the solution is not significantly different than a solution of water and salt alone.) The formula is... 

The predicted values for the various solid phases shown in Table IV were calculated using the hydroxide and carbonate activity printout of the model. These values were used to calculate the equilibrium trace cation activities in the brine. The activity values were then divided by the predicted single ion activity coefficients and thereby converted to the molal concentration scale. These molal units were then converted to molar units, and then into the milligrams per kilogram of solution units reported. 

Sample Cesium chloride (Nacalai Tesque Co.) was recrystallized from distilled water. Sample solutions were prepared by weight at the concentration of 0.100-5.000 ( 0.(XX)1) mol kg. The molality was converted into the molarity (c) using the density of aqueous CsCl... 

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