Solution molality

In an electrolyte solution, each formula unit contributes two or more ions. Sodium chloride, for instance, dissolves to give Na+ and Cl ions, and both kinds of ions contribute to the depression of the freezing point. The cations and anions contribute nearly independently in very dilute solutions, and so the total solute molality is twice the molality of NaCl formula units. In place of Eq. 5a we write... 

Step 1 Convert the observed freezing-point depression into solute molality by writing F.q. 5b in the form... 

If the validity of Eq. (1.3.31) is assumed for the mean activity coefficient of a given electrolyte even in a mixture of electrolytes, and quantity a is calculated for the same measured electrolyte in various mixtures, then different values are, in fact, obtained which differ for a single total solution molality depending on the relative representation and individual properties of the ionic components. 

The amount is measured in terms of the molality of the solute. Molality (note the spelling) is defined as the amount of solute dissolved per unit mass of solvent ... 

We already have the van t Hoff factor, the Kb, and solution molality so we can simply substitute ... 

Notice that this equation uses kilograms of solvent, not solution. The other concentration units use mass or volume of the entire solution. Molal solutions use only the mass of the solvent. For dilute aqueous solutions, the molarity and the molality will be close to the same numerical value. 

Molarity, M = moles solute per liter solution Molality, m = moles solute per kilogram solvent... 

Figure 8,13 Activity of H2O solvent in aqueous solutions of various solute molalities. Reprinted from Garrels and Christ (1965), with kind permission from Jones and Bartlett Publishers Inc., copyright 1990.

Figure 8.23B shows the effect of adding sulfur and carbon in solution (solute molality = 10 ). In reducing-alkaline conditions, both rhodochrosite MnC03 and alabandite MnS are stable. However, the field of alabandite is quite restricted, which explains why this mineral is rarely found in nature (Brookins, 1988). 

As already mentioned, the Eh-pH extension of the field of native sulfur depends on the total sulfur concentration in the system. With solute molality lower than approximately 10 moles/kg, the field of native sulfur disappears. 

Molarity= Moles of solute Molality = Moles of solute... 

Table 3.14 gives the solubilities of the Group 1 halides at 25 °C in terms of the molalities of their saturated solutions. Molalities of solutes of 12.0 and greater are indicated in colour. 

The general features of the experimental results are shown in Figures 1-4. As a first approximation, the variation of total pressure P with solute molality may be represented by a linear relationship P = Pq + km. Figure 2 compares... 

In the limit of small xB, the solution molality mB (= moles of solute per kilogram of solution) is also proportional to xB ... 

The overall proportionality between ATbp and solute molality mB can therefore be expressed as... 

As shown in the first diagram in this sidebar (for water), the melting point of solution is also displaced toward lower values by addition of a nonvolatile solute, the freezing-point depression effect. By arguments similar to those given above, the freezing-point depression ATfp = T p — 7fp(.xB) will also be found to be proportional to solute molality ... 

Molality (in) is concentration expressed as moles of substance per kilogram of solvent (not total solution). Molality is independent of temperature. Molarity changes with temperature because the volume of a solution usually increases when it is heated. 

SI base units include the meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), and mole (mol). Derived quantities such as force (newton, N), pressure (pascal. Pa), and energy (joule, J) can be expressed in terms of base units. In calculations, units should be carried along with the numbers. Prefixes such as kilo- and milli- are used to denote multiples of units. Common expressions of concentration are molarity (moles of solute per liter of solution), molality (moles of solute per kilogram of solvent), formal concentration... 

FIG. 2 Effect of solute molality (m) on the mean molal activity coefficient (y ) for sodium chloride (O), sodium acetate (O), and sodium propionate ( ) at 25°C, as extracted from Robinson and Stokes (2002). The continuous lines were calculated using Eq. 9 and the empirical coefficients At extracted from Fidaleo and Moresi (2005a,b, 2006). 

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