Molality Concentration expressed

Molality, or molal concentration, expresses concentration in terms of moles of solute per kilogram of solvent. Molality can be used as a conversion factor between moles of solute and kilograms of solvent. Molality is abbreviated with a lower case m. Notice we said kilograms of solvent, not kilograms of solution. If we dissolved 1.0 mol of NaCl in 1.0 kilograms of water, we would obtain a 1.0 molal solution of NaCl. 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

The symbol used is dependent upon the method of expressing the concentration of the solution. The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are as follows concentration in moles per litre (molarity), activity coefficient represented by y, concentration in mols per kilogram (molality), activity coefficient represented by y, concentration expressed as mole fraction, activity coefficient represented by f... 

Electrostatic and statistical mechanics theories were used by Debye and Hiickel to deduce an expression for the mean ionic activity (and osmotic) coefficient of a dilute electrolyte solution. Empirical extensions have subsequently been applied to the Debye-Huckel approximation so that the expression remains approximately valid up to molal concentrations of 0.5 m (actually, to ionic strengths of about 0.5 mol L ). The expression that is often used for a solution of a single aqueous 1 1, 2 1, or 1 2 electrolyte is... 

Figure 5.12. Electrode potential of Ag/Ag electrode as a function of Ag concentration. Molality is the concentration expressed as gram-molecules or gram-ions solute per liter (55 mol) of water. (From Ref. 5, with permission from Van No strand Reinhold.)...

It is essential to take note here of the relationship between concentrations expressed in molal and weight units (Wells, 1984) ... 

Here, m is the molal concentration of the /-component in mol/1000 g water ct is the weight concentration of the /-component in g/ml Vi and vz (with bars) are the specific volumes of water and biopolymer in ml/g and Mf is the molar weight of the biopolymer in g/mol (Da). In turn, the relationship between the second virial coefficients expressed in the different units (molal, At weight, ) is as follows (Wells, 1984) ... 

If the conductivity of an electrolyte in a polar solvent is measured up to high concentrations, the conductivity-concentration relation usually shows a maximum as in Fig. 7.3. Such a relationship is explained by the competition between the increase in the number of charge carriers and the decrease in ionic mobilities, mainly due to the strengthening of ion-ion interactions. Various empirical equations have been reported to express such a relation. The Casteel-Amis equation [21] for the relation between k and the molal concentration m is... 

His procedure was used for the calculation of the activity coefficients in the aqueous solution of two electrolytes with a common ion from isopiestic data (3). Kelly, Robinson, and Stokes (4) proposed a treatment of isopiestic data of ternary systems with two electrolytes by a procedure based on the assumption that at all values of molal concentrations, mi,m2, the partial derivatives may be expressed by a sum of two functions in their differential form as follows ... 

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. 

Concentrations expressed as molality or mole fractions are temperature-independent and are most useful when a physical measurement is related to theory over a range of temperature, e.g., in freezing point depression or boiling point elevation measurements (Chapter 11). Since the density of water is close to 1 g/cm3, molal and molar concentrations are nearly equal numerically for dilute aqueous solutions (<0.1 M). 

The first term on the right is the salt dependence of In Kohs, expressed in molal concentration units. The second term can be calculated from the dependence of the salt activity coefficient on salt concentration... 

The constant KV) which is called the ionic product of water, may be computed from equations (V-44) and (V-46), if partial molal free energies (potentials) of formation of all the reaction components in the corresponding standard states are known. For such standard states we select both the state of a hypothetical ideal solution with molal concentration of hydrogen and hydroxyl ions equalling unity and the state of hypothetical, absolutely undissociatcd pure water. Since in actual diluted solutions the activity of undissociated water hardly differs from the activity in its standard state, aji2 in the equation (V-51) may be considered as equalling unity so that then Km = K . The following expression is valid for a temperature of 25° C ... 

Debye-Hiickel equation is valid in unchanged form for concentrations expressed both by molality and molarity. 

In working with Fick s law, one may use mass flux per unit area and mass concentration as in Eq. (11-1), or the equation may be expressed in terms of molal concentrations and fluxes. There is no general rule to say which type of expression will be most convenient, and the specific problem under consideration will determine the one to be used. For gases, Fick s lawTnay expressed in terms of partial pressures by making use of the perfect-gas equa bn... 

It is admitted to use the concentrations expressed in moles per 1000 g of HjO (molality), instead of activities for poorly soluble compounds, and the index pL = - IgL, instead of concentrations product. 

Now, the key thermodynamic aspects of this mechanism (reviewed in [4,78,79]) will be examined in more detail. Setting component 1 = principal solvent (here water), component 2 = protein, and component 3 = solute (e.g., sucrose or PEG), the preferential interaction of component 3 with a protein is expressed, within close approximation, by the parameter (5m3/5m2) jj at constant temperature and pressure, where p, and m, are the chemical potential and molal concentration of component /, respectively. A positive value of this interaction parameter indicates an excess of component 3 in the vicinity of the protein over the bulk concentration (i.e., preferential binding of the solute). A negative value for this parameter indicates a deficiency of component 3 in the protein domain. Component 3 (the solute) is preferentially excluded and component 1 (water) is in excess in the protein domain. 

Molality is a measure of solute concentration, expressed as moles of solute per kilogram of solvent. 

Based on the theory of colligative properties and the principles of osmometry, it is understood that osmometer will read osmolalities and not osmolarities because colligative properties are directly proportional to the total solute concentration expressed in molality [see Eqs. (1)-(16)]. The relationship between osmolality and osmolarity and its significance can be found in the Remington s Pharmaceutical Sciences and in a review article by Deardorff. However, it is more convenient to use osmolarity because it is based on weight/volume rather than on weight/weight as in... 

This is rigorous only if concentrations are expressed in mol kg (i.e., in molal units). The mixed acidity constants K and are the same whether molar or molal concentration units are used. Ajo for calcite is given in molar units. We would correct by considering the density of the seawater at any Tand P, but the correction is much smaller (< 3%) than the uncertainty in the value. 

For solutes, which include all dissolved aqueous species (including ions and neutral or molecular species), the activity of the solute ( ,) is related to the solute s molal concentration (m,) (moles of i in I kg of water) by the expression... 

Molality is expressed as the number of moles of solute dissolved per kilogram of solvent, and is therefore independent of temperature since all of the quantities are expressed on a temperature-independent weight basis. The molality of a solution is useful in describing solubility-related phenomena at various temperatures, and as the concentration unit of colligative property studies. When the density of the solvent equals unity, or in the case of dilute aqueous solutions, the molarity and the molality of the solution would be equivalent. 

Because of the inconvenient nature of the standard state defined above, the concentration units used to describe the concentration dependence of the chemical potential are usually different. More convenient choices for concentration are molality and molarity. When the solution is dilute the relationship between mole fraction and molality is quite simple (see equation (1.2.3)). In terms of molality, the expression for the concentration dependence of the chemical potential of component B becomes... 

The molality (m) of a solution is a concentration expressed as the number of moles of the solute in a kilogram of solvent. 

The first right-hand expression is written in activities, and this quotient gives the intrinsic dissociation constant. The second right-hand expression is made up of two factors, a quotient of (molar or molal) concentrations that may be called the stoichiometric dissociation constant, and a quotient of activity coefficients. All dissociation constants, association constants K = 1 /ATD), and solubility products in reference books are intrinsic constants. They apply to concentrations only if the solution is extremely dilute for all ionic species. In other cases, one has to know the activity coefficients. y0, i.e., y for a nonionic species, will mostly be close to unity, but y+ and y will generally be < 1, the more so for a higher ion concentration. One may define the free... 

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