Molality Concentration expressed solvent

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. 

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... 

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. 

In principle, [Gd] should be expressed in molality (mol/kg solvent), however, for dilute solutions molarity is generally used (mol/L or in practice mmol/L). If the longitudinal relaxation rate of water protons is considered and the concentration of Gd is given in mM, the parameter r, is called proton relaxivity (its unity is mM-1s-1). Proton relaxivity directly refers to the efficiency of a paramagnetic substance to enhance the relaxation rate of water protons, thus to its efficiency to act as a contrast agent. 

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. 

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. 

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

Before leaving this section, one comment about the concentration units used should bp made. Molality, which we have used here. and indicated by.the symbol M, is concentration expressed as moles of solute per kilogram of solvent. Molarity, defined as the number of moles of solute per liter of solution, is also a commonly used concentration unit. However, because the volume of a solution varies with composition and with temperature, molarity can be more difficult to deal with than molality, which is... 

In the practice of mixed solvents application, though more seldom, molar, Cm, and molal, c, concentrations are used. Correlations between these various methods of concentration expression are shown in Table 9.1. 

Both the freezing point depression and the boiling point elevation are directly proportional to the number of moles of solute per kilogram of solvent. When we deal with the colligative properties of solutions, another concentration expression, molality, is used. The molality (m) of a solution is the number of moles of solute per kilogram of solvent ... 

In this equation, m is the solution concentration expressed as a molality, a unit we have not discussed. For very dilute solutions, the molality m and molarity M are essentially equal, and M can be used in Equation 7.12 instead of m. This approximation will be used for calculating colligative properties of solutions in this book. The symbol AT is the boiling point or freezing point difference between pure solvent and solution. The specific equations used to calculate AT for boiling and freezing points are... 

Since the volume of a solution changes with temperature, so will the molarity, even though the amount of solute remains the same. If, however, the concentration of a given solution is expressed as moles of solute per kilogram of solvent (called molal concentration or molality), it will be independent of temperature. The units of molality are mol kg (or m, for short). 

Many physical properties are related to solution concentration expressed as molality, m, the number of moles of solute dissolved in one kilogram of solvent. The defining equation is... 

X is expressed as °C/m, m is expressed in mol solute/kg solvent (molality), and Atj is expressed in °C. Sample Problems C and D show how this relationship can be used to determine the freezing-point depression and molal concentration of a solution. 

Molality A measure of concentration expressed in mols per kilogram of solvent. 

When diffusion effects are negligible, the resin phase is assumed to be freely permeable to solvent and substrate (R). The distribution of the latter between the two phases is expressed by a distribution coefficient Ar, defined in equation 1, where Wr denotes the molal concentration of reactant R in the resin phase and Wr the corresponding concentration in the solution phase. ... 

PRACTICE EXAMPLE B Ionic liquids (ILs) are salts with relatively low melting points and vapor pressures. Because of their low volatilities, chemists continue to investigate the potential of ILs as safer and "greener" solvents. l-Butyl-3-methylimidazolium hexafluorophosphate, [BMIM][PF6], is a viscous, colorless, hydrophobic, and insoluble ionic liquid with a molar mass of 284.1 g/mol and a density of 1.38 g/mL. In a solution of [BMIM][PF6] and carbon dioxide at 8 MPa, the mole fraction of CO2 is 0.60. What is the solution concentration expressed as the (a) molarity of carbon dioxide and (b) molality of carbon dioxide Assume that there is no volume change when CO2 is added to [BMIM][PF6]. 

Solution Concentration—Any description of the composition of a solution must indicate the quantities of solute and solvent (or solution) present. Solution concentrations expressed as mass percent, volume percent, and mass/volume percent all have practical importance, as do the units, parts per million (ppm), parts per billion (ppb), and parts per trillion (ppt). However, the more fundamental concentration units are mole fraction, molarity, and molality. Molarity (moles of solute per liter of solution) is temperature dependent, but mole fraction and molality (moles of solute per kilogram of solvent) are not. 

Molality, m, is a solution concentration expressed as the amount of solute, in moles, divided by the mass of solvent, in kg. 

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state... 

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