Concentration ratios: molality

The most easily diagnosed finite size artifact is the presence of a concentration mismatch between the counter- and coion to water ratio (molality) and the actual electrolyte concentration at the edge of the simulation box. This is detected by calculating the macromolecule-counterion and macromolecule—coion radial distribution functions (RDFs) from an equilibrated trajectory. Examples of RDFs based on previous work on the... 

Molality Way of expressing concentration. Ratio of moles of solute to kilograms of solvent. 

SO4/CI) designates the molal concentration ratio of sulfate to chloride. In seawater this ratio is 0.0516. 

Rate models that express the rate of change of concentration (R, molal/sec) due to the dissolution or precipitation of a solid must account for the surface area to volume Al V) or surface area to mass of solution (AIM) ratio of the reacting system. Table 6.1 gives AIV and AIM ratios for some common geometries. 

Table 16.1 makes these ratios specific for percentage concentration, molarity, molality, and normality. 

Molality, abbreviated molal or m, is useful for colligative properties because it is a more direct ratio of molecules of solute to molecules of solvent. The unit molarity automatically includes the concept of partial molar volumes because it is defined in terms of liters of solution, not liters of solvent. It is also dependent on the amounts of solvent and solute (in mole and kilogram units), but independent of volume or temperature. Thus, as T changes, the concentration in molality units remains constant while the concentration in molarity units varies due to expansion or contraction of the solutions volume. 

Tbe mass-transfer coefficients k c and /cf by definition are equal to tbe ratios of tbe molal mass flux Na to tbe concentration driving forces p — Pi) and (Ci — c) respectively. An alternative expression for tbe rate of transfer in dilute systems is given by... 

Two measures of concentration that are useful for the study of colligative properties, because they indicate the relative numbers of solute and solvent molecules, are mole fraction and molality. We first met the mole fraction, x, in Section 4.8, where we saw that it is the ratio of the number of moles of a species to the total number of moles of all the species present in a mixture. The molality of a solute is the amount of solute species (in moles) in a solution divided by the mass of the solvent (in kilograms) ... 

The concentration of lyonium or lyate ions cannot be increased arbitrarily. A reasonable limit for a dilute solution can be considered to be a molality of about 1 mol kg-1 (e.g. in water, one mole of solute per 55 moles of water). When the ratio is greater than 1 55, it is difficult from a thermodynamic point of view to consider the system as a solution, but it should rather be viewed as a mixture. This situation becomes increasingly... 

For the more general case of arbitrary rate constants, the analysis is more complex. Various approximate techniques that are applicable to the analysis of reactions 5.4.1 and 5.4.2 have been described in the literature, and Frost and Pearson s text (11) treats some of these. One useful general approach to this problem is that of Frost and Schwemer (12-13). It may be regarded as an extension of the time-ratio method discussed in Section 5.3.2. The analysis is predicated on a specific choice of initial reactant concentrations. One uses equivalent amounts of reactants A and B (A0 = 2B0) instead of equi-molal quantities. 

Levenspiel (11) has evaluated the right side of equation 8.3.14 for various values of n and SA. His results are presented in graphical form in Figure 8.8. For identical feed concentrations (CA0) and molal flow rates (FA0) the ordinate of the figure indicates the volume ratio required for a specified conversion level. 

The reactant concentration at the reactor inlet is given by the ratio of the molal and volumetric flow rates at the same spot. Therefore,... 

In a rate equation the concentrations are replaced by ratios of molal and volumetric flows,... 

The ratio of the molecular to the ionic concentrations of the electrolyte is determined by the dissociation constant K. The activity is related to the molality through the activity coefficient... 

The scaling tendency of the lime or limestone processes for flue gas desulfurization is highly dependent upon the supersaturation ratios of calcium sulfate and calcium sulfite, particularly calcium sulfate. The supersaturation ratios cannot be measured directly. They are determined by measuring experimentally the molalities of dissolved sulfur dioxide, sulfate, carbon dioxide, chloride, sodium and potassium, calcium, magnesium, and pH. Then by calculation, the appropriate activities are determined, and the supersaturation ratio is determined. Using the method outlined in Section IV, the concentrations of all ions and ion-pairs can be readily determined. The search variables are the molalities of bisulfite, bicarbonate, calcium, magnesium, and sulfate ions. The objective function is defined from the mass balance expressions for dissolved sulfur dioxide, sulfate, carbon dioxide, calcium, and magnesium. This equation is... 

System NH -S02 H20 For comparison with calculated data only the experimental results of Johnstone (16) and Boublik et al. (JT 1 ) were used. (Boublik et al. investigated the system NH3-SO2-SO3-H2O only some of their results with very low SO3/SO2 ratios were used for comparison with calculated data). Experimental results by other authors mostly cover very high solute concentrations in the liquid phase (20 molal and more) and are, therefore, not suitable for comparison with the models discussed here. As van Krevelen s method cannot be used for this system, the comparison is limited to the other procedures. Partial pressures of ammonia calculated from the BR-model are generally too large the calculated values exceed the experimental results mostly by a factor larger than 5. The EMNP method generally yields partial pressures which are only about half as large as the measured ones. The calculated partial pressures of SO2 are always too small, for temperatures between 50 and 90 °C the mean deviations a-mount from 20 to 40 per cent for the EMNP-model and from 40 to 70 per cent for the BR-model. 

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... 

The composition of a mixture need not be given in terms of the mole fractions of its components. Other scales of concentration are frequently used, in particular, when one of the components, say. A, can be designated as the solvent and the other (or others), B, (C,...) as the solute (or solutes). When the solute is an electrolyte capable of dissociation into ions (but not only for such cases), the molal scale is often employed. Here, the composition is stated in terms of the number of moles of the solute, m, per unit mass (1 kg) of the solvent. The symbol m is used to represent the molal scale (e.g., 5 m = 5 mol solute/1 kg solvent). The conversion between the molal and the rational scale (i.e., the mole fraction scale, which is related to ratios of numbers of moles [see Eq. (2.2)] proceeds according to Eqs. (2.32a) or (2.32b) (cf. Fig. 2.4) ... 

If the ratio of the concentrations is equal to the ratio of the activities in terms of molalities, as is probably the case if the solutions are dilute. 

With the same samples, several determinations were made with either increasing or decreasing concentration so that the results could be plotted on a graph where each line represents the points of one equilibrated system with the same water activity and different ratio of the solutes. The points on the coordinates are the molalities of isotonic binary solutions. The experimental points must lie simultaneously on the straight line of the constant ratio of the concentrations of the solutes (Figures 1 and 2). 

The proof strength at which the volatility curve of a particular component intersects that of ethyl alcohol indicates that proof at which the minor constituent will be concentrated in a fractionating column at the limiting condition of total reflux. For practical conditions, the maximum concentration of a particular congener or minor component occurs at a proof in the column at which its volatility is approximately equal to the internal reflux ratio (L/V where L is the molal liquid or overflow rate and V the molal vapor rate). This can be established by the technique... 

HILDEBRAND RULE. The entropy of vaporization, i.e.. the ratio of the heal of vaporization to the temperature at which it occurs, is a constant for many substances if it is determined at the same molal concentration of vapor for each substance. 

Another way to express vapor concentration is by molal saturation, which is the ratio of the moles of vapor to the moles of vapor-free gas. 

The slope of this line is the distribution coefficient (Kd), which is the ratio of the arsenic concentration on the adsorbent (Cads) to the concentration of the associated remaining arsenic in the aqueous solution (Csdn). With each linear adsorption isotherm, Kd has only one value. That is, a linear distribution indicates that the partitioning of arsenic between the adsorbent and the solution is constant over the given range of arsenic concentrations (Eby, 2004), 221. If both concentrations (Cads and Csoin) are in the same units (such as molal), Kd is unitless. However, if the adsorbed concentration is given in molal and the dissolved concentration is molar, then Kd has the units of liter/kilogram. 

Catalytic conversion of l-Octanol-2-d to ketone A quantity (29.7 ml.) of l-octanol-2-d was charged (space velocity 0.2) to a 5-mm. reactor tube containing 18 ml. of 8- to 10-mesh chromium oxide catalyst maintained at 400°. The 27.7 ml. of liquid product was fractionated in a concentric-tube etjlumn. A 60.6% yield of di-n-heptyl ketone was obtained. Approximately 17% of the alcohol was recovered "unconverted. Mass spectrometric analysis of the gaseous product showed the atomic ratio of deuterium to hydrogen to be 0.106. The molal yields of deuterium, hydrogen, and carbon monoxide produced per mole of ketone were 0.216, 2.040, and 0.815 respectively. 

Activity coefficient the ratio of the activity (of an electrolyte) as measured by some property, such as the depression of the freezing point of a solution, to the true concentration (molality). It is usually less than 1 and increases as the solution becomes more dilute, when the attractive forces between oppositely charged ions become negligible. 

It will be seen from Table 2 that with increasing concentration the activity-coefficient first falls more rapidly than the conductance-ratio, being about 10% smaller than the latter at concentrations 0.1 to 0.5 molal. This shows that at these concentrations there is an error of this magnitude in the common practice of employing in mass-action expressions the conductance-ratio as a measure of the activity of the ions of the add. The activity-coeffident, moreover, unlike the conductance-ratio, passes through a minimum at about 0.50 molal, and then increases rapidly with the concentration, becoming about equal to that... 

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