Concentration units mole fraction

Usually the diffusant will be present in low concentrations. In dilute solutions all concentration units (mole fractions, volume fraction, molarity, etc.) are proportional to one another, therefore... 

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. 

On the basis of the values of AS° derived in this way it appears that the chelate effect is usually due to more favourable entropy changes associated with ring formation. However, the objection can be made that and /3l-l as just defined have different dimensions and so are not directly comparable. It has been suggested that to surmount this objection concentrations should be expressed in the dimensionless unit mole fraction instead of the more usual mol dm. Since the concentration of pure water at 25°C is approximately 55.5 moldm , the value of concentration expressed in mole fractions = cone in moldm /55.5 Thus, while is thereby increased by the factor (55.5), /3l-l is increased by the factor (55.5) so that the derived values of AG° and AS° will be quite different. The effect of this change in units is shown in Table 19.1 for the Cd complexes of L = methylamine and L-L = ethylenediamine. It appears that the entropy advantage of the chelate, and with it the chelate effect itself, virtually disappears when mole fractions replace moldm . ... 

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

When data are available for the solute over the entire concentration range, from mole fraction 0 to 1, the choice of standard state, either the hypothetical unit mole fraction (Henry s law) or the actual unit mole fraction (Raoult s law), is arbitrary, but it is frequently easier to demonstrate Raoult s law as a limiting law than Heiuy s law. Figure 16.2 shows the relationships for activity and activity coefficient when Heiuy s law is used to define the standard state, and Figure 16.3 shows the same relationships when pure solute is chosen as the standard state. 

Note. Notation as in Table 1-la. Unit of concentration is mole fraction. 

Absorption by a liquid of a single component from a mixture of gases. Let the unprimed phase be a mixture of a soluble gas A and an insoluble gas, the initial mole fraction of A being Yo. Similarly the concentration in the primed phase in volumes of dissolved gas per unit volume of liquid is initially equal to Co. At the interface a Henry s law expression is satisfied, so that, by Eq. (38), C (X, t) = K Y(X, t), where Ki is the solubility of A in the liquid, expressed as volumes of gaseous A per unit volume of liquid per unit mole fraction of A in the gas. The growth constant is then obtained by means of the result... 

Still another way to express solution concentration is mole fraction, which is moles of solute or moles of solvent dissolved in total moles of solution. The mole fraction has no units since moles appear in the numerator and denominator and thus cancel out. 

Standard-State conventions for chemical elements and dissolved solutes are summarized in Table si. 1. Note that the Standard states for gases and for solutes are hypothetical, ideal states and not actual states. For gases, this choice of Standard State is useful because the ideal gas represents a good limiting approximation to the real behavior of gases and possesses equations of state that are mathematically tractable in applications. For solutes, the choice of a hypothetical Standard State is of value because the alternative choice, consisting simply of the pure solute at unit mole fraction, is not very relevant to a solution component whose concentration must always remain small. Moreover, by... 

It should be pointed out, however, that the thermodynamic explanation of the chelate effect, in particular the contribution of entropy as presented above, is actually not as straightforward as it might appear. The entropy change for a reaction depends on the standard state chosen for reference and for very concentrated solutions one might chose unit mole fraction instead of one molal and the chelate effect would disappear. However, this is not realistic and for solutions one molal (or less) there is a real chelate effect. In very dilute solutions (0.1 M or less) where complexation of metal ions is generally most important, the chelate effect is of major importance and is properly understood as entropically driven. 

AAf al equals N — Nj0, and Jw equals < alAA al (we will use the same symbol for conductance in either system, the units being dictated by whether changes in concentration or mole fraction represent the driving force). Also, AA ° al is equal to AN + AA, 4- (see Eq. 8.17). The magnitude of each of these differences in water vapor mole fraction is inversely proportional to the conductance across which the drop occurs—i.e., g AA = g A/V 01—and so A/V is larger when g is smaller, where superscript x refers to any series component in the pathway (see Eq. 8.18). 

Let us first derive the units of the overall mass transfer coefficients when the concentration units used are in mole fractions. Let the overall mass transfer coefficient for the gas side be Kyf and that for the liquid side be K. Gd Y is mole of solute flowing per unit time. Mass transfer is a process where mass crosses an area perpendicular to the direction of motion of the solute particles. This area is the contact area for mass transfer. Let the differential area be designated as dA. Thus, in terms of mass transfer, Gd[Y] is equal to j,/([y/] - y )dA. From this expression, the dimensions of Kyf are mole per unit time per unit mole fraction per unit square area or MItImole fraction-1. In an analogous manner, Ld X is equal to ] -... 

Activity is given in the same units as concentration—molarity, mole fraction, and so forth. In (2-9) the concentration C usually is expressed either in moles per liter of solution (molarity M) or in moles per kilogram of solvent (molality m). In dilute aqueous solutions the molarity and molality are nearly equal in nonaqueous solutions molarity is usually larger than molality, since the density of the solvent is usually less than unity. Analytical chemists ordinarily find it more convenient to express concentration in molarity, even though it varies slightly with temperature. The analytical concentration is represented by the symbol C, to indicate the moles of solute added per liter of solution. Analytical concentration should be distinguished from the equilibrium concentration, which is indicated by enclosure in square brackets. 

F7-21g Sketch the polypiet concentration, Pj, mole fraction of polymer with j monomer units, yj, and the corresponding weight fraction, Wj, for j = 2, 10, 30 as a function of monomer conversion in Styrene polymerization for (a) Termination by means other than combination. 

Rather than consider reactions at unit mole fraction, standard states can be conceived at much lower concentrations than the usual one molal concentration. For example, if a standard state of 0.0010 molal were employed, the chelate effect would be quite large, 21.7 entropy units per mole of solute formed in solution or per metal chelate ring formed in the displacement reaction. 

The standard state of unit activity corresponds to pure solvent or unit mole fraction. (All solutions approach ideality at zero solute concentration.) Although the standard state is different, the form of this equation is identical to that of equation 7.11. The activity may be linked with the actual mole fraction by the activity coefficient, y that is a=yx. For ideal solutions, y= 1. 

Overall volumetric mass-transfer coefBcient, kg mol/m -h-unit mole fraction or lb mol/ft -h-unit mole fraction K a, based on liquid phase KyO, based on gas phase K a, Kya, including one-way diffusion factors, for liquid and gas phases, respectively Overall volumetric mass-transfer coefBcient for liquid phase, based on concentration difference, h ... 

The standard state for a pure liquid or solid is taken to be the substance in that state of aggregation at a pressure of 1 bar. This same standard state is also used for liquid mixtures of those components that exist as a liquid at the conditions of the mixture. Such substances are sometimes referred to as liquids that may act as a solvent. For substances that exist only as a solid or a gas in the pure component state at the temperature of the mixture, sometimes referred to as substances that can act only as a solute, the situation is more complicated, and standard states based on Henry s law may be used. In this case the pressure is again fixed at 1 bar, and thermal properties such as the standard-state enthalpy and heat capacity are based on the properties of the substance in the solvent at infinite dilution, but the standard-state Gibbs energy and entropy are based on a hypothetical state.of unit concentration (either unit molality or unit mole fraction, depending on the form of Henry s law used), with the standard-state fugacity at these conditions extrapolated from infinite-dilution behavior in the solvent, as shown in Fig. 9.1-3a and b. Therefore just as for a gas where the ideal gas state at 1 bar is a hypothetical state, the standard state of a substance that can only behave as a solute is a hypothetical state. However, one important characteristic of the solute standard state is that the properties depend strongly upon the solvent. used. Therefore, the standard-state properties are a function of the temperature, the solute, and the solvent. This can lead to difficulties when a mixed solvent is used. 

It has been pointed out by Adamson (34) and others (35,36) that the entropy-related chelate effect, as manifested in the stability constants, disappears when unit mole fraction replaces unit molality as the standard state of solutes in aqueous systems. On this basis the stability constants assumed for the model compounds in Table II (20) would have to be equivalent in magnitude regardless of the number of chelate rings formed. On the other hand the relative degrees of dissociation of the model compounds in Table II remain an experimental fact, with the larger concentration unit giving smaller numerical concentrations for the solutions illustrated, thus compensating for the disappearance of the chelate effect in the numerical values of the stability constants. 

Concentrations in mole fractions are used in the kinetics of the TAME reactions. Aspen accepts other concentrations units such as molarity, partial pressure and activity (called... 

The rate constant in die above equation is expressed in terms of pressure independent units (mole fraction). If the rate constant is expressed in terms of pressiue dependent units (such as concentration), the relevant equation is ... 

Fundamentally, it becomes the transformation from concentration units to mole fraction units. And, whereas the permeation of a pure liquid may be expressed for instance in terms of its liquid volume per se, the permeation of a component (or components) from a liquid mixture requires the introduction of the idea of composition namely, the component concentration or mole fraction. For the purposes here, the mole fraction is regarded as of more utility than component concentration. (For one thing, the totality of component mole fractions always sums to unity.) Therefore, the conversion is from concentration units to mole fraction units. 

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