Quantities mean molar quantity

If the process is carried out at constant volume, the heat evolved Qi will be equal to an energy change AE2 or, per mole of adsorbate, qi = Ae2 (small capital letters will be used to denote mean molar quantities). Alternatively, the process may be... 

Now consider the partial (mean) molar quantities of i if Ui moles are placed alone in the same volume V and at the same temperature T. If we call these (5 )5, hi)g and then we wish to show that... 

Define the mean molar quantity of any extensive parameter Z as... 

The mean molar quantities are convenient due to their independence on n, so they are unambiguously defined by (p + 1) parameters (T, F,xi,..., x.-i) only, and not by (p + 2) parameters (T, P, ni,..., n.). From here on, when speaking of the mean molar quantities we will consider the mole frcictions of the first (p —1) components as independent variables. 

The above considerations also hold good for the mean molar quantities defined by (i/+ 1)-indepcnde.nt parameters only (see subsection 1.1.1). 

Euler s theorem can also be written in terms of the mean molar quantity, defined... 

A modified version of the method generally gives better accuracy. In this method we make a graph of the change in the mean molar quantity on mixing (forming the solution from the pure substances) ... 

Yxa Symbol used to stand for a general molar or mean molar quantity,... 

Thermodynamics requires a precise and accurate use of quantities the convention suggested by lUPAC for a proper thermodynamics nomenclature is here summarized. For any extensive quantity X we define (i) the mean molar quantity x = j, which is the quantity normalized to the amount of matter expressed as moles n, and is indicated by the lower case ii) the correspondent differential quantity, which is defined as the derivative of the quantity X with respect to the amount of matter expressed as moles n, and is indicated by the bar lower case x. 

We shall also use the mean molar quantities y associated with the extensive variable Y and defined by... 

Partial molar quantities have per mole units, and for Yj this is understood to mean per mole of component i. The value of this coefficient depends on the overall composition of the mixture. Thus Vj o the same for a water-alcohol mixture that is 10% water as for one that is 90% water. 

Given this context, the use of chemical symbols, formulae and equations can be readily misinterpreted in the classroom, because often the same representations can stand for both the macroscopic and sub-microscopic levels. So H could stand for an atom, or the element hydrogen in an abstract sense H2 could mean a molecule or the substance. One common convention is that a chemical equation represents molar quantities, so in Example 9 in Table 4.1,... 

Apparent molar quantities for multicomponent systems, other than binary systems, have been used to only a limited extent because of the difficulty of dealing with more than two mole numbers. Actually, there is no single definition of an apparent molar quantity for such systems. If we limit the discussion to the volume and refer to the definition of the apparent molar volume of the binary system (Eq. 6.53)), then we see that for multicomponent systems we must consider the difference between the volume of the solution and some other volume, and the meaning of the molar quantity. There appear to be two possible cases for these definitions. In the first case we could choose... 

A combination of 150 mg/kg caffeine administered by injection to pregnant rats in conjunction with a single dose of 9,756 mg/kg DEHP on day 12 of gestation caused a 5-fold increase in the number of dead and resorbed fetuses and nearly a 4-fold increase in the malformed survivors as compared to the effects of DEHP alone (Ritter et al. 1987). The mean fetal weight was also depressed. The addition of the caffeine to the treatment using equimolar quantities of 2-ethylhexanol and 2-ethylhexanoic acid at doses half of the molar quantity used for DEHP resulted in 2-30-fold increases in the dead and malformed fetuses and malformed survivors, but only minor decreases in the fetal weights. 

The dependence of XE on mole fraction can be analysed to obtain the dependence on mole fraction of the relative partial molar quantities, Xx — X and X2 — X2, which are calculated from the intercepts on the and X2-axes of the tangent to the XE -curve. Consequently the XE -data must be precise if these partial molar values are to be meaningful. For example, one of the features of some aqueous mixtures is a minimum in the value of V2 — V2 at low values of x2. This means that the VE -curve has a point of inflexion at this mole fraction. 

The heat resistance of a polymer may be characterised by its temperatures of "initial" and of "half" decomposition. The latter quantity is determined by the chemical structure of the polymer and can be estimated by means of an additive quantity the molar thermal decomposition function. The amount of char formed on pyrolysis can be estimated by means of another additive quantity the molar char-forming tendency. 

The reference values may be estimated by means of additive molar quantities often the values at 298 K and atmospheric pressure are used as such. Division of an intrinsic quantity by its reference value gives the reduced, dimensionless, intrinsic quantity. 

The adjective molar before the name of an extensive quantity generally means divided by amount of substance. The subscript m on the symbol for the extensive quantity denotes the corresponding molar quantity. 

When the main purpose of the gas adsorption measurements is to characterize the adsorbent surface or its pore structure, the preferred approach must be to follow the change in the thermodynamic quantity (e.g. the adsorption energy) with the highest available resolution. This immediately leads to a preference for the differential option, simply because the integral molar quantity is equivalent to the mean value of the corresponding differential quantity taken up to a recorded amount adsorbed. Their relationship is indicated by the mathematical form of Equation (2.64), which is explained in the following section. 

Pp is the pure polymer density while is the modulus of temporary elasticity and Mm is the mean molar weight of one skeletal bond. It is considered that the mean number Ne is also involved in NMR properties. However, the relevant experimental quantity which is directly associated with the characterisation of... 

The expression stoichiometric quantities of reactants means molar amounts of the reactants numerically equal to their stoichiometric coefficients. For the calcium carbide reaction, stoichiometric quantities of the reactants in the SI system of units would be I mol of CaC (s) and 2 mol of H20(1). If stoichiometric quantities of the reactants are fed and the reaction proceeds to completion, both reactants would be completely consumed and stoichiometric quantities of the products would be formed. (Convince yourself.)... 

Another asp>ect of partial molar volumes and heat contents, in particular, arises from the thermod3mamic requirement that for an ideal gas mixture or for an ideal liquid solution, as defined for example in 30a and 34a, respectively, there is no change of volume or of heat content upon mixing the components. This means that the partial molar volume and heat content of each substance in the mixture are equal to the respective molar values for the pure constituents. Any deviation of the partial molar quantity from the molar value then gives an indication of departure from ideal behavior this information is useful in connection with the study of solutions. 

Using the definitions of mean molar and partial molar quantities, Eqn (3.14) becomes... 

A Many starting materials could be used, but barium oxide (BaO) is not a suitable choice. BaO is highly hygroscopic and absorbs carbon dioxide from the air. This means an amount of BaO/Ba(OH) / BaCO would be weighed out rather than the molar quantity of BaO required. The mixture of starting materials would be deficient in barium, and hence, so would the product. In cases like these, where the logical choice is unsuitable, a metal carbonate or nitrate would be used. These metal salts decompose stoichiometrically to the oxide on heating ... 

Water is unique among polar solvents in that it is a small molecule with a low molar volume. As a result, the concentration of water in pure water is 55.5 M. This means that the mole fraction of water in dilute aqueous solutions is close to one, and the partial molar quantities in these solutions are close to the corresponding quantities for the pure solvent. Other solvents have considerably higher molar volumes, and therefore, lower concentrations in the pure solvent. The... 

The simulated plots calculated from Equations (5.15) and (5.16) are shown in Figure 5.5a and b, respectively. The partial molar quantities determined from the Monte Carlo simulation are in a good agreement with experimental results. It is noteworthy that a similar conclusion was drawn from results obtained when using the mean-field approximation based upon the lattice gas model in Section 5.2.3.I. 

The addition of solute will also influence the cmc of the surfactant, which in turn means that a correction is needed for the overall partial molar quantity, F This has been taken into account in the models proposed by Roux et al. and DeLisi et al. ° The models have been applied to different thermodynamic properties, mostly volumes and heat capacities, and for different surfactant-solute systems. 

Hi- Once we know the partial molar quantities /ij, Su Vi, etc., we get Ae solution properties as G = EinjGj, S = HiriiSi, V = Y.i riiVi, etc. Note that knowing P as a function of T, P, and composition means we know the equation of state of the solution. 

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