Mole defined

Reaction scale in moles defined by synthesis tree (column K)... 

As we have seen, the mole (defined in Section 2.6) is a convenient quantity of matter to work with. What volume does 1 mol of a gas occupy according to Avogadro s law Experiments show that 1 mol of any gas molecules has a volume of 22.4 L at STP (see I Figure 6.7). 

The relationship required is the gas expansion factor (E), and is defined for a given quantity (mass or number of moles) of gas as... 

To define the thennodynamic state of a system one must specify fhe values of a minimum number of variables, enough to reproduce the system with all its macroscopic properties. If special forces (surface effecls, external fields—electric, magnetic, gravitational, etc) are absent, or if the bulk properties are insensitive to these forces, e.g. the weak terrestrial magnetic field, it ordinarily suffices—for a one-component system—to specify fliree variables, e.g. fhe femperature T, the pressure p and the number of moles n, or an equivalent set. For example, if the volume of a surface layer is negligible in comparison with the total volume, surface effects usually contribute negligibly to bulk thennodynamic properties. 

Van der Waals (1890) extended his theory to mixtures of components A and B by introducing mole-fraction-dependent parameters a and b defined as quadratic averages... 

The treatment of such order-disorder phenomena was initiated by Gorsky (1928) and generalized by Bragg and Williams (1934) [5], For simplicity we restrict the discussion to the synnnetrical situation where there are equal amounts of each component (x = 1/2). The lattice is divided into two superlattices a and p, like those in the figure, and a degree of order s is defined such that the mole fraction of component B on superlattice p is (1 +. s)/4 while that on superlattice a is (1 -. s)/4. Conservation conditions then yield the mole fraction of A on the two superlattices... 

The extent of reaction is defined in tenns of the amount n. of species B. (i.e. the amount of substance or enplethy n., usually expressed in moles [10]) ... 

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

A7 Ethane/methane selectivity calculated from grand canonical Monte Carlo simulations of mixtures in slit IS at a temperature of 296 K. The selectivity is defined as the ratio of the mole fractions in the pore to the ratio of mole fractions in the bulk. H is the slit width defined in terms of the methane collision diameter (Tch,- (Figure awn from Crackncll R F, D Nicholson and N Quirke 1994. A Grand Canonical Monte Carlo Study ofLennard-s Mixtures in Slit Pores 2 Mixtures of Two-Centre Ethane with Methane. Molecular Simulation 13 161-175.)... 

Reflux ratio. This is defined as the ratio between the number of moles of vapour returned as refluxed liquid to the fractionating column and the number of moles of final product (collected as distillate), both per unit time. The reflux ratio should be varied according to the difficulty of fractionation, rather than be maintained constant a high efficiency of separation requires a liigh reflux ratio. ... 

If we know the moles of A and the number of reaction units associated with A and B, then we can calculate the moles of B. Note that a conservation of reaction units, as defined by equation 2.3, can only be applied between two species. There are five important principles involving a conservation of reaction units mass, charge, protons, electron pairs, and electrons. 

Equivalent Weights Acid-base titrations can be used to characterize the chemical and physical properties of matter. One simple example is the determination of the equivalent weighf of acids and bases. In this method, an accurately weighed sample of a pure acid or base is titrated to a well-defined equivalence point using a mono-protic strong acid or strong base. If we assume that the titration involves the transfer of n protons, then the moles of titrant needed to reach the equivalence point is given as... 

As an alternative to the ratios ni/n2 and [Mi]/[M2] in Eq. (7.15), it is convenient to describe the composition of both the polymer and the feedstock in terms of the mole fraction of each monomer. Defining F as the mole fraction of the ith component in the polymer and fj as the mole fraction of component i in the monomer solution, we observe that... 

We define Fj to be the mole fraction of component 1 in the vapor phase and fi to be its mole fraction in the liquid solution. Here pj and p2 are the vapor pressures of components 1 and 2 in equihbrium with an ideal solution and Pi° and p2° are the vapor pressures of the two pure liquids. By Dalton s law, Plot Pi P2 Pi/Ptot these are ideal gases and p is propor-... 

Mass transfer rates may also be expressed in terms of an overall gas-phase driving force by defining a hypothetical equiHbrium mole fractionjy as the concentration which would be in equiHbrium with the bulk Hquid concentration = rax ) ... 

By convention, the components C and D are assigned so that the ratio exceeds unity. The greater the selectivity, the easier is the separation of C and D using solvents A and B. Selectivity can be defined in terms of mass ratio, mole ratio, or concentration. 

The mechanism by which tin flame retardants function has not been well defined, but evidence indicates tin functions in both the condensed and vapor phases. In formulations in which there is at least a 4-to-l mole ratio of halogen to tin, reactions similar to those of antimony and halogen are assumed to occur. Volatile stannic tetrahaUde may form and enter the flame to function much in the same manner as does antimony trihaUde. 

Where T)is flame temperature in K MC is moisture content of the waste, expressed on a total weight basis SR is defined as stoichiometric ratio or moles O2 avadable/moles O2 required for complete oxidation of the carbon, hydrogen, and sulfur in the fuel, ie, 1/SR = equivalence ratio and is temperature of the combustion air, expressed in K. In Fnglish units, this equation is as follows ... 

In principle, one molecule of a chemiluminescent reactant can react to form one electronically excited molecule, which in turn can emit one photon of light. Thus one mole of reactant can generate Avogadro s number of photons defined as one einstein (ein). Light yields can therefore be defined in the same terms as chemical product yields, in units of einsteins of light emitted per mole of chemiluminescent reactant. This is the chemiluminescence quantum yield which can be as high as 1 ein/mol or 100%. 

For a PVnr system of uniform T and P containing N species and 7T phases at thermodynamic equiUbrium, the intensive state of the system is fully deterrnined by the values of T, P, and the (N — 1) independent mole fractions for each of the equiUbrium phases. The total number of these variables is then 2 + 7t N — 1). The independent equations defining or constraining the equiUbrium state are of three types equations 218 or 219 of phase-equiUbrium, N 7t — 1) in number equation 245 of chemical reaction equiUbrium, r in number and equations of special constraint, s in number. The total number of these equations is A(7t — 1) + r -H 5. The number of equations of reaction equiUbrium r is the number of independent chemical reactions, and may be deterrnined by a systematic procedure (6). Special constraints arise when conditions are imposed, such as forming the system from particular species, which allow one or more additional equations to be written connecting the phase-rule variables (6). 

Thermodynamic Relationships. A closed container with vapor and liquid phases at thermodynamic equiUbrium may be depicted as in Figure 2, where at least two mixture components ate present in each phase. The components distribute themselves between the phases according to their relative volatiUties. A distribution ratio for mixture component i may be defined using mole fractions ... 

Heat Capacity, C° Heat capacity is defined as the amount of energy required to change the temperature of a unit mass or mole one degree typical units are J/kg-K or J/kmol-K. There are many sources of ideal gas heat capacities in the hterature e.g., Daubert et al.,"" Daubert and Danner,JANAF thermochemical tables,TRC thermodynamic tables,and Stull et al. If C" values are not in the preceding sources, there are several estimation techniques that require only the molecular structure. The methods of Thinh et al. and Benson et al. " are the most accurate but are also somewhat complicated to use. The equation of Harrison and Seaton " for C" between 300 and 1500 K is almost as accurate and easy to use ... 

Enthalpy of Vaporization The enthalpy (heat) of vaporization AHv is defined as the difference of the enthalpies of a unit mole or mass of a saturated vapor and saturated liqmd of a pure component i.e., at a temperature (below the critical temperature) anci corresponding vapor pressure. AHy is related to vapor pressure by the thermodynamically exact Clausius-Clapeyron equation ... 

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