Molarity, defined

The concentration of a substance is the number of moles per unit volume. The SI units moles per cubic meter are inconveniently large for chemical work, so instead we use the molarity, defined as the number of moles of solute per liter of solution ... 

The most common unit of concentration in chemistry is molarity, defined as the number of moles of solute dissolved per liter (or cubic decimeter) of solution. It can also be defined as the number of millimoles of solute per milliliter of solution. The symbol for molarity is an italic capital M its unit is molar, symbolized M. (Some books use M for both.) Do not use lowercase letters for either We use mol as an abbreviation for mole we do not use either capital M or lowercase m. 

In this chapter (as in Chapter 9) molality, which is number of moles of solute per kilogram of solvent and indicated by the symbol M, will be used. Molarity, defined as the number of motes of solute per liter of solution, is another commonly used concentration unit, but can be somewhat more difficult to deal with since the volume of a solution varies with composition and temperature. However, if the solvent is water and the solution is dilute in solute (so that one liter of solution contains one kilogram of water), as-is generally the case in this chapter, molality and molarity are equal. Therefore, in some of the calculations that follow, especially the titration calculations in this section, we may ignore the distinction between molality (moles of solute per kilogram of water) and molarity (moles of solute, per liter of solution.) -... 

Under the given conditions, there are only four possible states for the receptor free BB, the partially bound 1 1 open complex o-AA-BB, the fuUy bound 1 1 cyclic complex c-AA-BB and the 1 2 complex BB-(AA)2. The macroscopic equffibrium constants in Scheme 24 have been factored as the product of statistical factors and microscopic equffibrium constants specifically, K is the microscopic intermolecular constant that expresses the strength of the binding interaction between A and B, and EM is the microscopic effective molarity, defined as the microscopic equffibrium constant of the reaction in Eq. [6] (see Section 5.1). It is useful to recall that positive allosteric cooperativity is characterized by a low concentration of partially bound species. In the most extreme cases only the unbound and... 

The critical molar volume is defined using the acentric factor by the following, relations . 

The cross-sectional average molar fluxes are defined by... 

Now consider Che cross-sectional average N of the total molar flux and the cross-sectional average diffusion fluxes J, defined by... 

We define a partial molar volume Vi such that V = riiVi -I- U2V2... 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

The sulfur atom of the thiocarbonyl group is a good nucleophile, and reaction between benzyl bromide and l-(2-thiazolyl)thiourea yields the isothiouronium salt (496). The sulfur atom may also be engaged in a chelate, as exemplified by the Cu chelate of 2-thioureido-4-methylthiazole (491). These chelates with metal ions were thoroughly studied in acidic, neutral, and alkaline media for 66 metal ions in order to define their analytical use. They are formed in the molar ratio of 1 2 for metal II compounds (498). 

Similarly, one may define the molar integral enthalpy of adsorption, SJt as... 

To characterize the state of the adsorbed phase, it is useful to evaluate its molar entropy, s , defined as the mean molar value for all the molecules adsorbed over the complete range of surface coverage up to the given amount adsorbed. The molar integral entropy of adsorption. As, is then defined as... 

Similarly, the differential molar enthalpy of adsorption, Ji is defined as... 

The way in which these factors operate to produce Type III isotherms is best appreciated by reference to actual examples. Perhaps the most straightforward case is given by organic high polymers (e.g. polytetra-fluoroethylene, polyethylene, polymethylmethacrylate or polyacrylonitrile) which give rise to well defined Type III isotherms with water or with alkanes, in consequence of the weak dispersion interactions (Fig. S.2). In some cases the isotherms have been measured at several temperatures so that (f could be calculated in Fig. 5.2(c) the value is initially somewhat below the molar enthalpy of condensation and rises to qi as adsorption proceeds. In Fig. 5.2(d) the higher initial values of q" are ascribed to surface heterogeneity. 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

We may define, say, partial molar volume, enthalpy, or entropy by analogy with Eq. (8.5) ... 

As noted above, all of the partial molar quantities are concentration dependent. It is convenient to define a thermodynamic concentration called the activity aj in terms of which the chemical potential is correctly given by the relationship... 

Traditional chemical kinetics uses notation that is most satisfactory in two cases all components are gases with or without an inert buffer gas, or all components are solutes in a Hquid solvent. In these cases, molar concentrations represented by brackets, are defined, which are either constant throughout the system or at least locally meaningful. The reaction quotient Z is defined as... 

For caustic crevice environment, a plant-specific chemical impurity molar ratio <0.5 is defined, eg, Na Cl molar ratio <0.5. ... 

A number of high melting poiat semiaromatic nylons, iatroduced ia the 1990s, have lower moisture absorption and iacreased stiffness and strength. Apart from nylon-6 /6,T (copolymer of 6 and 6,T), the exact stmcture of these is usually proprietary and they are identified by trade names. Examples iaclude Zytel HTN (Du Pont) Amodel, referred to as polyphthalamide or PPA (Amoco) and Aden (Mitsui Petrochemical). Properties for polyphthalamide are given ia Table 2. A polyphthalamide has been defined by ASTM as "a polyamide ia which the residues of terephthaUc acid or isophthahc acid or a combination of the two comprise at least 60 molar percent of the dicarboxyhc acid portion of the repeating stmctural units ia the polymer chain" (18). 

The volumetric properties of fluids are conveniently represented by PVT equations of state. The most popular are virial, cubic, and extended virial equations. Virial equations are infinite series representations of the compressibiHty factor Z, defined as Z = PV/RT having either molar density, p[ = V ), or pressure, P, as the independent variable of expansion ... 

When M = the requited derivatives are given by equations 62 and 63. Moreover, the derivative on the left side of equation 64 defines the partial molar Gibbs energy, G. Therefore,... 

Analogous to the defining equation for the residual Gibbs energy is the definition of a partial molar residual Gibbs energy (eq. 161) ... 

If M represents the molar value of any extensive thermodynamic property, an excess property is defined as the difference between the actual property value of a solution and the value it would have as an ideal solution at the same temperature, pressure, and composition. Thus,... 

Foi an ideal solution, G, = 0, and tlieiefoie 7 = 1- Compatison shows that equation 203 relates to exactiy as equation 163 relates ( ) to GG Moreover, just as ( ) is a partial property with respect to G /E.T, so In y is a partial property with respect to G /RT. Equation 116, the defining equation for a partial molar property, in this case becomes equation 204 ... 

Ai), /is the path length in centimeters of the absorber, and S is the molar extinction coefficient having units cm . The absorbance is defined as... 

Catalyst Selectivity. Selectivity is the property of a catalyst that determines what fraction of a reactant will be converted to a particular product under specified conditions. A catalyst designer must find ways to obtain optimum selectivity from any particular catalyst. For example, in the oxidation of ethylene to ethylene oxide over metallic silver supported on alumina, ethylene is converted both to ethylene oxide and to carbon dioxide and water. In addition, some of the ethylene oxide formed is lost to complete oxidation to carbon dioxide and water. The selectivity to ethylene oxide in this example is defined as the molar fraction of the ethylene converted to ethylene oxide as opposed to carbon dioxide. 

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