Molar definition

Normality makes use of the chemical equivalent, which is the amount of one chemical species reacting stoichiometrically with another chemical species. Note that this definition makes an equivalent, and thus normality, a function of the chemical reaction in which the species participates. Although a solution of 1T2S04 has a fixed molarity, its normality depends on how it reacts. 

The units of concentration most frequently encountered in analytical chemistry are molarity, weight percent, volume percent, weight-to-volume percent, parts per million, and parts per billion. By recognizing the general definition of concentration given in equation 2.1, it is easy to convert between concentration units. 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

From the definition of the partial molar quantities [Eq. (8.8)] we write... 

The Gibbs-Duhem equation also follows from the definition of partial molar quantities nid/Hi + r 2d 2 0. With the Gibbs-Duhem equation, d G/dc2 becomes... 

Within the scope of the original definition, a very wide variety of ionomers can be obtained by the introduction of acidic groups at molar concentrations below 10% into the important addition polymer families, followed by partial neutralization with metal cations or amines. Extensive studies have been reported, and useful reviews of the polymers have appeared (3—8). Despite the broad scope of the field and the unusual property combinations obtainable, commercial exploitation has been confined mainly to the original family based on ethylene copolymers. The reasons for this situation have been discussed (9). Within certain industries, such as flexible packaging, the word ionomer is understood to mean a copolymer of ethylene with methacrylic or acryhc acid, partly neutralized with sodium or zinc. 

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

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

Equation (4-49) is merely a special case of Eq. (4-48) however, Eq. (4-50) is a vital new relation. Known as the summahility equation, it provides for the calculation of solution properties from partial properties. Thus, a solution property apportioned according to the recipe of Eq. (4-47) may be recovered simply by adding the properties attributed to the individual species, each weighted oy its mole fraction in solution. The equations for partial molar properties are also valid for partial specific properties, in which case m replaces n and the x, are mass fractions. Equation (4-47) applied to the definitions of Eqs. (4-11) through (4-13) yields the partial-property relations ... 

If M represents a molar thermodynamic property of fluid solution, then by definition. a homogeneous... 

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

The chemical reactions that occnr in flames transform an initial reactant mixtnre into final reaction prodncts. In the case of fnel-oxygen combns-tion, the final prodncts are principally water vapor and carbon dioxide, althongh nnmerons other prodncts snch as carbon monoxide may be formed, depending on the reactant composition and other factors. If the ratio of fnel-to-oxygen is stoichiometric, the final reaction prodncts, by definition, contain no excess fnel or oxygen. Theoretically, this means that partial oxidation prodncts snch as CO (itself a fnel) are not formed. In reality, partial oxidation prodncts snch as CO or OH are formed by high tem-peratnre reactions. For example, the molar stoichiometric reaction of methane is written ... 

FIGURE 9.9 Definition of column test parameters using a SEC chromatogram of a polymer standard mixture (PSS Polystyrene ReadyCal) and a low molar mass compound (BHT). 

From the definition v = (l/V)(d /dt) find the rate of reaction in terms of molar concentration for the case in which the system volume V is not constant (Reference 44). 

In many situations, the actual molar amount of the enzyme is not known. However, its amount can be expressed in terms of the activity observed. The International Commission on Enzymes defines One International Unit of enzyme as the amount that catalyzes the formation of one micromole of product in one minute. (Because enzymes are very sensitive to factors such as pH, temperature, and ionic strength, the conditions of assay must be specified.) Another definition for units of enzyme activity is the katal. One katal is that amount of enzyme catalyzing the conversion of one mole of substrate to product in one second. Thus, one katal equals 6X10 international units. 

The following is a summary of definitions for the mass and molar compositions of a multicomponent system and the interrelationships between the various quantities. 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

A mole represents not only a specific number of particles but also a definite mass of a substance as represented by its formula (0,02, H20, NaCl,. . . ). The molar mass, MM, in grams per mole, is numerically equal to the sum of the masses (in amu) of the atoms in the formula. 

Finally, the definition of molar mass (MM = mitt) gives... 

Chemists often indicate the concentration of a substance in water solution in terms of the number of moles of the substance dissolved per liter of solution. This is called the molar concentration. A one-molar solution (1 M) contains one mole of the solute per liter of total solution. a two-molar solution (2 M) contains two moles of solute per liter, and a 0.1-molar solution (0.1 M) contains one-tenth mole of solute per liter. Notice that the concentration of water is not specified, though we must add definite amounts of water to make the solutions. 

The most widely used reference electrode, due to its ease of preparation and constancy of potential, is the calomel electrode. A calomel half-cell is one in which mercury and calomel [mercury(I) chloride] are covered with potassium chloride solution of definite concentration this may be 0.1 M, 1M, or saturated. These electrodes are referred to as the decimolar, the molar and the saturated calomel electrode (S.C.E.) and have the potentials, relative to the standard hydrogen electrode at 25 °C, of 0.3358,0.2824 and 0.2444 volt. Of these electrodes the S.C.E. is most commonly used, largely because of the suppressive effect of saturated potassium chloride solution on liquid junction potentials. However, this electrode suffers from the drawback that its potential varies rapidly with alteration in temperature owing to changes in the solubility of potassium chloride, and restoration of a stable potential may be slow owing to the disturbance of the calomel-potassium chloride equilibrium. The potentials of the decimolar and molar electrodes are less affected by change in temperature and are to be preferred in cases where accurate values of electrode potentials are required. The electrode reaction is... 

Mohr procedure exptl. details of, 349, 351 Molar absorption coefficient 649 Molar conductivity 520 Molar extinction coefficient see Molar absorption coefficient Molar solution definition, 260 Molarity 259 Mole 259... 

By definition, the molar mass of the end groups should be included in the molecular weight of a polymer but the corresponding quantity is not included in the degree of polymerization. 

Volume is an extensive property. Usually, we will be working with Vm, the molar volume. In solution, we will work with the partial molar volume V, which is the contribution per mole of component i in the mixture to the total volume. We will give the mathematical definition of partial molar quantities later when we describe how to measure them and use them. Volume is a property of the state of the system, and hence is a state function.1 That is... 

Applying this definition, the apparent molar enthalpy would be given by... 

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