Mole: definition

Key words Traceability Mole Definition Measurements Chemical metrology Calibration Validation Reference materials... 

Statements 2, 3, and 4 are all based on the mole definition, and are very useful in solving numerical problems involving balanced reaction equations and the factor-unit method described earlier in Section 1.9. Any two quantities from statements 2, 3, and 4 can be used to form factors that can be used to solve problems. For example, the following factors are just four of the many that can be obtained from stat ents 2, 3, and 4 by combining various quantities from the statements ... 

We remember from Chapter 5 that the coefficients in equations such as Equation 7.3 allow the relative number of moles of pure reactants and products involved in the reaction to be determined. These relationships coupled with the mole definition in terms of masses then yield factors that can be used to solve stoichiometric problems involving the reactants and products. Similar calculations can be done for reactions that take place between the solutes of solutions if the amount of solute contained in a specific quantity of the reacting solutions is known. Such relationships are known as solution concentrations. Solution concentrations may be expressed in a variety of units, but only two, molarity and percentage, will be discussed at this time. 

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volnme Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (lieat-impemieable) or diathermic (lieat-condncting). Flowever, becanse the concept of heat has not yet been introdnced, the definitions of adiabatic and diathemiic need to be considered carefiilly. Both kinds of walls are impemieable to matter a permeable wall will be introdnced later. 

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 ... 

Definitions Following the practice presented under Gas-Separation Membranes, distillation notation is used. Literature articles often use mass fraction instead of mole fraction, but the substitution of one to the other is easily made. 

To extract a desired component A from a homogeneous liquid solution, one can introduce another liquid phase which is insoluble with the one containing A. In theory, component A is present in low concentrations, and hence, we have a system consisting of two mutually insoluble carrier solutions between which the solute A is distributed. The solution rich in A is referred to as the extract phase, E (usually the solvent layer) the treated solution, lean in A, is called the raffinate, R. In practice, there will be some mutual solubility between the two solvents. Following the definitions provided by Henley and Staffin (1963) (see reference Section C), designating two solvents as B and S, the thermodynamic variables for the system are T, P, x g, x r, Xrr (where P is system pressure, T is temperature, and the a s denote mole fractions).. The concentration of solvent S is not considered to be a variable at any given temperature, T, and pressure, P. As such, we note the following ... 

In describing concentrations of pollutants in gaseous and aqueous wastes, a commonly confusing issue is the definition of parts r million, ppm. Sometinies, it is specified that these are compositions based on weight, moles, or volume (ppmw. 

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. 

More serious limitations and precautions apply to compounds in which not all three R, R, and R" groups are aromatic. Autocondensation of benzylideneacetone (111) yields an unstable chloroferrate which may be 113 or 115, according to whether a Michael addition to 112 or a crotonic condensation to 114 is first involved. Since compound 113 could readily be prepared from 2,6-dimethyl-4-phenylpyrylium and benzaldehyde, the structure of the reaction product should be easily soluble. Another equivocal product is formed from two moles of benzylideneacetone, but a definite structure (116) results from chalcone and benzylideneacetone. ... 

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. 

In electrochemistry it is customary to multiply each of those quantities by Avogadro s constant and, when a few additional ions enter the already saturated solution, to speak of the entropy of solution per mole. Let the entropy of one mole of the crystalline solid be denoted by Scr and let Si and S2 denote, respectively, the entropy of the solution before, and after, the entry of the additional solute, both expressed in calories per mole. The total initial entropy is obviously (S + Si) and the final entropy is St. The difference between the final and the initial entropy is by definition AS,at. 

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. 

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