One mole

The total enthalpy correction due to chemical reactions is the sum of all the enthalpies of dimerization for each i-j pair multiplied by the mole fraction of dimer i-j. Since this gives the enthalpy correction for one mole of true species, we multiply this quantity by the ratio of the true number of moles to the stoichiometric number of moles. This gives... 

XM(I,2) cols 21-30 measured liquid-phase composition of component one (mole or weight fraction)... 

Avogadro s number, L The number of particles (atoms or molecules) in one mole of any pure substance. L = 6 023 x 10. It has been determined by many methods including measurements of Brownian movement, electronic charge and the counting of a-particles. 

Langmuir [ 146] gave an instructive interpretation to this rule. The work W to transfer one mole of solute from bulk solution to surface solution should be... 

This can be illustrated by showing the net work involved in various adiabatic paths by which one mole of helium gas (4.00 g) is brought from an initial state in whichp = 1.000 atm, V= 24.62 1 [T= 300.0 K], to a final state in whichp = 1.200 atm, V= 30.7791 [T= 450.0 K]. Ideal-gas behaviour is assumed (actual experimental measurements on a slightly non-ideal real gas would be slightly different). Infomiation shown in brackets could be measured or calculated, but is not essential to the experimental verification of the first law. 

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

A/ij the lattice energy of sodium chloride this is the heat liberated when one mole of crystalline sodium chloride is formed from one mole of gaseous sodium ions and one mole of chloride ions, the enthalpy of formation of sodium chloride. 

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. 

Esters are alkylated in the presence of strong bases in aprotic solvents. A common combination is LDA in tetrabydrofuran at low temperatures. Equimolar amounts of base are sufficient and only the mono-carbanion Js formed. After addition of one mole of alkyl halide the products form rapidly, and no dialkylation, which is a problem in the presence of excess base, is possible. Addition of one more mole of LDA and of another alkyl halide leads to asymmetric dialkylation of one or-carbon atom in high yield (R.J. Cregge, 1973). 

Yield in mole reported to one mole of benzoic peroxide. 

Equations (1) and (2) are the heats of formation of carbon dioxide and water respectively Equation (3) is the reverse of the combustion of methane and so the heat of reaction is equal to the heat of combustion but opposite in sign The molar heat of formation of a substance is the enthalpy change for formation of one mole of the substance from the elements For methane AH = —75 kJ/mol... 

Induced dipole/induced dipole forces are the only intermolecular attractive forces available to nonpolar molecules such as alkanes In addition to these forces polar molecules engage m dipole-dipole and dipole/mduced dipole attractions The dipole-dipole attractive force is easiest to visualize and is illustrated m Figure 4 3 Two molecules of a polar substance experience a mutual attraction between the positively polarized region of one molecule and the negatively polarized region of the other As its name implies the dipole/induced dipole force combines features of both the induced dipole/mduced dipole and dipole-dipole attractive forces A polar region of one mole cule alters the electron distribution m a nonpolar region of another m a direction that produces an attractive force between them... 

Many of the most interesting and useful reactions of aldehydes and ketones involve trans formation of the initial product of nucleophilic addition to some other substance under the reaction conditions An example is the reaction of aldehydes with alcohols under con ditions of acid catalysis The expected product of nucleophilic addition of the alcohol to the carbonyl group is called a hemiacetal The product actually isolated however cor responds to reaction of one mole of the aldehyde with two moles of alcohol to give gem mal diethers known as acetals... 

The use of penodic acid oxidation m structure determination can be illustrated by a case m which a previously unknown methyl glycoside was obtained by the reaction of D arabmose with methanol and hydrogen chlonde The size of the nng was identified as five membered because only one mole of penodic acid was consumed per mole of glycoside and no formic acid was produced Were fhe nng six membered fwo moles of penodic acid would be required per mole of glycoside and one mole of formic acid would be produced... 

In terms of moles, Avogadro s hypothesis can be stated The same volume is occupied by one mole of any gas at a given temperature and pressure. The number of molecules in one mole is known as the Avogadro number constant. ... 

The values of fH° and Ay.G° that are given in the tables represent the change in the appropriate thermodynamic quantity when one mole of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25°C for each element has been chosen to be the standard state that is thermodynamically stable at 25°C and 1 atm pressure. The standard reference states are indicated in the tables by the fact that the values of fH° and Ay.G° are exactly zero. 

The nickel ion freed may then be determined by an EDTA titration. Note that two moles of silver are equivalent to one mole of nickel and thus to one mole of EDTA. 

Exact numbers, such as the stoichiometric coefficients in a chemical formula or reaction, and unit conversion factors, have an infinite number of significant figures. A mole of CaCb, for example, contains exactly two moles of chloride and one mole of calcium. In the equality... 

The balanced chemical reaction provides the stoichiometric relationship between the moles of Fe used and the moles of oxalic acid in the sample being analyzed— specifically, one mole of oxalic acid reacts with two moles of Fe. As shown in Example 2.6, the balanced chemical reaction can be used to determine the amount of oxalic acid in a sample, provided that information about the number of moles of Fe is known. 

Charge is proportional to the number of electrons that must be moved. For a reaction in which one mole of reactant is oxidized or reduced, the charge, in coulombs, is... 

If HgCh is added in excess, each mole of produces one mole of Hg2Cl2. The... 

The desired final precipitate, Mg2P207, contains two moles of Mg, and the impurity, Mg(P03)2, contains only one mole of Mg. Conservation of mass, therefore, requires that two moles of Mg(P03)2 must form in place of each mole of Mg2P207. One mole of Mg2P207 weights 222.6 g. Two moles of Mg(P03)2 weigh 364.5 g. Any replacement of Mg2P207 with Mg(P03)2 must increase the precipitate s mass. 

Where Is the Equivalence Point In discussing acid-base titrations and com-plexometric titrations, we noted that the equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. If you look back at Figures 9.8 and 9.28, you will see that for acid-base and com-plexometric titrations the inflection point is also in the middle of the titration curve s sharp rise (we call this a symmetrical equivalence point). This makes it relatively easy to find the equivalence point when you sketch these titration curves. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve s sharp rise. In this case the equivalence point is said to be asymmetrical. Example 9.12 shows how to calculate the equivalence point potential in this situation. 

Besides pH, other preparative variables that can affect the microstructure of a gel, and consequendy, the properties of the dried and heat-treated product iaclude water content, solvent, precursor type and concentration, and temperature (9). Of these, water content has been studied most extensively because of its large effect on gelation and its relative ease of use as a preparative variable. In general, too Httie water (less than one mole per mole of metal alkoxide) prevents gelation and too much (more than the stoichiometric amount) leads to precipitation (3,9). Other than the amount of water used, the rate at which it is added offers another level of control over gel characteristics. 

Xanthenes date from 1871 when von Bayer synthesized fluorescein (5) by the condensation of two moles of resorcinol with one mole of phthaUc anhydride in the presence of concentrated sulfuric acid (1). 

Unsyimnetiical rhodainines can be piepaied by the condensations of one mole of a yW-aminophenol with phthahc anhydride to give an o-benzoyl benzoic acid (27) which is then further condensed with a different yW-aminophenol to give the requited product, Rhodamine 3GO (28) (2). A general route to asymmetrical acid xanthenes has been patented (39). 

Aminohydroxy-substituted xanthenes ate of Httle commercial importance. They are synthesized by condensing one mole of y -diaLkylaminophenol with phthahc anhydride, and then condensing that product with an appropriately substituted phenol. For example. Mordant Red 77 [6528-43 ] (Cl45300) (45) is prepared by condensing m- dim ethyl am in opb en o1 with phthaUc anhydride, and then condensing the product with 2,4-dihydroxybenzenesulfonic acid. 

The base-catalyzed reaction of acetaldehyde with excess formaldehyde [50-00-0] is the commercial route to pentaerythritol [115-77-5]. The aldol condensation of three moles of formaldehyde with one mole of acetaldehyde is foUowed by a crossed Cannizzaro reaction between pentaerythrose, the intermediate product, and formaldehyde to give pentaerythritol (57). The process proceeds to completion without isolation of the intermediate. Pentaerythrose [3818-32-4] has also been made by condensing acetaldehyde and formaldehyde at 45°C using magnesium oxide as a catalyst (58). The vapor-phase reaction of acetaldehyde and formaldehyde at 475°C over a catalyst composed of lanthanum oxide on siHca gel gives acrolein [107-02-8] (59). 

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