Avogadro constant conversion

Here a short remark on the designations atomic weight and atomic mass is necessary They are atomic mass ratio numbers, since they are scaled according to the atomic mass of They are relative atomic masses and therefore they are often given without the unit u. Ideally, these numbers should be used as molar mass of the specific element, M(E), with the units g mol . The conversion of relative atomic masses into molar masses is accomplished by using the Avogadro constant as given in Eq. (6.1). Details can be obtained elsewhere [36, 37). 

In calculations requiring the Avogadro constant, students often ask when to multiply and when to divide by. One answer is always to use the constant in a way that gives the proper cancellation of units. Another answer is to think in terms of the expected result. In calculating a number of atoms, we expect the answer to be a very large number and certainly never smaller than one. The number of moles of atoms, conversely, is generally a number of more modest size and will often be less than one. 

Ultimately we need to complete the conversion mL milk atoms There is no single conversion factor that allows us to complete this conversion in one step, so we anticipate having to complete several steps or conversions. We are told the milk contains 1.65 mg K/mL = 1.65 X 10 g K/mL, and this information can be used to carry out the conversion mL milk g K. We can carry out the conversions g K mol K atoms K by using conversion factors based on the molar mass of K and the Avogadro constant. The final conversion, atoms K atoms K, can be carried out by using a conversion factor based on the percent isotopic abundance of K. A complete conversion pathway is shown below ... 

Molar mass and the Avogadro constant are used in a variety of calculations involving the mass, amount (in moles), and number of atoms in a sample of an element. Other conversion factors may also be involved in these calculations. The mole concept is encountered in ever broader contexts throughout the text. 

TABLE 3.1 Density, Molar Mass, and the Avogadro Constant as Conversion Factors ... 

The central focus is again the conversion of a measured quantity to an amount in moles. Because the density is given in g/mL, it will be helpful to convert the measured volume to milliliters. Then, density can be used as a conversion factor to obtain the mass in grams, and the molar mass can then be used to convert mass to amount in moles. Finally, the Avogadro constant can be used to convert the amount in moles to the number of molecules. In summary, the conversion pathway is /xL L g — mol molecules. 

As always, the required conversions can be combined into a single line calculation. However, it is instructive to break the calculation into three steps (1) a conversion from volume to mass, (2) a conversion from mass to amount in moles, and (3) a conversion from amount in moles to molecules. These three steps emphasize, respectively, the roles played by density, molar mass, and the Avogadro constant in the conversion pathway. (See Table 3.1.)... 

Table 47. Constants and Conversion Factors Avogadro s number = 6.023 X 10s per mole Electronic charge = 4.802 X 10-10 e.s.u.

Note that calculated energies are the first ionization energies per one atom because we used only one photon. To calculate the first ionization energies in eV as asked in the exercise, the above energies must be multiplied by the Avogadro s constant (to obtain the energies in J mof ) and then divided by the conversion factor 96485 J moT eV to obtain the values in eV ... 

Maryott, A. A., and Buckley, E, U. S. National Bureau of Standards Circular No. 537, 1953. A tabulation of dipole moments, dielectric constants, and molar refractions measured between 1910 and 1952, and used here to determine polarizabilities if no more recent result exists. The polarizability is 3/(4ttA/ ) times the molar polarization or molar refraction, where is Avogadros number. The value 3/(4tiA/ ) = 0.3964308 x 10 cm was used for this conversion. A dagger (t) following the reference number in the tables indicates that the polarizability was derived from the molar refraction and hence may not include some low-frequency contributions to the static polarizability these static polarizabilities are therefore low by 1 to 30%. Hirschfelder, J. O., Curtis, C. E, and Bird, R. B., Molecular Theory of Gases and Liquids, Wiley, New York, 1954, p. 950. Fundamental information on molecular polarizabilities. 

The conversion from activity to mass or molar units is dependent on the half-life of the isotope in question. Activity (A) is the product of the number of atoms of the isotope present (N) and its decay constant (1) A = IN. The decay constant, 1, is related to the half-life by txjx = (/ 2)/7. Using this equation, it is simple to convert from Bq to mol, given the decay constants in units of s, and Avogadro s number of 6.023 X 10 atoms moU. ... 

In an emulsion where the polymerization only takes place within the particle interior, [M] is replaced by Cp (concentration of monomer in the particle phase) the total radical concentration is flNp = Na, where n is the average number of radicals per particle, Np is the number of particles per unit volume of the continuous phase, and Na is Avogadro s constant. Since it is experimentally convenient to measure the fractional conversion of monomer into polymer (denoted by x, where 0< x <1), a change in variable is made and the rate of fractional conversion is now considered, giving ... 

Avogadro s Law is an example of a direct proportionality. This means that the volume of a gas at constant temperature and pressure is equal to a constant times the number of gas particles in the container. Also, volume is zero when the nnmber of particles is zero. If the number of particles is doubled the voliune is doubled when the niunber of particles is tripled, the volnme is tripled, etc. In dimensional-analysis terms, a Per expression can be written that allows conversion between container volume and number of particles for a gas at constant T and P. 

Plotting the collected charge as a function of time after the radiation pulse gives a straight line. From the slope, the recombination coefficient is obtained. The recombination coefficient is usually given in cm /s or as a chemical rate constant in l/(mol s). Conversion of the two units is obtained by means of Avogadro s number and taking into account that 1 1 = 10 cm, ... 

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