Molecule mass, calculation

As emphasized in Section 2-, many of the calculations in chemistry involve converting back and forth among the mass of a substance, the number of moles, and the number of atoms and/or molecules. These calculations are all centered on the mole. The connections shown in Figure apply to chemical compounds as well as to atoms of pure elements. Molar mass and Avogadro s number provide links between mass of a sample, the number of moles, and the number of molecules. 

The presence of one carbon atom in a molecule of carbon dioxide results in registration of the molecular ion peak of m/z 44 and of the A + 1 isotopic peak of m/z 45. The intensity of the latter is 1.1 % of that of M+. It appears due to the presence of 13C02 molecules. An increase in the number of carbon atoms in a molecule leads to an increase of the intensity of the M + 1 ion peak to 1.1 n% of M+, where n is the number of carbon atoms in the molecule. To calculate the number of carbon atoms in a molecule using a mass spectrum one should divide the intensity of the M + 1 peak as a percentage of M by 1.1. The result defines the maximum possible number of carbon atoms. One should remember that calculations may be more complicated if an [M — H]+ ion peak is present. 

This study is one of the earliest attempts to calculate equilibrium fractionation factors using measured vibrational spectra and simple reduced-mass calculations for diatomic molecules. For the sake of consistency I have converted reported single-molecule partition function ratios to units. 

EXAMPLE 2.4 Solvation and Ellipticity of Human Hemoglobin from Sedimentation Data. The diffusion coefficient of the human hemoglobin molecule at 20°C is 6.9 10 11 m2 s "1. Use this value to determine f for this molecule. Evaluate f0 for hemoglobin using the particle mass calculated in Equation (35). Indicate the possible states of solvation and ellipticity that are compatible with the experimental flfQ ratio. 

The treatment of the mass spectral data was similar to that of Hightower and Hall (1). The number of hydrogen atoms which had been exchanged per molecule was calculated using ... 

Because one mole of any substance is a specific number of molecules (1 mol things = 6.02 x 1023 things from Chapter 2), the relative numbers of moles undergoing reaction are the same as the relative numbers of molecules. Because of the relationship of molecules to moles, the equation above can be interpreted in terms of masses calculated directly from the Periodic Table (H = 1,0 = 16, N = 24, all in g/mol). 

The approximate molar mass, calculated from the gas density data, is 89 g/mol. The empirical formula, calculated from the percentage composition data, is C2H3O with the empirical formula unit mass of 43.0. The exact molar mass must be (2)(43) = 86.0 g/mol since this is the only multiple of 43.0 (whole-number multiple) reasonably close to the approximate molecular formula of 89 g/mol. The molecule must be the equivalent of 2 empirical formulas CqHgO. 

In work by Kaplan et al. (1984) the ji decay in a valine molecule was calculated with allowance for electron correlation. The method of calculation is presented in Section II,C,4. We have taken 50 configurations which give the largest contribution to the excitation probabilities. The results of calculations for valine II are presented in Table VIII (the numbers in parentheses) and in the histogram of Fig. 10. These results have been used by the ITEP group (Boris et al., 1983) in data reduction of their latest series of experiments. (The obtained values of the neutrino rest mass mv are presented in Table I.)... 

Because the number of grams per element defines the mole, the atomic masses on the periodic table can be given in the units g/mol. Carbon has a molar mass of 12.01 g/mol, and iron has a molar mass of 55.85 g/mol. The molar mass of a molecule is calculated by adding all the atomic molar masses. 

A compound consists of 92.26% C and 7.74% H. Its molecular mass is 65.0 amu. (a) Calculate its empirical formula, (b) Calculate its empirical formula mass, (c) Calculate the number of empirical formula units in one molecule, (d) Calculate its molecular formula. 

The theoretical treatment of linear AB2 molecules to calculate force constants is simple, since in this case the symmetry coordinates are identical with the normal coordinates (2.3.2) the three expected vibrations belong to different irreducible representations (S+ (r l), E+ (ZZ3), n (i/2). Thus, a simple mathematical relation exists between the frequencies on the one hand and the force constants and the geometry (masses and distances) on the other hand (e.g., Siebert, 1966) the difference between the two stretching vibrations caused by coupling is large if the mass iha of the central atom is small and if the force constant/(AB) is large (Cans, 1975) ... 

Vitamin B]2, cyanocobalamin, is essential for human nutrition. It is concentrated in animal tissue but not in higher plants. Although nutritional requirements for the vitamin are quite low, people who abstain completely from animal products may develop a deficiency anemia. Cyanocobalamin is the form used in vitamin supplements. It contains 4.34% cobalt by mass. Calculate the molar mass of cyanocobalamin, assuming that there is one atom of cobalt in every molecule of cyanocobalamin. 

In the formula for a hydrate, the number of water molecules associated with each formula unit of the compound is written following a dot for example, Na2CO3T0H2O. This compound is called sodium carbonate decahydrate. In the word decahydrate, the prefix deca- means ten and the root word hydrate refers to water. Decahydrate means that ten molecules of water are associated with one formula unit of compound. The mass of water associated with a formula unit must be included in molar mass calculations. Hydrates are found with a variety of numbers of water molecules. Table 11-1 lists some common hydrates. 

For most practical purposes we are interested in the masses of reactants and products, because those are the quantities that are directly measured. In this case, the molar masses (calculated from a table of atomic masses) are used to convert the number of moles of a substance (in moles) to its mass (in grams), as illustrated by Example 2.6. Sometimes, however, we are also interested in knowing the number of molecules in a sample. The mole allows us to convert easily from mass to numbers of molecules as follows ... 

The intrinsic volume of the solute molecule was calculated from the molar mass MW and density p of the respective pure compound as follows... 

Once /z-and thus a value for the puckering coordinate at the minimum of the well-is obtained, it is possible to extract some structural information about the molecule in the ground state, such as the ring dihedral angle. A number of papers have appeared in which dihedral angles are reported where neither geometric information nor the details of the reduced mass calculation are given. In some cases the reduced mass has been assumed by comparison with p s calculated for other... 

The aluminum sulfate hydrate [Al2(S04)3 XH2O] contains 8.20 percent A1 hy mass. Calculate x, that is, the number of water molecules associated with each Al2(S04)3 unit. 

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