Calculations counting molecules

The effect of the solute on the vapor pressure of a solution gives us a convenient way to count molecules and thus provides a means for experimentally determining molar masses. Suppose a certain mass of a compound is dissolved in a solvent, and the vapor pressure of the resulting solution is measured. Using Raoult s law, we can determine the number of moles of solute present. Since the mass of this number of moles is known, we can calculate the molar mass. 

Previously, we saw how to use the balanced equation for a reaction to calculate the numbers of moles of reactants and products for a particular case. However, moles represent numbers of molecules, and we cannot count molecules directly. In chemistry we count by weighing. Therefore, we need to review the procedures for converting between moles and masses and see how these procedures are applied to chemical calculations. 

By convention, n must be greater than nn for a system with an od number of electrons. Also, this counting should ignore the core electrons i the molecule (these are treated in step 6). Gaussian will indicate the numbt of electrons of each type. Look for the line containing NOB in the outpt from the single point energy calculation in step 3 ... 

El0.7 Carbonyl sulfide (OCS) is a linear molecule with a moment of inertia of 137 x 10-40 g em2. The three fundamental vibrational frequencies are 521.50, 859.2, and 2050.5 cm-1, but one is degenerate and needs to be counted twice in calculating the entropy. A Third Law measurement of the entropy of OCS (ideal gas) at the normal boiling point of T = 222.87 K andp = 0.101325 MPa gives a value of 219.9 J-K- -mol"1. Use this result to decide which vibrational frequency should be given double weight. 

The MO diagram shown in Figure 10-28 can be applied to any of the possible diatomic molecules or ions formed from the first-row elements, hydrogen and helium. Count the electrons of He2" , place the electrons in the MO diagram, and calculate the bond order. If the bond order is greater than zero, the species can form, under the right conditions. 

The effect of double counting is most easily seen in the following calculation. Suppose that the density of molecules is Pa = Pb = 10 and that A and B are identical. Consequently, the number of collisions between A and B is... 

For the calculation of AhP we must count contacts within the surface layer, and between the surface layer and the neighbouring layer (which has bulk composition). This calculation is simplified very much if we assume that at the critical point the surface is almost saturated with displacer (i.e. g 1), since not only the polymer, but also the still more weakly adsorbing solvent will have been almost completely displaced. Before exchange, we have a displacer molecule at the surface, and a segment in the solution, giving contributions to the mixing energy h = X Jx 0 and ... 

Underneath all of the ideas of atomic and molecular detection, counting the number of molecules in a particular line of sight, requires the intensity of the transition to be calculated via the transition moment to the Einstein B coefficient. If the total photon flux through a sample is known and the transition moment is also known, then the absolute number of atoms or molecules present can be determined. 

Figure 5A, B shows the isotopic distribution, of protonated bosentan (C27H30N5O6S, Mr 552.6) with a mass resolution of 0.5 and 0.1 at FWHM, respectively. It is worthwhile to observe the mass shift of the most abundant ion from m/z 552.2006 to m/z 552.1911. This value does not change with a mass resolving power of 15 000 (Fig. 1.5C) or even 500000 (Fig. 1.5D). Accurate mass measurements are essential to obtain the elemental composition of unknown compounds or for confirmatory analysis. An important aspect in the calculation of the exact mass of a charged ion is to count for the loss of the electron for the protonated molecule [M+H]+. The mass of the electron is about 2000 times lower than of the proton and corresponds to 9.10956 x 10 kg. The exact mass of protonated bosentan without counting the electron loss is 552.1917 units, while it is 552.1911 units with counting the loss of the electron. This represents an error of about 1 ppm.

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