True formula determination

Using the approximate formula weight of the simplest formula, determine the true molecular formula and the exact molecular weight. 

If the empirical formula ofthis compound had been found to be (CH2F)j., this mole weight determination could be used to find the true formula. The mole weight of the CH2F unit is 33.0. The true mole weight must be some integral multiple U)of 33.0 ... 

We recall from Chapter 10 that the percentages of the elements in a compound can be used to compute the simplest formula for the compound. When the substance is soluble in some suitable liquid, we can combine the empirical formula with a molecular-weight determination by freezing-point depression to get the true formula. 

I When 0 532 g of a certain solid organic compound is dissolved in 16 8 g of urethane, whose freezing point is 49 50°C, the freezing point of the solution is lowered to 48 32°C Chemical analysis shows this compound to be 69 5% C, 7 25% H, and 23 25% O Determine the true formula of this compound... 

By analysis, a certain solid organic compound is found to be 40 0% C, 6 1% H, and 53 3% O When a 0 650 g sample of this compound is dissolved m 27 80 g of diphenyl, the freezing point is lowered by 1 56°C Determine the true formula of this compound... 

The determination of the empirical formula of a compound can be made experimentally, by determining the percentage amounts of elements present in the substance using the methods of quantitative chemical analysis. At the same time the relative molecular mass of the compound has to be measured as well. From these data the empirical formula can be determined by a simple calculation. If, for some reason, it is impossible to determine the relative molecular mass the simplest (assumed) formula only can be calculated from the results of chemical analysis the true formula might contain multiples of the atoms given in the assumed formula. 

Empirical formulas are the simplest chemical formulas they are written by re-dncing the subscripts in molecnlar formnlas to the smallest possible whole numbers. Molecular formulas are the true formulas of molecules. As we will see in Chapter 3, when chemists analyze an nnknown componnd, the first step is usually the determination of the compound s empirical formnla. 

Peuzin 1994, 1996) found the magnetostriction coefficient for thick nickel films twice as large as observed in bulk nickel. The same problem of calibration has probably led van de Riet (1994) and Weber et al. (1994) to the recalculation of the Klokholm s formula. Their results are consistent with those reported independently by du Tremolet de Lacheisserie and Peuzin (1994) that the true formula to determine the magnetostriction of thin films is (also referred to as TL,P s formula)... 

The molecular formula, or true formula, tells you the kinds of atoms in the compound and the actual number of each atom. You may determine, for example, that the empirical formula C2H6O is actually the molecular formula, too, meaning that there are actually two carbon atoms, six hydrogen atoms, and one oxygen atom in the compound. 

In order to determine the best procedure for calculating match values, we need to determine the match values for each candidate and sort them in descending order to rank the candidates (cf. Section 8.4). The quality of a ranking can then be evaluated using either the absolute or the relative position of the true formula among formula candidates. We define the absolute ranking position (ARP) simply by the number of better candidates plus 1... 

In Subsection 8.8.2 we presented three match values for MS isotope peak comparison. Table 8.22 shows the number of formula candidates with at least one carbon atom as well as the absolute and relative ranking positions of the true formulas. Calculations are based on g and MS accuracy 5 = 10 ppm. Numbers in the row headers cross-reference with the compounds in Table 8.20. Using MS data alone, only two compounds have ARP = 1, of which one has only one possible candidate (i.e. a trivial result) and the other has only two possible candidates. Using the ARP, it is not possible to choose the best method for calculating MS match values. While NDP works best for most of the samples, NSSE yields the best result for maltopentaose, and NSAE is best for cyclosporin C. If we look at the RRP results, creatine is excluded (RRP is not defined for only one candidate), but calculation of the arithmetic mean is possible. Thus, it appears that NDP performs best on average for these ten samples, but the other methods deliver quite similar mean results, and considering the small number of samples, this conclusion is by no means a statistically reliable result. What is clear from these results, the MS match value alone is by no means sufficient to unambiguously determine the correct molecular formula in most cases without further information or restrictions. 

Empirical formulas You can use percent composition data to help identify an unknown compound by determining its empirical formula. The empirical formula is the simplest whole-number ratio of atoms of elements in the compound. In many cases, the empirical formula is the actual formula for the compound. For example, the simplest ratio of atoms of sodium to atoms of chlorine in sodium chloride is 1 atom Na 1 atom Cl. So, the empirical formula of sodium chloride is Na Clj, or NaCl, which is the true formula for the compound. The following example problem will show you how to determine empirical formulas. 

The next step in determining the molecnlar formnla of a substance is to determine the weight of one mole of that substance. This may be accomplished in a variety of ways. Without knowledge of the molecular mass of the unknown, there is no way of determining whether the empirical formula, which is determined directly from elemental analysis, is the true formula of the substance or whether the empirical formula must be multiplied by some integral factor to obtain the molecular formula. In the example cited in Section 1.1, without knowledge of the molecular mass of the unknown, it is impossible to tell whether the molecular formula is C7H14O2 or... 

The comparatively inexpensive long-scale thermometer, widely used by students, is usually calibrated for complete immersion of the mercury column in the vapour or liquid. As generally employed for boiling point or melting point determinations, the entire column is neither surrounded by the vapour nor completely immersed in the liquid. The part of the mercury column exposed to the cooler air of the laboratory is obviously not expanded as much as the bulk of the mercury and hence the reading will be lower than the true temperature. The error thus introduced is not appreciable up to about 100°, but it may amount to 3-5° at 200° and 6-10° at 250°. The error due to the column of mercury exposed above the heating bath can be corrected by adding a stem correction, calculated by the formula ... 

Naphthenic acid is a collective name for organic acids present in some but not all crude oils. In addition to true naphthenic acids (naphthenic carboxylic acids represented by the formula X-COOH in which X is a cycloparaffin radical), the total acidity of a crude may include various amounts of other organic acids and sometimes mineral acids. Thus the total neutralization number of a stock, which is a measure of its total acidity, includes (but does not necessaiily represent) the level of naphthenic acids present. The neutralization number is the number of milligrams of potassium hydroxide required to neutralize one gram of stock as determined by titration using phenolphthalein as an indicator, or as determined by potentiometric titration. It may be as high as 10 mg KOH/gr. for some crudes. The neutralization number does not usually become important as a corrosion factor, however, unless it is at least 0.5 mg KOH/gm. 

Most people believe someone is obese if they look fat. This is not true. Health-care professionals and scientists have developed specific definitions for the words overweight and obese. Overweight and obesity are not determined solely by an individual s weight, but are defined in terms of a person s weight relative to his or her height. Doctors and researchers use a special set of measurements and mathematical formulas to determine whether a person is overweight or obese. 

Reynolds numbers are an order of magnitude below turbulence. The D/1 ratios are less than 1/10 except for the 10 hi" pore membrane in which Foiseuille flow formulas need to be corrected for end effects to determine true viscosities or shear rates. 

In NaCl (18189), this principle would require all atoms to be identical. Clearly this symmetry is already broken by the constraint imposed by the chemical formula which requires half the atoms to be Na" " and half CP. However, all the Na" " ions are indistinguishable from each other, and the same is true for the CP ions. The bonds likewise, six for each formula unit, are also equivalent in the bond graph (Fig. 2.4). The crystal structure (Fig. 1.1) is then determined by applying the principle of maximum symmetry to the constraints imposed by three-dimensional space as described in Section 11.2.2.4. The crystal structure is thus uniquely determined by the principle of maximum symmetry and the chemical and spatial constraints. 

With regard to the previous discussion, there are several observations to be made thus, in the derivation of the formula for the heat of mixing it was assumed that the molecules were of equal size, which is not true in all the examples cited. However, it can be shown that the variation in size does not make much difference provided the molecules can be considered as approximately spherical. A more difficult point occurs when, in contradiction to the theory, the heat of formation is positive, as, for example, with alcohol and water. This arises from the fact that in the calculation it was postulated that the molecules in the mixture were distributed according to chance. This is no longer true if the energy of the two molecules, as a result of their particular structure, is favourable to combinations with low energies which occur to a greater extent than if they were determined by probability alone. If, however, this... 

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