Empirical formulas, 344 from mass

EXAMPLE F.2 Determining the empirical formula from mass percentage composition... 

We can obtain an empirical formula from mass data instead of a percent composition. 

Calculating an Empirical Formula from Mass Data... 

SAMPLE PROBLEM 3.4 Determining an Empirical Formula from Masses of Elements... 

Calculating an Empirical Formula from Mass Data The mineral ilmenite is usually mined and processed for titanium, a strong, light, and flexible metal. A sample of ilmenite contains 5.41 g of iron, 4.64 g of titanium, and 4.65 g of oxygen. Determine the empirical formula for ilmenite. 

Strategy First, we can determine the empirical formula from mass percent data. Then, we can determine the molar mass from the freezing-point depressioiL Finally, from the empirical formula and the molar mass, we can find the molecular formula. 

In Chapter 3, graphic elements highlighting the correct approach to problem solving have been added to Sample Exercises on calculating an empirical formula from mass percent of the elements present, combustion analysis, and calculating a theoretical yield. 

The procedure developed in Example Problem 3.8 allows us to find an empirical formula from mass percentage data. As we saw in Chapter 2, though, the empirical formula does not tell us the exact composition of a molecule of the compound. In the RDX example above, we know now that the ratio of C atoms to H, N, and O atoms is 1 2, but we don t know how many of these CH2N2O2 units make up an actual molecule. To go from the empirical formula to the molecular formula, we will need an additional piece of information—the molar mass of the compound. Fortunately, modern instrumentation, such as the mass spectrometer we discussed in Section 2.2, makes it fairly simple to measure the molar mass of a substance. Once we are armed with both the elemental analysis and the molar mass, we can find the molecular formula. 

This example also points out that the ratio may be any whole number multiple of 5 2 2 3 (any multiple of 12 hydrogens). Therefore, 10 4 4 6 (24 H), 15 6 6 9 (36 H), etc. must also be considered, but this information is tempered by knowledge of the empirical formula from mass spectrometry. If the empirical formula is C20H24O2, for example, then the integration for this molecule is 10 4 4 6. The first goal is to establish the integration ratio and then compare it with the empirical formula to be certain that the number of hydrogen atoms match. 

D chemical structure drawing on Macintosh. ChemWindow for 2D chemical structure drawing. C-13 NMR module for predicting chemical shifts. MS Calculator for obtaining empirical formulas from masses. SciWords for spell checking. Art of Science clip art. Entropy for chemical database management. PCs (DOS and Windows) and Macintosh. 

Determining the empirical formula from masses of elements and percentage composition Given the masses of elements in a known mass of compound, or given its percentage composition, obtain the empirical formula. (EXAMPLES 3.10,3.11)... 

Next, we determine the empirical formula from the masses of the combustion products. 

Note The assignment of empirical formulae from accurate mass measurements always must be in accordance with the experimentally observed and the calculated isotopic pattern. Contradictions strongly point towards erroneous interpretation of the mass spectrum. 

Sometimes elemental microanalysis results are given as percentages by mass. The process used to calculate the empirical formula from the percentage by mass is similar to that just shown, assuming the total mass of the sample to be 100 g. 

In the following first example the liquid ozone concentration and the OH-radical concentration are calculated with semi-empirical formula from the mass balance for ozone (Laplanche et al., 1993). For ozonation in a bubble column, with or without hydrogen peroxide addition, they developed a computer program to predict the removal of micropollutants. The main influencing parameters, i. e. pH, TOC, U V absorbance at 254 nm (SAC254), inorganic carbon, alkalinity and concentration of the micropollutant M are taken into consideration. 

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. 

If 1.00 g of the unknown contains 0.817 g carbon, the mass percent of carbon is 81.7 percent, leaving the remaining 18.3 percent as hydrogen. Therefore, we need to use the procedures for determining an empirical formula from a percentage composition. The problem will progress as follows (remember with percents, assume a 100 g sample) ... 

To use the basic chemical quantity— the mole—to make calculations convenient To determine the empirical formula from percent composition or other mass-ratio data... 

We can find the empirical formula from percent composition data. The empirical formula represents a ratio therefore, it does not depend on the size of the sample under consideration. Because the empirical formula reflects a mole ratio, and percent composition data are given in terms of mass, we have to convert the masses to moles. We then convert the mole ratio, which is unlikely to be an integral ratio, to the smallest possible whole-number ratio, from which we write the empirical formula. 

Let s say that you want to find an empirical formula from the percentage composition. First, convert the mass percentage of each element to grams. Second, convert from grams to moles using the molar mass of each element as a conversion factor. (Keep in mind that a formula for a compound can be read as a number of atoms or as a number of moles.) Third, as shown in Sample Problem C, compare these amounts in moles to find the simplest whole-number ratio among the elements in the compound. 

To find the empirical formula from the percent mass composition, you assume that you have a 100 gram sample. Now the percent translates directly to grams. 

Empirical formulas can also be calculated from the mass of each element in a sample of a compound. Analysis of a sample of a compound shows that it contains 1.179 g Na and 0.821 g S. You could calculate the percent of each element from these numbers, but that s not necessary. The mass of each element is converted directly to moles for the empirical formula. From the table of atomic masses, we find the molar masses are 22.99 g for Na and 32.07 g for S. 

Peroxyacylnitrate (PAN) is one of the components of smog. It is a compound of C, H, N, and O. Determine the percent composition of oxygen and the empirical formula from the following percent composition by mass 19.8 percent C, 2.50 percent H, 11.6 percent... 

Plan The molecular formula subscripts are whole-number multiples of the empirical formula subscripts. To find this whole number, we divide the given molar mass (90.08 g/moI) by the empirical formula mass, which we find from the sum of the elements molar masses. Then we multiply the whole number by each subscript in the empirical formula. Solution The empirical-formula molar mass is 30.03 g/mol. Finding the whole-number multiple ... 

These are very simple examples, but provide a plan of attack for the problems at the end of the chapter. It is highly unlikely that an analyst can identify a complete unknown by its IR spectrum alone (especially without the help of a spectral library database and computerized search). For most molecules, not only the molecular weight, but also the elemental composition (empirical formula) from combustion analysis and other classical analysis methods, the mass spectrum, proton and C NMR spectra, possibly heteroatom NMR spectra (P, Si, and F), the UV spectrum, and other pieces of information may be required for identification. From this data and calculations such as the unsaturation index, likely possible structures can be worked out. 

EMPIRICAL FORMULAS FROM ANALYSES We apply the mole concept to determine chemical formulas from the masses of each element in a given quantity of a compound. 

Chemical formulas are expressed in terms of numbers of particles. In this problem, we have to start with masses and somehow infer information about the numbers of particles. We did a similar problem in this chapter the determination of an empirical formula from percentage by mass data. In this case, with the experiment described, we can determine the mass information for each element in the unknown compound—providing the same type of data we had from percentage mass calculations. Then, because we know the empirical formula and we know the molar mass of the oxygen, we can determine the molar mass of the unknown metal. 

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