Empirical formulas using percentage composition

What three types of information are used to find an empirical formula from percentage composition data ... 

The following Sample Problem illustrates how to use percentage composition to obtain the empirical formula of a compound. 

The sum of the percentages is 5.926% + 94.06% = 99.99%. The small discrepancy from 100 percent is due to round-off error. Note, if we had used the empirical formula for hydrogen peroxide (HO) instead, we would get the same answer, because both the molecular formula and the empirical formula reveal the composition of a compound. 

Once you determine the empirical formula for a compound, you can calculate its empirical formula weight. If you have an experimental determination of its molecular weight, you can calculate n and then the molecular formula. The next example illustrates how you use percentage composition and molecular weight to determine the molecular formula of acetic acid. 

When 1 try to determine the empirical formula of a compound, 1 often have percentage data available. The determination of the percentage composition is one of the first analyses that a chemist does in leeirning about a new compound. Here s how to find an empirical formula using moles and the percentages of each element ... 

In the problem above, we determined the percentage data from the chemical formula. We can determine the empirical formula if we know the percent compositions of the various elements. The empirical formula tells us what elements are present in the compound and the simplest whole-number ratio of elements. The data may be in terms of percentage, or mass or even moles. However, the procedure is still the same—convert each element to moles, divide each by the smallest, and then use an appropriate multiplier if necessary. We can then determine the empirical formula mass. If we know the actual molecular mass, dividing the molecular formula mass by the empirical formula mass, gives an integer (rounded if needed) that we can multiply each of the subscripts in the empirical formula. This gives the molecular (actual) formula, which tells what elements are in the compound and the actual number of each. 

After we receive the results of a combustion analysis from the laboratory, we need to convert the mass percentage composition to an empirical formula. For this step, we need to determine the relative number of moles of each type of atom. The simplest procedure is to imagine that we have a sample of mass 100 g exactly. That way, the mass percentage composition tells us the mass in grams of each element. Then we can use the molar mass of each element to convert these masses into moles and go on to find the relative numbers of moles of each type of atom. Let s do that for vitamin C, which was once identified in this way, and suppose that the laboratory has reported that the sample you supplied is 40.9% carbon, 4.58% hydrogen, and 54.5% oxygen. 

The chemical makeup of a substance is described by its percent composition—the percentage of the substance s mass due to each of its constituent elements. Elemental analysis is used to calculate a substance s empirical formula, which gives the smallest whole-number ratio of atoms of the elements in the compound. To determine the molecular formula, which may be a simple multiple of the empirical formula, it s also necessary to know the substance s molecular mass. Molecular masses are usually determined by mass spectrometry. 

Answer The first step is to calculate the empirical formula. To begin, we need to determine the number of moles of each element. However, the percentage composition does not tell us a mass. To get around this, the commonly used technique is to assume that you have a 100.0-gram sample of the substance. Because 100.0 grams is equal to 100%, you can simply take the percentages and say that the masses are equal to that same amount in grams. From there, the problem proceeds just like the previous example ... 

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) ... 

In the previous section, you learned how to calculate the percentage composition of a compound from its chemical formula. Now you will do the reverse. You will use the percentage composition of a compound, along with the concept of the mole, to calculate the empirical formula of the compound. Since the percentage composition can often be determined by experiment, chemists use this calculation when they want to identify a compound. 

In practice, you can determine a compound s empirical formula by analyzing its percentage composition. There are several different ways to do this. One way is to use a synthesis reaction in which a sample of an element with a known mass reacts with another element to form a compound. Since you know the mass of one of the elements and you can measure the mass of the compound produced, you can calculate the percentage composition. 

In section 6.2, you learned how to calculate the empirical formula of a compound based on percentage composition data obtained by experiment. In section 6.3, you will learn how chemists use the empirical formula of a compound and its molar mass to determine the molecular formula of a compound. 

If we calculated the percent compositions of C2H2 and CeHg (Figure 7.3), we would find that both have the same percentages of carbon and the same percentages of hydrogen (compare Problem 7.100 at the end of the chapter). Both have the same empirical formula—CH. This result means that we cannot tell these two compounds apart from percent composition data alone. However, if we also have a molar mass, we can use that information with the percent composition data to determine not only the empirical formula but also the molecular formula. 

Percentage Composition, and using the Law of Constant Composition to find the Empirical and Chemical Formula of a Compound... 

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. 

The empirical formula H2O specifies that for every atom of oxygen in water, there are two atoms of hydrogen. Equivalently, one mole of H2O contains two moles of hydrogen atoms and one mole of oxygen atoms. The number of atoms and the number of moles of each element are present in the same ratio, namely, 2 1. The empirical formula for a substance is clearly related to the percentage composition by mass of that substance. This connection can be used in various ways. 

The empirical formula of a compound can be simply related to the mass percentage of its constituent elements using the mole concept. For example, the empirical formula for ethylene (molecular formula C2H4) is CH2. Its composition by mass is calculated from the masses of carbon and hydrogen in 1 mol of CH2 formula units ... 

The procedure used in the example can be reversed if necessary. Given the percent composition by mass of a compound, we can determine the empirical formula of the compound. Since we are dealing with percentages and the sum of aU the percentages is 100 percent, it is convenient to assume that we started with 100 g of a compound, as Example 3.9 shows. 

Check the answer to see that it is reasonable. Some problems have reasonable checks built in, like the percent composition problems in Section 4.3. If the percentages don t add up to 100%, there is a mistake somewhere. For others, we can use the answer to calculate one of the original values, as in empirical formula problems (Section 4.4). Still others require that we know the range of possibilities for our answer. For example, if we get a molarity of 10,000 M (Section 6.1) we know there is a mistake, because... 

The percentage composition result may be used to calculate the empirical formula of the substance being studied. Note that the empirical formula expresses the correct simplest whole-number ratios of the elements in the test substance. The empirical formula may not be the true, or molecular, formula of the substance being examined. The molecular formula may be some multiple of the empirical formula. The mathematical methods used to obtain the empirical formula are familiar from general chemistry. As an illustration, however, a sample calculation, using the same unknown sample that was presented earlier, is shown in Table 1.2. 

The empirical formula of an unknown compound can be worked out from its percentage composition using the calculations in Unit 8. 

You can also use the mole concept to calculate the empirical formula of a compound using the percentage composition data for that compound — the percentage by weight of each element in the compound. (The empirical formula indicates the different types of elements in a molecule and the lowest whole-number ratio of each kind of atom in the molecule. See Chapter 7 for details.)... 

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