Percent composition calculating empirical formulas from

Calculating Empirical Formulas from Percent Composition... 

Be able to calculate the empirical formula from percent composition data or quantities from chemical analysis. 

Just as we can derive the empirical formula of a substance from its percent composition, we can also calculate the percent composition of a substance from its empirical (or molecular) formula. The strategies for the two kinds of calculations are exactly opposite. Aspirin, for example, has the molecular formula C9H8O4 and thus has a CH 0 mole ratio of 9 8 4. We can convert this mole ratio into a mass ratio, and thus into percent composition, by carrying out mole-to-gram conversions. 

The steps we take to obtain an empirical formula from percent composition data are given in the left column (Steps) that follows. In the right column (Example), the empirical formula of a compound containing 39.2% phosphorus and 60.8% sulfur is calculated. 

For more practice calculating an empirical formula from percent composition, go to Supplemental Practice Problems in Appendix A. 

When a compound is analyzed to determine the relative amounts of the elements present, the results are usually given in terms of percentages by masses of the various elements. Previously we learned to calculate the percent composition of a compound from its formula. Now we will do the opposite. Given the percent composition, we will calculate the empirical formula. 

When chemistry teachers prepare an exam question on determining the empirical formula of a compound, they usually take a known compound and calculate the percent composition of the compound from the formula. They then give students this percent composition data and have the students calculate the original formula. Using a compound of your choice, first use the molecular formula of the compound to calculate the percent composition of the compound. Then use this percent composition data to calculate the empirical formula of the compound. 

EMPIRICAL FORMULAS FROM ANALYSIS (SECTION 3.5) The empirical formula of any substance can be determined from its percent composition by calculating the relative number of moles of each atom in 100 g of the substance. If the substance is molecular in nature, its molecular formula can be determined from the empirical formula if the molecular weight is also known. Combustion analysis is a special technique for determining the empirical formulas of compounds containing only carbon, hydrogen, and/or oxygen. 

Our approach will require several steps (1) Use the combustion data to determine the percent composition of the compound (similar to Example 3-6). (2) Determine the empirical formula from the percent composition (similar to Example 3-5). (3) Obtain the molecular formula from the empirical formula and the molecular mass. (4) Determine how the C, H, and O atoms represented in the molecular formula might be assembled into a dicarboxylic acid. Use molar masses with (at least) one more significant figure than in the measured masses where possible store intermediate results in your calculator without rounding off. 

In the problems above, the percentage data was calculated from the chemical formula, but the empirical formula can be determined if the percent compositions of the various elements are known. 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. But the procedure is still the same convert each to moles, divide each by the smallest number, then use an appropriate multiplier if needed. The empirical formula mass can then be calculated. If the actual molecular mass is known, dividing the molecular mass by the empirical formula mass gives an integer (rounded if needed) that is used to multiply each of the subscripts in the empirical formula. This gives the molecular (actual) formula, which tells which elements are in the compound and the actual number of each. 

What if you don t know the formula of a compound Chemists sometimes find themselves in this disconcerting scencirio. Instead of cursing Avogadro (or perhaps after doing so), they analyze samples of the frustrating unknown to identify the percent composition. From there, they calculate the ratios of different types of atoms in the compound. They express these ratios as an empirical formula, the lowest whole-number ratio of elements in a compound. 

To determine a moleculcir formula, you must know the gram formula mass of the compound as well as the empirical formula (or enough information to calculate it yourself from the percent composition see the preceding section for details). With these tools in hand, calculating the molecular formula involves three steps ... 

The percent composition of glucose can be calculated either from the molecular formula (CgH Og) or from the empirical formula (CH20). Using the molecular formula, for instance, the C H 0 mole ratio of 6 12 6 can be converted into a mass ratio by assuming that we have 1 mol of compound and carrying out mole-to-gram conversions ... 

From the weight of CuCl2, and the weight of Cu, subtraction will give the weight of Cl. From these weights, the mole ratio of copper to chlorine, the empirical formula, and the percent composition of CuCl2 can then be calculated. 

The meaning of a chemical formula was discussed in Chapter 5, and we learned how to interpret formulas in terms of the numbers of atoms of each element per formula unit. In this chapter, we will learn how to calculate the number of grams of each element in any given quantity of a compound from its formula and to do other calculations involving formulas. Formula masses are presented in Section 7.1, and percent composition is considered in Section 7.2. Section 7.3 discusses the mole—the basic chemical quantity of any substance. Moles can be used to count atoms, molecules, or ions and to calculate the mass of any known number of formula units of a substance. Section 7.4 shows how to use relative mass data to determine empirical formulas, and the method is extended to molecular formulas in Section 7.5. 

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. 

Even if we cannot see how to solve this problem completely at first glance, we can tell immediately that the empirical formula can be calculated from the percent composition and that the number of moles can be calculated from its pressure-volume-temperature data. 

The steps in determining empirical and molecular formulas from percent composition or mass data are outlined below. As in other calculations, the route leads from mass through moles because formulas are based on the relative numbers of moles of elements in each mole of compound. 

If you know the formula of a compound, you can calculate its percent composition. Just the reverse can be done too. If you know the percent composition of a compound, you can calculate a formula for the compound. A formula calculated from percent composition data is called an empirical formula (one calculated from experimental data). The formulas of ionic compounds are always empirical formulas. The formulas of molecular compounds may be the same as their empirical formulas or they may be some whole-number multiple of it. You will learn how to do composition-from-fbrmula and fbrmula-from-composition calculations in this chapter. 

There are two broad classes of formulas for compounds empirical formulas and molecular formulas. The empirical formula shows the simplest ratio of elements in a compound and uses the smallest possible set of subscript numbers. Empirical formulas are also called simple formulas. The formulas of a// ionic compounds are empirical formulas. Since ionic compounds do not exist as molecules, their formulas are not molecular formulas. The formulas calculated from percent composition data are empirical formulas. (We ll get to these calculations later.)... 

Empirical formulas can be calculated from the percent composition of a compound. You have already learned that the subscript numbers in formulas can be read in terms of the number of moles of each element. In 1 mole of N2Os, there are 2 moles of N and 5 moles of O. Read the formula as N2moies05 moies. The reason this is mentioned again is because any data that allows the number of moles of each element in a compound to be known allows the calculation of the empirical formula of that compound. Percent composition data does this. Here s the step-by-step way it is done ... 

It is important to realize that only empirical formulas are calculated from percent composition data or mass data. That s fine for ionic compounds because their formulas are always empirical formulas. But the complete formulas of molecular compounds, the molecular formulas, can only be obtained from the empirical formulas if the molecular mass or molar mass of the compound is also known. 

The formula calculated from percent composition by mass is always the empirical formula because the coefficients in the formula are always reduced to the smallest whole numbers. To calculate the actual, molecular formula we must know the approximate molar mass of the compound in addition to its empirical formula. Knowing that the molar mass of a compound must be an integral multiple of the molar mass of its empirical formula, we can use the molar mass to find the molecular formula, as Example 3.11 demonstrates. 

An empirical formula is the chemipal formula which represents the basic combining ratios of the compound s elements. It cannot tell us the actual numbers of each kind of atom in the molecule. That information is contained in the molecular formula of a compound. For example, the percent composition of glucose is the following carbon, 40.00 percent hydrogen, 6.714 percent oxygen, 53.29 percent. From these data we can calculate the empirical formula ... 

The sum of the percentages is 5.926% + 94.06% = 99.99%. The small discrepancy from 100 percent is due to the way we rounded off the molar masses of the elements. If we had used the empirical formula HO for the calculation, we would have obtained the same percentages. This is so because both the molecular formula and empirical formula tell us the percent composition by mass of the compound. 

Figure 3.5 Procedure for calculating the empirical formula of a compound from its percent compositions.

The procedure used in Example 0.15 can be reversed, if necessary, to calculate the empirical formula of a compound from the percent composition by mass of the compound (Figure 0.16). Because we are dealing with percentages and the sum of all the percentages is 100 percent, it is convenient to assume that we started with 100 g of a compound, as shown in Example 0.16. 

---