Mass Percent Composition and Empirical Formulas

Propane gas, CgHg, is used as a fuel for many barbecues. 

The characteristic odor of garlic is due to a sulfur-containing compound. 

Because the atoms of the elements in a compound are combined in a definite proportion, they are also combined in a definite proportion by mass. Thus, when we know the mass of an element in a sample of a compound, we can calculate its mass percent composition or mass percent, which is the mass of an element divided by the total mass of the compound and multiplied by 100%. 

Given the formula of a compound, calculate the mass percent composition from the mass percent composition, determine the empirical formula of a compound. 

CONCEPT CHECK lA Calculating Mass Percent from 

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A 0.1888 g sample of a hydrocarbon produces 0.6260 g CO2 and 0.1602 g H2O in combustion analysis. Its molecular mass is found to be 106 u. For this hydrocarbon, determine its (a) mass percent composition (b) empirical formula (c) molecular formula. 

If the mass percent composition and molar mass of a compound are known, its empirical and molecular formulas can be determined. 

Suppose that we want to determine the formula of an unknown hydrocarbon. With combustion analysis we can establish the mass percent composition, and from this, we can determine the empirical formula. The method of Example 6-7 gives us a molar mass, in g moP, which is numerically equal to the molecular mass, in u. This is all the information we need to establish the true molecular formula of the hydrocarbon (see Exercise 96). 

Making particle numbers manageable with Avogadro s number Converting between masses, mole counts, and volumes Dissecting compounds with percent composition Moving from percent composition to empirical and molecular formulas... 

To determine the molecular formula from percent composition and molecular mass data or from the empirical formula and molecular mass data... 

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. 

Formulas describe the composition of compounds. Empirical formulas give the mole ratio of the various elements. However, sometimes different compounds have the same ratio of moles of atoms of the same elements. For example, acetylene, C2H2, and benzene, CeHe, each have 1 1 ratios of moles of carbon atoms to moles of hydrogen atoms. That is, each has an empirical formula CH. Such compounds have the same percent compositions. However, they do not have the same number of atoms in each molecule. The molecular formula is a formula that gives all the information that the empirical formula gives (the mole ratios of the various elements) plus the information of how many atoms are in each molecule. In order to deduce molecular formulas from experimental data, the percent composition and the molar mass are usually determined. The molar mass may be determined experimentally in several ways, one of which will be described in Chap. 12. 

If we know the composition of a compound in terms of the masses (or mass percentages) of the elements present, we can calculate the empirical formula but not the molecular formula. For reasons that will become clear as we consider Example 6.15, to obtain the molecular formula we must know the molar mass. Next we will consider compounds where both the percent composition and the molar mass are known. 

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. 

Calculate the percent composition and determine the molecu- 42. lar formula and the empirical formula for the nitrogen-oxygen compound that results when 12.04 g of nitrogen are reacted with enough oxygen to produce 39.54 g of product. The molar mass of the product is 92.02 g. 

Calculate the percent composition and determine the molecular formula and the empirical formula for the carbon-hydrogen-oxygen compound that results when 30.21 g of carbon, 40.24 g of oxygen, and 5.08 g of hydrogen are reacted to produce a product with a molar mass of 180.18 g. 

What is the mathematical formula for calculating mass percent composition from a chemical formula How are the empirical formula and the molecular formula of a compound related ... 

Tetrachloroethene is a colorless liquid used for dry cleaning. What is the empirical formula of tetrachloroethene if its mass percent composition is 14.5% C and 85.5% Cl ... 

Sulfate of potash is the common name of a compound used in fertilizers to supply potassium and sulfur. What is the empirical formula of this compound if it has a mass percent composition of 44.9% K, 18.4% S, and 36.7% O ... 

Ascorbic acid (vitamin C), found in citrus fruits and vegetables, is important in metabolic reactions in the body, in the synthesis of collagen, and in the prevention of scurvy. If the mass percent composition of ascorbic acid is 40.9% C, 4.58% H, and 54.5% O, what is the empirical formula of ascorbic acid ... 

The elemental mass percent composition of ascorbic acid (vitamin C) is 40.92% C, 4.58% H, and 54.50% O. Determine the empirical formula of ascorbic acid. 

EXAMPLE 3-5 Determining the Empirical and Molecular Formulas of a Compound from Its Mass Percent Composition... 

PRACTICE EXAMPLE A Sorbitol, used as a sweetener in some sugar-free foods, has a molecular mass of 182 u and a mass percent composition of 39.56% C, 7.74% H, and 52.70% O. What are the empirical and molecular formulas of sorbitol ... 

Explain why, if the percent composition and the molar mass of a compound are both known, the molecular formula can be determined much more readily by using the molar mass rather than a 100 g sample in the first step of the five-step procedure in Example 3-5. In this instance, how would you then obtain the empirical formula ... 

At this point we can choose either of two alternatives. The first is to obtain the empirical formula from the mass percent composition, in the same manner illustrated in Example 3-5. The second is to note that we have already determined the number of moles of C and H in the 0.2000 g sample. The number of moles of O is... 

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. 

A compound has a percent composition of 49.5% carbon, 5.2% hydrogen, 16.5% oxygen, and 28.8% nitrogen. The compound s gram molecular mass is 194.2 g/mol. What are the empirical and molecular formulas ... 

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 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 ... 

Step 1 Find the empirical formula of the gas, using the molar masses of carbon and hydrogen and the percent compositions. 

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. 

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. 

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