Percent Composition and Formulas of Compounds

If the formula of a compound is known, its chemical composition can be expressed as the mass percent of each element in the compound (percent composition). For example, one carbon dioxide molecule, CO2, contains one C atom and two O atoms. Percentage is the part divided by the whole times 100% (or simply parts per hundred), so we can represent the percent composition of carbon dioxide as follows  

One mole of CO2 (44.0 g) contains one mole of C atoms (12.0 g) and two moles of O atoms (32.0 g). We could therefore have used these masses in the preceding calculation. These numbers are the same as the ones used—only the units are different. In Example 2-12 we will base our calculation on one mole rather than one molecule. 

Calculate the percent composition by mass of HNO3. Plan We first calculate the mass of one mole as in Example 2-8. Then we express the mass of  

Nitric acid is 1.6% H, 22.2% N, and 76.2% O by mass. All samples of pure HNO3 have this composition, according to the Law of Definite Proportions. 

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Percent Composition and Formulas of Compounds 2-9 Derivation of Formulas from Elemental Composition 2-10 Determination of Molecular Formulas... 

One of the most common methods used to determine percent composition and empirical formulas, particularly for compounds containing carbon and hydrogen, is combustion analysis. In this method, a compound of unknown composition is burned with oxygen to produce the volatile combustion products C02 and H20, which are separated and weighed by an automated instrument called a gas chromatograph. Methane (CH4), for instance, burns according to the balanced equation... 

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. 

Would it surprise you to learn that two or more substances with distinctly different properties can have the same percent composition and the same empirical formula How is this possible Remember that the subscripts in an empirical formula indicate the simplest whole-number ratio of moles of the elements in the compound. But the simplest ratio does not always indicate the actual number of moles in the compound. To identify a new compound, a chemist must go one step further and determine the molecular formula, which specifies the actual number of atoms of each element in one molecule or formula unit of the substance. Figure 11-11 shows an important use of the gas, acetylene. It has the same percent composition and empirical formula, CH, as benzene which is a liquid. Yet chemically and structurally acetylene and benzene are very different. 

In Section 2-10 we distinguished between simplest and molecular formulas of compounds. We showed how simplest formulas can be calculated from percent compositions of compounds. The molecular weight must be known to determine the molecular formula of a compound. For compounds that are gases at convenient temperatures and pressures, the ideal gas law provides a basis for determining molecular weights. 

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. 

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. 

A compound contains 6.0 g of carbon and 1.0 g of hydrogen, and has a molar mass of 42.0 g/mol. What are the compounds percent composition, empirical formula, and molecular formula ... 

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. 

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. 

One of the first steps in determining the molecular structure of a compound is to establish the compound s molecular formula. In the past, this was most commonly done by elemental analysis, combustion to determine the percent composition, and so forth. More commonly today, we determine molecular weight and molecular formula by a technique known as mass spectrometry (an explanation of the technique is beyond the scope of this book). In the examples that follow, we assume that the molecular formula of any unknown compound has already been determined, and we proceed from there, using spectral analysis to determine a structural formula. 

Percent Composition of a Compound The makeup of a compound is most conveniently expressed in terms of its percent composition, which is the percent by mass of each element the compound contains. A knowledge of its chemical formula enables us to calculate the percent composition. Experimental determination of percent composition and the molar mass of a compound enables us to determine its chemical formula. 

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

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 ... 

Vitamin C is essential for the prevention of scurvy. Combustion of a 0.2000 g sample of this carbon-hydrogen-oxygen compound yields 0.2998 g CO2 and 0.0819 g H2O. What are the percent composition and the empirical formula of vitamin C ... 

Ibuprofen is a compound used in painkillers. When a 2.174 g sample is burned in an excess of oxygen, it yields 6.029 g CO2 and 1.709 g H2O as the sole products. (a) What is the percent composition, by mass, of ibuprofen 0 ) What is the empirical formula of ibuprofen ... 

We illustrate how the mass percent composition of a compound is related to its chemical formula using ammonium nitrate (NH4 NO3). The molar masses of NH4 NO3 and its constituent elements can be used to convert the chemical formula into mass percentages. 

The elemental analysis of a compound is usually determined by a laboratory that specializes in this technique. A chemist who has prepared a new compound sends a sample to the laboratory for analysis. The laboratory charges a fee that depends on the type and number of elements analyzed. The results are returned to the chemist as a listing of mass percent composition. The chemist must then figure out which chemical formula matches this composition. If a chemist has reason to expect a particular chemical formula, the observed percentages can be matched against the calculated percentages for the expected formula. This process is illustrated in Example 3-13. 

C03-0125. A 3.75-g sample of compound that contains sulfur and fluorine contains 2.93 g of fluorine. The molar mass Is less than 200 g/mol. Calculate the percent composition of the compound and determine its molecular formula. 

Atoms and their symbols were introduced in Chap. 3 and 1. In this chapter, the representation of compounds by their formulas will be developed. The formula for a compound (Sec. 4.3) contains much information of use to the chemist. We will learn how to calculate the number of atoms of each element in a formula unit of a compound. Since atoms are so tiny, we will learn to use large groups of atoms—moles of atoms—to ease our calculations. We will learn to calculate the percent by mass of each element in the compound. We will learn how to calculate the simplest formula from percent composition data, and to calculate molecular formulas from simplest formulas and molecular weights. The procedure for writing formulas from names or from knowledge of the elements involved will be presented in Chaps. 5. ft. and 13. 

The concept of percentage is often used to describe the composition of compounds. If the formula of a compound is known, the percent by mass of an element in the compound is determined by computing the fraction of the formula weight which is made up of that element, and multiplying that fraction by 100%. Thus, an element X with atomic weight 40.0 amu in a compound XY of formula weight 99.0 amu will be present in... 

In laboratory work, the identity of a compound may be established by determining its percent composition experimentally and then comparing the results with the percent composition calculated from its formula. 

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