Chemical formulas whole-number ratios

A major task of chemical analysis is to determine the formulas of compounds. The formula found by the approach described here is the simplest formula, which gives the simplest whole-number ratio of the atoms present. For an ionic compound, the simplest formula is ordinarily the only one that can be written (e.g., CaCl2, Cr203). For a molecular compound, the molecular formula is a whole-number multiple of the simplest formula, where that number may be 1,2. 

The Law of Conservation of Mass states that the total mass remains unchanged. This means that the total mass of the atoms of each element represented in the reactants must appear as products. In order to indicate this, we must balance the reaction. When balancing chemical equations, it is important to realize that you cannot change the formulas of the reactants and products the only things you may change are the coefficients in front of the reactants and products. The coefficients indicate how many of each chemical species react or form. A balanced equation has the same number of each type of atom present on both sides of the equation and the coefficients are present in the lowest whole number ratio. For example, iron metal reacts with oxygen gas to form rust, iron(III) oxide. We may represent this reaction by the following balanced equation ... 

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. 

Answer all three of the following questions. Each question will have two parts—writing the balanced chemical equation and answering a question about the reaction. Coefficients in the balanced chemical equation must be in the lowest whole-number ratio. Do not include formulas for substances that remain unchanged during the reaction. Unless otherwise noted, assume all the reactions occur in aqueous solution. If a substance is extensively ionized and therefore is present as ions in solution, write its formula as ions. 

Dalton s Law of Multiple Proportions meant that two elements combine in simple whole number ratios. Dalton believed that compounds found in nature would be simple combinations. Hence, knowing that hydrogen combines with oxygen to give water, Dalton s formula for water would consist of 1 H and 1 O. Its formula would be HO using modern nomenclature. Both Proust s Law of Definite Proportions and Dalton s Law of Multiple Proportions are outcomes of an atomic view of nature. In 1808 Dalton published his table of relative atomic weights along with his ideas on atomism in A New System of Chemical Philosophy. 

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. 

Column (5) is determined in this problem, as in the previous problem, by dividing both numbers by the smallest (0.0559) which preserves the mole ratio of 0.0559 0.391 and leads to the whole-number ratio required to write a chemical formula. Column (5) contains 6.99, a number that is so close to a whole number that the difference can be taken for experimental error. The mole ratio of Na2SC>4 to H2O is 1 to 7, providing us with an empirical formula of Na2S04- 7H20. 

Through the use of chemical symbols and numerical subscripts, the formula of a compound can be written. The simplest formula that may be written is the empirical formula. In this formula, the subscripts are in the form of the simplest whole number ratio of the atoms in a molecule or of the ions in a formula unit. The molecular formula, however, represents the actual number of atoms in a molecule. For example, although CH20 represents the empirical formula of the sugar, glucose, C6H1206, represents the molecular formula. For water, H20, and carbon dioxide, C02, the empirical and the molecular formulas are the same. Ionic compounds are generally written as empirical formulas only for example, common table salt is NaCl. 

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. 

An empirical formula gives the simplest whole number ratio of atoms in a chemical compound. In contrast, a molecular formula specifies the number of atoms in a molecule. Two or more substances may have the same empirical formula but different... 

In each case, we identify the chemical formulas of the ions from Table 2-3. These ions must be present in the simplest whole-number ratio that gives the compound no net charge. Recall that the formulas and names of ionic compounds are written by giving the positively charged ion first. 

The nomenclature for molecular compounds is much less complicated than for ionic compounds. Molecular compounds are formed from covalently bonded nonmetallic elements. The formula for a molecule represents a stable unit of atoms, unlike a formula for an ionic compound, which only represents the simplest whole number ratio of ions. As a result, molecular formulas cannot be simplified like formulas for ionic compounds. An example would be hydrogen peroxide, H O. Although the formula could be reduced to HO, this would be inappropriate because 11,0, is a molecule. Changing the structure to HO would change the chemical composition. 

Because chemical formulas use only whole numbers, we next find the whole-number ratio of the atoms. To do this we start by dividing both numbers by the smallest of the two. This converts the smallest number to 1. 

The balanced equation for the reaction between aluminum and bromine, shown in Figure 9.5, reflects the law of conservation of mass. To balance an equation, you must find the correct coefficients for the chemical formulas in the skeleton equation. A coefficient in a chemical equation is the number written in front of a reactant or product. Coefficients are usually whole numbers and are not usually written if the value is one. The coefficients in a balanced equation describe the lowest whole-number ratio of the amounts of all of the reactants and products. 

Chemical formulas that indicate the actual numbers of atoms in a molecule are called molecular formulas. (The formulas in Figure 2.18 are molecular formulas.) Chemical formulas that give only the relative number of atoms of each type in a molecule are called empirical formulas. The subscripts in an empirical formula are always the smallest possible whole-number ratios. The molecular formula for hydrogen peroxide is H2O2, for example, whereas its empirical formula is HO. The molecular formula for ethylene is C2H4, and its empirical formula is CH2. For many substances, the molecular formula and the empirical formula are identical, as in the case of water, H2O. 

Empirical formula (2.4) Chemical formula that shows the composition of a compound in terms of the simplest whole-number ratio of the atoms of each element. 

Check The subscripts are reduced to the smallest whole number ratio of the atoms because the chemical formula of an ionic compound is usually its empirical formula. 

The answer is a qualified yes. We can determine a chemical formula, but it is the empirical formula, not the molecular formula. As we saw in Section 5.3, an empirical formula only gives the smallest whole-number ratio of each type of atom in a compound, not the specific number of each type of atom in a molecule. Recall that the molecular formula is always a whole-number multiple of the empirical formula Molecular formula = Empirical formula X n, where n = 1,2,3. .. 

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