Calculations percent composition

Chemists are often concerned with precisely what percentage of a compound s mass consists of one particular element. Lying awake at night, uttering prayers to Avogadro, they fret over this quantity, called percent composition. Calculating percent composition is trickier than you may think. Consider the following problem, for example. 

The composition analysis of SBR, i.e., styrene, czs-1,4, trans-1,4 and 1,2 (vinyl) units, has been carried out by 13C-NMR based on signal assignments indicated in Table 11.2. The integrated intensities of regions A to I are used to calculate percent composition by using following equations [17]. 

Example Problem 10.10 covers calculating percent composition. 

Calculating Percent Composition Sodium hydrogen carbonate (NaHCOa), also called baking soda, is an active ingredient in some antacids used for the relief of indigestion. Determine the percent composition of NaHCOa. 

Chemical stoichiometry is the area of study that considers the quantities of materials in chemical formulas and equations. Quite simply, it is chemical arithmetic. The word itself is derived from stoicheion, the Greek word for element and metron, the Greek word for measure. When based on chemical formulas, stoichiometry is used to convert between mass and moles, to calculate the number of atoms, to calculate percent composition, and to interpret the mole ratios expressed in a chemical formula. Most topics in chemical arithmetic depend on the interpretation of balanced chemical equations. Mass/mole conversions, calculation of limiting reagent and percent yield, and various relationships among reactants and products are commonly included in this topic area. 

Problem-Solving Strategy for Calculating Percent Composition from Formula... 

Table 5. Calculated percent composition of steroid esters ...

The formula of a compound indicates the number of atoms of each element in a unit of the compound. From a molecular or empirical formula, we can calculate what percent of the total mass is contributed by each element in a compound. A list of the percent by mass of each element in a compound is known as the compound s percent con osition by mass. One way that the purity of a compound can be verified is by comparing its percent composition by mass, determined experimentally, with its calculated percent composition. Percent composition is calculated by dividing the mass of each element in a unit of the compound by the molecular or formula mass of the compound and then multiplying by 100 percent. Mathematically, the percent by mass of an element in a compound is expressed as... 

Because both the molecular formula and the empirical formula tell us the composition of the compound, they both give the same percent composition by mass. Sample Problem 3.2 shows how to calculate percent composition by mass. 

Combustion analysis is used to determine the empirical formula of a compound. The empirical formula can be used to calculate percent composition. 

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. 

C03-0081. Portland cement contains CaO, Si02, AI2 O3, and FC2 O3. Calculate the mass percent composition of each compound. 

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. 

EXAMPLE 4.10. Calculate the percent composition of MgS04 that is, the percent by mass of each element in the compound. 

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. 

Calculate the percent composition of each of the following (a) C4HN and (b) ChHl2. 

Calculate the percent composition of C2H4. (h) Calculate the percent composition of C4HK. (c) Compare the results and explain the reason for these results. 

The feed stream consists of 60 mole percent hydrogen, 20% nitrogen, and 20% argon. Calculate the composition of the exit gases, assuming equilibrium is achieved in the reactor. Make sure that you take deviations from the ideal gas law into account. The equilibrium constant expressed in terms of activities relative to standard states at 1 atm may be assumed to be equal to 8.75 x 10 3. The fugacity of pure H2 at 450 °C and 101.3 MPa may be assumed to be equal to 136.8 MPa. 

If we know the formula of a compound, it is a simple task to determine the percent composition of each element present. For example, suppose you wanted the percentage carbon and hydrogen in methane, CH4. First, calculate the molecular mass of methane ... 

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. 

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

Calculate the percent composition for each element in sodium sulfate, Na2SO,. 

Calculate the percent composition of potassium chromate, K2CrO. ... 

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. 

Calculate the empirical formula of a compound with a percent composition of 88.9% oxygen and 11.1% hydrogen. 

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 denominator for Equation E6.2 is calculated by performing steps 1 and 2 for all of the FAMEs present in a single triacylglycerol sample. The mole-corrected peak areas are added together to obtain the total of all mole-corrected areas. If we assume that the extent of conversion of free fatty acids to FAMEs is essentially quantitative, or at least equal for all fatty acids in our experiment, the above calculation leads directly to the combined mole percent composition of fatty acids in all positions of the triacylglycerol. 

Knowing a compound s percent composition makes it possible to calculate the compound s chemical formula. As shown in Figure 3.8, the strategy is to find the relative number of moles of each element in the compound and then use the numbers to establish the mole ratios of the elements. The mole ratios, in turn, give the subscripts in the chemical formula. 

A FIGURE 3.8 A flow diagram for calculating the formula of a compound from its percent composition. 

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 ... 

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. 

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