Problems Percentage composition

The MCAT often contains percentage composition problems. Percentage composition is the percentage contribution (by weight) of each element to the total mass. Let s explore this idea by looking at some examples. 

Problem 5.31 The specific rotation of (R)-(-)-2-bromooctane is-36°. What is the percentage composition of a mixture of enantiomers of 2-bromooctane whose rotation is +18° ... 

Since this is an ionic compound, the empirical formula is the only formula that is possible. However, for a molecular compound, it is possible to have an empirical formula that does not represent the molecular formula. Here is a look at such an example. In the first problem, we will also show the procedure for beginning with a percentage composition, which is quite typical for these problems. 

Answer The first step is to calculate the empirical formula. To begin, we need to determine the number of moles of each element. However, the percentage composition does not tell us a mass. To get around this, the commonly used technique is to assume that you have a 100.0-gram sample of the substance. Because 100.0 grams is equal to 100%, you can simply take the percentages and say that the masses are equal to that same amount in grams. From there, the problem proceeds just like the previous example ... 

If 1.00 g of the unknown contains 0.817 g carbon, the mass percent of carbon is 81.7 percent, leaving the remaining 18.3 percent as hydrogen. Therefore, we need to use the procedures for determining an empirical formula from a percentage composition. The problem will progress as follows (remember with percents, assume a 100 g sample) ... 

Examine the following Sample Problem to learn how to calculate the percentage composition of a compound from the mass of the compound and the mass of the elements that make up the compound. Then do the Practice Problems to try expressing the composition of substances as mass percents. 

Does the unknown compound in the Sample Problem contain any elements other than zinc and sulfur How do you know Use the periodic table to predict the formula of the compound. Does the percentage composition support your prediction ... 

In the previous Practice Problems, you used mass data to calculate percentage composition. This skill is useful for interpreting experimental data when the chemical formula is unknown. Often, however, the percentage composition is calculated from a known chemical formula. This is useful when you are interested in extracting a certain element from a compound. For example, many metals, such as iron and mercury, exist in mineral form. Mercury is most often found in nature as mercury(II) sulfide, HgS. Knowing the percentage composition of HgS helps a metallurgist predict the mass of mercury that can be extracted from a sample of HgS. 

Sometimes there are more than two elements in a compound, or more than one atom of each element. This makes determining percentage composition more complex than in the example above. Work through the Sample Problem below to learn how to calculate the percentage composition of a compound from its molecular formula. 

The following Sample Problem illustrates how to use percentage composition to obtain the empirical formula of a compound. 

The percentage composition calculated from the empirical formula matches the percentage composition given in the problem. 

Problem 2.7 Calculate the percentage composition and then the empirical formula for each of the following compounds (a) Combustion of a 3.02-mg sample of a compound gave 8.86 mg of carbon dioxide and 5.43 mg of water, (b) Combustion of an 8.23-mg sample of a compound gave 9.62 mg of carbon dioxide and 3.94 mg of water. Analysis of a 5.32-mg sample of the same compound by the Carius method gave 13.49 mg of silver chloride. 

Let s say that you want to find an empirical formula from the percentage composition. First, convert the mass percentage of each element to grams. Second, convert from grams to moles using the molar mass of each element as a conversion factor. (Keep in mind that a formula for a compound can be read as a number of atoms or as a number of moles.) Third, as shown in Sample Problem C, compare these amounts in moles to find the simplest whole-number ratio among the elements in the compound. 

Verify your answer by calculating the percentage composition of C3H8O. If the result agrees with the composition stated in the problem, then the formula is correct. 

Sample Problem G Determining an Empirical Formula from Percentage Composition... 

Sample Problem I Using a Chemical Formula to Determine Percentage Composition... 

When percentage composition is given, assume 100 g of the compound. Set up the table and complete the problem. 

Sample Problem J Find the percentage composition of copper(I) sulfide, Cu S. 0 ANALYZE... 

Sometimes mass composition is known instead of percentage composition. To determine the empirical formula in this case, convert mass composition to composition in moles. Then calculate the smallest whole-number mole ratio of atoms. This process is shown in Sample Problem M. 

Q CHECK YOUR WORK Calculating the percentage composition of the compoimd based on the empirical formula determined in the problem reveals a percentage composition of 32.37% Na, 22.58% S, and 45.05% O. These values agree reasonably well with the given percentage composition. 

Determine the percentage composition of each of the following compounds. (Hint See Sample Problem J.)... 

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. 

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. 

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