Percent composition of compounds

The calculation of the percent of an element in a compound is derived from the general definition of percent. 

If the part is a weight and the whole is a weight, then we have the following  

The term percent means the quantity or number of units out of 100 units total. Percentage is computed by finding the fraction of the total quantity represented by the quantity under discussion and multiplying by 100%. For example, if a group of 30 persons includes 6 females, the percent of females in the group is 

In other words, if there were 100 persons in the group and the ratio of females to males were the same, 20 of the group would be female. Percentage is a familiar concept to anyone who pays sales taxes. 

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 mass which is made up of that element, and multiplying that fraction by 100%. Thus, an element X with atomic mass 12.0 amu in a compound XY of formula mass 28.0 amu will be present in 

The chemical formula gives the number of moles of atoms of each element in each mole of the compound then the number of grams of each element in tlie number of grams of compound in 1 mol of the compound can be directly computed. Knowing the mass of 1 mol of the compound and the mass of each element in that quantity of compound allows calculations of the percent by mass of each element. 

EXAMPLE 7.10. Calculate the percent composition of CaS04, that is, the percent by mass of each element in the compound. 

We need to use the atomic masses from the inside front cover of the text to find the molar mass of H2O. 

How many molecules of hydrogen chloride (HCl) are there in 25.0 g of hydrogen chloride  

Percent means parts per 100 parts. Just as each piece of pie is a percent of the whole pie, each element in a compound is a percent of the whole compound. The percent composition of a compound is the mass percent of each element in the compound. The molar mass represents the total mass, or 100%, of the compound. Thus, the percent composition of water, H2O, is 11.19% H and 88.79% O by mass. According to the law of definite composition, the percent composition must be the same no matter what size sample is taken. 

The percent composition of a compound can be determined (1) from knowing its formula or (2) from experimental data. 

So far we have discussed the composition of a compound in terms of the numbers of its constituent atoms. It is often useful to know a compound s composition in terms of the masses of its elements. We can obtain this information from the formula of the compound by comparing the mass of each element present in 1 mole of the compound with the total mass of 1 mole of the compound. 

For example, consider ethanol, which has the formula C2H5OH. The mass of each element present and the molar mass are obtained through the following procedure. 

The mass percent (often called the weight percent) of carbon in ethanol can be computed by comparing the mass of carbon in 1 mole of ethanol with the total mass of 1 mole of ethanol and multiplying the result by 100%  

The mass percents of hydrogen and oxygen in ethanol are obtained in a similar manner  

Notice that the percentages add to 100% if rounded to two decimal places this is the check of the calculations. 

The mass fraction is converted to mass percent by multiplying by 100%. 

Note from its formula that each molecule of ethanol contains two carbon atoms, six hydrogen atoms, and one oxygen atom. This means that each mole of ethanol contains 2 mol of carbon atoms, 6 mol of hydrogen atoms, and 1 mol of oxygen atoms. We calculate the mass of each element present and the molar mass for ethanol as follows  

The formula for ethanol is written CjHjOH, although you might expect it to be written simply as CjHgO. 

Sometimes, because of rounding-off effects, the sum of the mass percents in a compound is not exactly 100%. 

Note from its formula (C2H5OH) that each molecule of ethanol contains two carbon atoms, six hydrogen atoms, and one oxygen atom. 

Experiment 14 Composition 1 Percentage Composition and Empirical Formula of Magnesium Oxide 

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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 

The sum of percentages is 5.296% + 94.06% = 99.99%. The small discrepancy Ifom 100 percent is due to rounding of the atomic masses of the elements. We could equally well have used the empirical formula of hydrogen peroxide (HO) for the calculation. In this case, we would have used the empirical formula mass, 17.01 amu, in place of the molecular mass. 

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. 

Lithium carbonate, Li2C03, was the first mood-stabilizing drug approved by the FDA for the treatment of mania and manic-depressive illness, also known as bipolar disorder. Calculate the percent composition by mass of lithium carbonate. 

As we have seen, the formula of a compoimd tells us the numbers of atoms of each element in a unit of the compoimd. However, suppose we needed to verify the purity of a compound for use in a laboratory experiment. We could calculate what percent of the total mass of the compoimd is contributed by each element from the formula. Then, by comparing the result to the percent composition obtained experimentally for our sample, we could determine the purity of the sample. 

The percent composition is the percent by mass of each element in a compound. Percent composition is obtained by dividing the mass of each element in 1 mole of the compound by the molar mass of the compound and multiplying by 100 percent. Mathematically, the percent composition of an element in a compound is expressed as 

The sum of the percentages is 5.926 percent + 94.06 percent = 99.99 percent. The small discrepancy from 100 percent is due to the way we rounded off the molar masses of the elements. Note that the empirical formula (HO) would give us the same results. 

Phosphoric acid (H3PO4) is a colorless, sympy liquid used in detergents, fertilizers, toothpastes, and in carbonated beverages for a Tangy flavor. Calculate the percent composition by mass of H, P, and O in this compound. 

Strategy Recall the procedure for calculating a percentage. Assume that we have 1 mole of H3PO4. The percent by mass of each element (H, P, and O) is given by the combined molar mass of the atoms of the element in 1 mole of H3PO4 divided by the molar mass of H3PO4, then multiplied by 100 percent. 

Trancis William Aston (1877-1945). English chemist and physicist. He was awarded the Nobel Prize in Chemistry in 1922 for developing the mass spectrometer. 

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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. 

CHAPTER 6 Formula Calculations 49 Percent Compositions of Compounds... 

If you missed 19, go to Calculating the Percent Composition of Compounds, page 135. 

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