Chemists often need to know what elements are present in a compound and in what percentage. The percent composition is the percent by mass of each element in a compound. It is calculated in a similar way to what was just indicated for the peanut butter.
\[\% \: \text{by mass} = \frac{\text{mass of element}}{\text{mass of compound}} \times 100\%\nonumber \]
The percent composition of a compound can also be determined from the formula of the compound. The subscripts in the formula are first used to calculate the mass of each element in one mole of the compound. That is divided by the molar mass of the compound and multiplied by \(100\%\).
\[\% \: \text{by mass} = \frac{\text{mass of element in} \: 1 \: \text{mol}}{\text{molar mass of compound}} \times 100\%\nonumber \]
The percent composition of a given compound is always the same as long as the compound is pure.
Example \(\PageIndex{2}\): Percent Composition from Chemical Formula
Dichlorineheptoxide \(\left( \ce{Cl_2O_7} \right)\) is a highly reactive compound used in some organic synthesis reactions. Calculate the percent composition of dichlorineheptoxide.
Solution
Step 1: List the known quantities and plan the problem.
Known
- Mass of \(\ce{Cl}\) in \(1 \: \text{mol} \: \ce{Cl_2O_7} = 70.90 \: \text{g}\)
- Mass of \(\ce{O}\) in \(1 \: \text{mol} \: \ce{Cl_2O_7} = 112.00 \: \text{g}\)
- Molar mass of \(\ce{Cl_2O_7} = 182.90 \: \text{g/mol}\)
Unknown
- Percent \(\ce{Cl} = ? \%\)
- Percent \(\ce{O} = ? \%\)
Calculate the percent by mass of each element by dividing the mass of that element in 1 mole of the compound by the molar mass of the compound and multiplying by \(100\%\).
Step 2: Calculate.
\[\% \ce{Cl} = \frac{70.90 \: \text{g} \: \ce{Cl}}{182.90 \: \text{g}} \times 100\% = 38.76\% \: \ce{Cl}\nonumber \]
\[\% \: \ce{O} = \frac{112.00 \: \text{g} \: \ce{O}}{182.90 \: \text{g}} \times 100\% = 61.24\% \: \ce{O}\nonumber \]
Step 3: Think about your result.
The percentages add up to \(100\%\).
Percent composition can also be used to determine the mass of a certain element that is contained in any mass of a compound. In the previous sample problem, it was found that the percent composition of dichlorine heptoxide is \(38.76\% \: \ce{Cl}\) and \(61.24\% \: \ce{O}\). Suppose that you need to know the masses of chlorine and oxygen present in a \(12.50 \: \text{g}\) sample of dichlorine heptoxide. You can set up a conversion factor based on the percent by mass of each element:
\[12.50 \: \text{g} \: \ce{Cl_2O_7} \times \frac{38.76 \: \text{g} \: \ce{Cl}}{100 \: \text{g} \: \ce{Cl_2O_7}} = 4.845 \: \text{g} \: \ce{Cl}\nonumber \]
\[12.50 \: \text{g} \: \ce{Cl_2O_7} \times \frac{61.24 \: \text{g} \: \ce{O}}{100 \: \text{g} \: \ce{Cl_2O_7}} = 7.655 \: \text{g} \: \ce{O}\nonumber \]
The sum of the two masses is \(12.50 \: \text{g}\), the mass of the sample size.
Science Friday: Stained Glass Conservation
Stained glass from the Middle Ages is often hundreds of years old. Unfortunately, many of these relics are in need of cleaning and maintenance. In this video by Science Friday, conservator Mary Higgins discusses the methods used to protect the stained glass.