Percent composition, often called percentage by mass, is a fundamental measurement describing the precise makeup of a chemical compound. This value represents the mass of a single element relative to the total mass of the compound, expressed as a percentage. Understanding this mass ratio is important for characterizing substances and confirming their chemical identity. Chemists use percent composition to verify the purity of a synthesized compound or to determine the empirical formula for chemical analysis.
The Essential Foundation: Calculating Molar Mass
The preparation for calculating percent composition requires the accurate determination of the compound’s total molar mass. This foundational figure begins with consulting the periodic table to find the atomic mass for every element present. The atomic mass, often expressed in grams per mole (\(g/mol\)), defines the mass of one mole of that specific element.
Once the individual atomic masses are known, the chemical formula dictates how many moles of each element are present. The small subscript number next to an element’s symbol indicates the quantity of that element within the molecular structure. For instance, in a compound like glucose (\(C_6H_{12}O_6\)), the subscript six next to carbon means one mole of glucose contains six moles of carbon atoms.
To establish the mass contribution of each element, its atomic mass is multiplied by its corresponding subscript value. This multiplication accounts for the total mass contributed by that element within the molecule. For example, the mass of six moles of carbon is six times the atomic mass of carbon.
After calculating these individual mass totals for all component elements, these values must be summed together. This final aggregate number represents the total molar mass of the compound, a figure measured in grams per mole.
The Formula for Percent Composition
With the total molar mass established, the next step involves applying the formula for percent composition. The general mathematical relationship is straightforward: the mass of the element is divided by the total molar mass of the compound, and the result is multiplied by one hundred to express the value as a percentage.
The procedure begins by identifying the numerator, which is the total mass of the element being determined. This figure is the element’s atomic mass multiplied by its corresponding subscript in the chemical formula. This accurately reflects the entire mass the element contributes to the compound.
The denominator is the total molar mass of the compound determined in the foundational step. This overall mass figure provides the complete reference against which the element’s individual mass is compared. Dividing the element’s mass by the compound’s total mass yields a decimal fraction that clearly represents the mass ratio.
To complete the process, the resulting decimal fraction is converted into the standard percentage format. This conversion is accomplished by multiplying the decimal result by one hundred. The final numerical output reflects the element’s proportional contribution to the compound based on mass.
Practical Application: A Worked Example
To illustrate this process, consider the common compound water, which has the chemical formula \(H_2O\). The goal is to determine the percentage by mass of oxygen within this molecule. This requires combining molar mass calculation with the percent composition formula.
First, the total molar mass of water must be calculated using the atomic masses found on the periodic table. Hydrogen (H) has an atomic mass of 1.008 grams per mole, and oxygen (O) has an atomic mass of 16.00 grams per mole. Since the formula indicates two hydrogen atoms, the hydrogen contribution is \(2 \times 1.008 \ g/mol\), which equals 2.016 grams per mole.
The oxygen contribution is determined by multiplying its atomic mass by its subscript, \(1 \times 16.00 \ g/mol\), resulting in 16.00 grams per mole. Summing these two elemental contributions yields the total molar mass of water: \(2.016 \ g/mol + 16.00 \ g/mol\), which totals 18.016 grams per mole. This calculated total mass provides the denominator for the subsequent percentage calculation.
Next, the mass of the element in question, oxygen, is isolated to serve as the numerator. The mass contributed by oxygen is 16.00 grams per mole. These two derived values are then inserted into the percent composition formula, setting up the division as \(16.00 \ g/mol\) divided by \(18.016 \ g/mol\).
Performing the division yields the decimal fraction 0.8881. The final action is to multiply this resulting value by one hundred to accurately obtain the percentage. This completed calculation shows that oxygen makes up approximately 88.81 percent of the total mass of a water molecule. The remaining percentage, \(11.19\%\), is the contribution of hydrogen.