Percentage composition by weight is a foundational concept in chemistry. It is a simple ratio, expressed as a percentage, that reveals the relative amount of each element present within a chemical compound by mass. This measurement breaks down the compound’s total mass and allocates a portion of that mass to each constituent atom.
Chemists use percentage composition for practical reasons, such as determining the purity of a substance or verifying the results of a chemical synthesis. If a newly created compound does not exhibit the expected composition, it indicates the product is either impure or structurally different from the intended target.
Prerequisites: Calculating Total Molar Mass
The first step in calculating percentage composition is determining the total molar mass of the compound, which serves as the total weight of the molecule. Molar mass is defined as the mass in grams of one mole of a substance, with one mole containing approximately 6.022 x 10^23 particles. This value is derived directly from the chemical formula of the compound and the atomic weights of the individual elements.
Atomic weights for each element are found on the periodic table and represent the average mass of an atom of that element. To find the contribution of a specific element to the compound’s total mass, multiply its atomic weight by the number of times that element appears in the chemical formula. The subscript number next to the element’s symbol indicates this count; if no subscript is present, the count is assumed to be one.
Once the mass contribution for every element has been calculated, these individual masses are summed together. The result of this summation is the total molar mass of the entire compound. This total molar mass forms the denominator of the percentage composition formula.
Step-by-Step Guide to Percentage Composition
The calculation of percentage composition relies on a straightforward formula applied to the mass values derived previously. The goal is to determine the fraction of the total mass contributed by a single element and then express that fraction as a percentage. This process must be repeated for every element present in the compound.
The first step involves identifying the total mass contributed by a specific element within the compound. This mass is the product of the element’s atomic weight and its count in the chemical formula, forming the numerator of the percentage equation. For example, if a compound contains two oxygen atoms, the total mass of oxygen is twice the atomic weight of a single oxygen atom.
Next, divide this elemental mass by the total molar mass of the compound. This division yields a decimal value between zero and one, representing the mass fraction of the element within the whole molecule. The final step is to multiply this decimal result by 100 to convert the mass fraction into a percentage.
The formula for this calculation is: Percentage Composition = [(Mass of Element in Compound) / (Total Molar Mass of Compound)] \(\times\) 100. When the percentage composition has been successfully calculated for every element, the sum of all these individual percentages should equal 100%.
Applying the Calculation: A Worked Example
The principles of calculating molar mass and percentage composition can be demonstrated using water, which has the chemical formula \(\text{H}_2\text{O}\). Water is composed of two atoms of hydrogen (\(\text{H}\)) and one atom of oxygen (\(\text{O}\)). The first step is to calculate the total molar mass using the approximate atomic weights of Hydrogen (\(\text{H} \approx 1.008\) g/mol) and Oxygen (\(\text{O} \approx 15.999\) g/mol).
The mass contribution of hydrogen is calculated by multiplying its atomic weight by two, resulting in a mass of approximately \(2.016\) g/mol. The mass contribution of oxygen is \(15.999\) g/mol, as there is only one atom of oxygen in the molecule. Summing these values (\(2.016 + 15.999\)) yields the total molar mass of water, which is approximately \(18.015\) g/mol.
With the total molar mass established, the percentage composition for each element can be determined. For hydrogen, the calculation involves dividing its total mass contribution (\(2.016\) g/mol) by the total molar mass (\(18.015\) g/mol) and multiplying by 100, resulting in approximately \(11.19\%\). The calculation for oxygen follows the same process, yielding a percentage of approximately \(88.81\%\). The sum of \(11.19\%\) and \(88.81\%\) confirms the total composition is \(100.00\%\).