Determining the mass of a specific element within a compound is a fundamental calculation in chemistry, forming the basis of stoichiometry. This calculation is necessary for applications such as assessing the purity of a material or predicting the theoretical yield of a chemical reaction. Knowing exactly how much of a constituent element is present within a given sample mass allows chemists to control reaction proportions and analyze products accurately. The method relies entirely on the compound’s chemical formula and the standardized masses of its component atoms.
Calculating the Compound’s Total Molar Mass
The first step is to establish the compound’s total mass, which is referred to as the molar mass. This value represents the mass in grams of one mole of the substance. To begin this calculation, you must consult a periodic table to find the atomic weight for every element listed in the compound’s chemical formula. The atomic weight, typically measured in atomic mass units (\(\text{amu}\)), is numerically equivalent to the molar mass in grams per mole (\(\text{g/mol}\)).
The chemical formula provides the number of atoms of each element present in a single molecule. For instance, in the common compound water, \(\text{H}_2\text{O}\), the formula indicates there are two hydrogen atoms and one oxygen atom. You must multiply the atomic weight of each element by its subscript quantity in the formula to find the element’s total mass contribution to the compound. These individual mass contributions are then summed together to yield the compound’s total molar mass.
Consider the calculation for the molar mass of carbon dioxide, \(\text{CO}_2\), using standard atomic weights for carbon (\(\text{C}\)) as \(12.01 \text{ g/mol}\) and oxygen (\(\text{O}\)) as \(16.00 \text{ g/mol}\). The single carbon atom contributes \(1 \times 12.01 \text{ g/mol}\), while the two oxygen atoms contribute \(2 \times 16.00 \text{ g/mol}\), totaling \(32.00 \text{ g/mol}\). Adding these contributions results in a final molar mass of \(44.01 \text{ g/mol}\) for \(\text{CO}_2\).
Determining the Element’s Percentage Contribution
Once the compound’s total molar mass is known, the next step is to determine the mass percentage of the target element. This percentage represents the proportion of the element’s mass relative to the entire compound’s mass. This relationship is mathematically expressed by dividing the total mass of the element in the compound by the total molar mass of the compound, and then multiplying the result by 100. The resulting percentage is a fixed value, meaning the element will always make up this exact proportion of the compound’s mass, regardless of the size of the sample being examined.
The numerator of this calculation is the element’s total mass contribution, which must account for the number of atoms of that element in the formula. If the target element is oxygen in sodium sulfate, \(\text{Na}_2\text{SO}_4\), the oxygen atomic weight of \(16.0 \text{ g/mol}\) must be multiplied by the subscript 4. This results in an oxygen mass contribution of \(64.0 \text{ g/mol}\), which is the specific mass portion contributed by oxygen in one mole of sodium sulfate. The denominator is the total molar mass of sodium sulfate, which was previously calculated by summing the masses of all constituent atoms.
Using the approximate atomic weights of sodium (\(23.0 \text{ g/mol}\)), sulfur (\(32.0 \text{ g/mol}\)), and oxygen (\(16.0 \text{ g/mol}\)), the total molar mass of \(\text{Na}_2\text{SO}_4\) is \(142.0 \text{ g/mol}\). To find the mass percentage of oxygen, the calculation is \((\text{Mass of Oxygen} / \text{Total Molar Mass}) \times 100\). Plugging in the values, we get \((64.0 \text{ g/mol} / 142.0 \text{ g/mol}) \times 100\), which yields a result of approximately \(45.07\%\).
Conversion to the Final Mass
The final stage of the process involves applying the calculated mass percentage to a specific sample size to determine the absolute mass of the element present. The mass percentage must first be converted back into a decimal fraction by dividing the percentage value by 100, which is necessary for the subsequent multiplication. This decimal value is then multiplied by the total mass of the sample provided in the problem.
Imagine a scenario where the goal is to find the mass of oxygen in a \(75.0 \text{ gram}\) sample of sodium sulfate, \(\text{Na}_2\text{SO}_4\). For \(\text{Na}_2\text{SO}_4\), the molar mass is \(142.0 \text{ g/mol}\), which is derived from two sodium atoms (\(46.0 \text{ g/mol}\)), one sulfur atom (\(32.0 \text{ g/mol}\)), and four oxygen atoms (\(64.0 \text{ g/mol}\)).
The mass percentage of oxygen was determined to be \(45.07\%\). Before using this percentage to find the final mass, it must be converted to the decimal \(0.4507\). This decimal represents the fraction of the total mass that is oxygen.
The third and final stage is to multiply the \(75.0 \text{ gram}\) sample mass by this decimal fraction. The calculation is \(75.0 \text{ g} \times 0.4507\), which results in a mass of \(33.80 \text{ grams}\) of oxygen. This method allows for the accurate prediction of elemental quantities in any measured amount of a pure chemical compound.