The mole represents a fundamental unit in chemistry, serving as a standardized way to count an immense number of atoms or molecules in a sample. This unit is formally defined by Avogadro’s number, which is approximately \(6.022 \times 10^{23}\) particles. Since chemical reactions involve the combination of these particles, chemists rely on measuring mass in grams and converting that measurement into moles. This conversion allows for a precise understanding of the relationships between reactants and products in any chemical process. The ability to perform this calculation is central to quantitative chemistry.
Determining the Molar Mass of Potassium Sulfate
The first step in converting the mass of any compound into moles requires determining its molar mass, which acts as the unique conversion factor for that substance. Molar mass is defined as the mass in grams that equals one mole of a substance. For potassium sulfate, which has the chemical formula \(\text{K}_2\text{SO}_4\), we must first account for every atom present in the compound.
The formula indicates that one unit contains two atoms of potassium (K), one atom of sulfur (S), and four atoms of oxygen (O). To find the total mass, the atomic mass of each element must be taken from the periodic table and multiplied by its corresponding count. Potassium has an approximate atomic mass of 39.098 grams per mole, sulfur is 32.065 grams per mole, and oxygen is 15.999 grams per mole.
The calculation involves summing the mass contributions from each element: \(\text{K}_2\) contributes \(2 \times 39.098\) grams, S contributes \(1 \times 32.065\) grams, and \(\text{O}_4\) contributes \(4 \times 15.999\) grams. This arithmetic totals \(78.196 + 32.065 + 63.996\), resulting in a molar mass for potassium sulfate of \(174.257\) grams per mole. This calculated value is often rounded to \(174.26\) g/mol for common use.
Solving for Moles in 15.0 Grams
With the molar mass of potassium sulfate established as \(174.26\) grams per mole, the moles present in a \(15.0\) gram sample can be answered directly. The conversion utilizes a simple ratio where the mass of the sample is divided by the calculated molar mass. This process ensures the correct conversion because the units of grams in the numerator and the grams in the denominator of the molar mass cancel each other out.
Setting up the specific calculation involves dividing \(15.0\) grams by \(174.26\) grams per mole. This dimensional analysis confirms that the resulting unit is indeed moles. The division yields a result of approximately \(0.08608\) moles.
Rounding to three significant figures, which is consistent with the precision of the initial mass measurement of \(15.0\) grams, the sample contains \(0.0861\) moles of potassium sulfate. This small decimal value reflects that \(15.0\) grams is only a fraction of the \(174.26\) grams required to make up a full one mole of the substance.
Generalizing the Conversion Method
The method used to convert mass into moles is a universally applicable technique in chemistry for any substance. The molar mass acts as the bridge between the macroscopic world, where mass is easily measured with a balance, and the microscopic world of atoms and molecules. By determining this single conversion factor, chemists can transition between mass and mole count for any compound, whether it is a simple salt or a complex organic molecule.
This conversion capability forms the foundation of stoichiometry, the branch of chemistry dealing with the quantitative relationships between chemical substances. Stoichiometry relies entirely on using the mole count to predict the amount of product that can be generated from a given amount of reactant.
The conversion is also easily reversed. If a chemist needed to measure out a specific number of moles, the same molar mass value would be used as a multiplier instead of a divisor. Multiplying the desired number of moles by the molar mass (grams per mole) gives the required mass in grams to weigh out.