Question

A compound containing only sulfur and nitrogen is \(69.6 \% \mathrm{~S}\) by mass; the molar mass is \(184 \mathrm{~g} / \mathrm{mol}\). What are the empirical and molecular formulas of the compound?

Short answer

The compound containing only sulfur and nitrogen with a molar mass of 184 g/mol is found to have an empirical formula of \(SN\) and a molecular formula of \(S_4N_4\).

Step-by-step solution

Mass conversion

First, we need to find the grams of S and N in the given compound. If we assume 100 grams of the compound, we have the following quantities: - 69.6 grams of sulfur (S) – This is already given as 69.6 % mass. - 30.4 grams of nitrogen (N) – This comes from the fact that 100% - 69.6% sulfur = 30.4 % nitrogen by mass.

Moles calculation

Next, we need to calculate the moles of S and N in the compound using the molar mass of each element: Molar mass of S = 32.06 g/mol Molar mass of N = 14.01 g/mol Moles of S = (69.6 g) / (32.06 g/mol) = 2.17 mol Moles of N = (30.4 g) / (14.01 g/mol) = 2.17 mol

Mole ratio calculation

Now, we need to find the ratio of the moles of S to the moles of N: Mole ratio (S:N) = 2.17 mol : 2.17 mol = 1:1

Empirical formula determination

The mole ratio obtained is 1:1, meaning that for one atom of sulfur, there is one atom of nitrogen in the compound. Therefore, the empirical formula is SN.

Molecular formula determination

We now need to compare the empirical formula mass with the known molar mass of the compound: Empirical formula mass of SN = (32.06 g/mol) + (14.01 g/mol) = 46.07 g/mol Now, divide the molar mass of the compound by the empirical formula mass: Molecular formula factor = (184 g/mol) / (46.07 g/mol) = 3.99 ≈ 4 Lastly, we multiply each element in the empirical formula by the molecular formula factor: Molecular formula = (SN) x 4 = S₄N₄ Hence, the empirical formula of the compound is \(SN\) and the molecular formula is \(S_4N_4\).

Key concepts

Chemical Composition

Understanding the chemical composition of compounds is fundamental in chemistry. It involves analyzing the proportion of each element within a substance. In a compound, elements combine in definite ratios that can be expressed as a percentage by mass. For instance, let’s assume we have a compound made of sulfur (S) and nitrogen (N). When given that sulfur constitutes 69.6% of the compound by mass, it implies that out of 100 grams of this compound, 69.6 grams are sulfur.
To deduce the rest of the compound's composition, we recognize that the total mass percentage must equal 100%, hence nitrogen must account for the remaining 30.4% (100% - 69.6%). This preliminary step is crucial as it sets the stage for further calculations to determine the molecular and empirical formulas. In educational practice, reinforcing the understanding of percentage composition aids students in visualizing the proportion of each element within a compound, an essential step before diving into mole ratio calculations and molar mass.

Mole Ratio Calculation

The mole ratio is a comparison of how many moles of one substance there are relative to another substance in a compound. The calculation is straightforward once the number of moles of each element is known. To find the moles, divide the mass of each element by its respective molar mass. In our exercise with a sulfur and nitrogen compound, the molar mass of sulfur (S) is 32.06 g/mol, and nitrogen (N) is 14.01 g/mol.
Using these molar masses, we calculate the moles of S and N separately. This gives us equal amounts of moles for both S and N, which results in a mole ratio of 1:1. This is a fundamental step, as the mole ratio reflects the simplest ratio in which atoms combine to form a compound. In teaching, we emphasize obtaining whole-number mole ratios by dividing through by the smallest number of moles. This simple ratio is the foundation of the compound's empirical formula. When explaining mole ratio calculations, it is useful to remind students that this ratio translates directly to the subscript values in the empirical formula of the compound, which shows the simplest whole-number ratio of elements.

Molar Mass

Molar mass is defined as the mass of one mole of a substance. It is crucial in chemistry, as it serves as a bridge between the mass of a substance and the number of moles. The molar mass for elements can be found on the periodic table and is usually expressed in grams per mole (g/mol). In our example, the sulfur and nitrogen compound has a given molar mass of 184 g/mol.
To determine the molecular formula, you'll first need to find the empirical formula mass by adding the molar masses of the individual elements in the empirical formula. Once you have this, compare the given molar mass of the compound with the empirical formula mass. The ratio of these two values indicates how many times the empirical unit is present in a molecule of the compound. It is often the case that students struggle with the concept of molar mass and its relevance. It's helpful to emphasize that molar mass acts as a conversion factor that allows us to move from the microscopic world of atoms and molecules to the macroscopic world we can measure in the laboratory. When discussing molar mass, ensuring comprehension of its application to finding molecular formulas can help bring the concept full circle for students.