Under special conditions, sulfur reacts with anhydrous liquid ammonia to form a binary compound of sulfur and nitrogen. The compound is found to consist of 69.6% S and 30.4% N. Measurements of its molecular mass yield a value of 184.3 g/mol. The compound occasionally detonates on being struck or when heated rapidly. The sulfur and nitrogen atoms of the molecule are joined in a ring. All the bonds in the ring are of the same length. (a) Calculate the empirical and molecular formulas for the substance.

Verified step by step guidance

1. Determine the molar mass of sulfur (S) and nitrogen (N). Sulfur has a molar mass of approximately 32.07 g/mol, and nitrogen has a molar mass of approximately 14.01 g/mol.
2. Calculate the moles of sulfur and nitrogen in 100 g of the compound using the percentage composition. For sulfur, use the formula: moles of S = mass of S / molar mass of S. For nitrogen, use the formula: moles of N = mass of N / molar mass of N.
3. Find the simplest whole number ratio of moles of sulfur to moles of nitrogen by dividing each by the smallest number of moles calculated in the previous step.
4. Write the empirical formula using the whole number mole ratios of sulfur and nitrogen obtained. This formula represents the simplest whole-number ratio of atoms in the compound.
5. Calculate the molecular formula by comparing the empirical formula mass to the given molecular mass (184.3 g/mol). Divide the molecular mass by the mass of the empirical formula to find the number of empirical units per molecule, and multiply the subscripts in the empirical formula by this number.

Key Concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. To determine it, one must convert the percentage composition of each element into moles, then simplify the ratio of these moles to the smallest whole numbers. In this case, with 69.6% sulfur and 30.4% nitrogen, the empirical formula can be calculated by finding the moles of each element and simplifying their ratio.

Molecular Formula

The molecular formula indicates the actual number of atoms of each element in a molecule of a compound. It can be derived from the empirical formula by comparing the molar mass of the compound to the molar mass of the empirical formula. Given the molecular mass of 184.3 g/mol, one can determine how many times the empirical formula fits into this mass to find the molecular formula.

Chemical Bonding and Structure

Understanding chemical bonding is crucial for analyzing the structure of a compound. In this case, the description of sulfur and nitrogen atoms forming a ring with equal bond lengths suggests a stable cyclic structure, likely involving resonance or delocalized electrons. This concept helps explain the compound's stability and reactivity, particularly its tendency to detonate under certain conditions.