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 empirical formula of the compound is SN, and the molecular formula is S₄N₄.

Step-by-step solution

Convert mass percentages to moles

First, we will use the percentage composition to assume a 100g of the compound. So, the mass of sulfur in 100g of the compound is 69.6 g, and the mass of nitrogen is 30.4 g (100 g - 69.6 g). Now, we can convert the mass of each element to moles by dividing with their respective molar masses: Moles of Sulfur = mass of sulfur / molar mass of sulfur \( Moles of Sulfur = \frac{69.6 g}{32.07 g/mol} = 2.17 mol \) Moles of Nitrogen = mass of nitrogen / molar mass of nitrogen \( Moles of Nitrogen = \frac{30.4 g}{14.01 g/mol} = 2.17 mol \)

Determine the mole ratio

Now, we can find the mole ratio by dividing both moles by the lowest value, 2.17 mol in this context: Mole ratio of S:N = (2.17/2.17) : (2.17/2.17) = 1:1 This implies the empirical formula of the compound is SN.

Calculate the empirical formula molar mass

Now that we have the empirical formula, we can calculate the molar mass of the empirical formula. The empirical formula is SN, so we just need to add the molar masses of one sulfur and one nitrogen atom: Empirical Formula Molar Mass = Molar Mass of S + Molar Mass of N \( Empirical Formula Molar Mass = 32.07 g/mol + 14.01 g/mol = 46.08 g/mol \)

Determine the molecular formula

With the molar mass of the compound and the molar mass of the empirical formula, we can determine the molecular formula of the compound. We simply divide the molar mass of the compound by the molar mass of the empirical formula, and then multiply the empirical formula by this value: Molecular Formula Multiplier = Molar Mass of Compound / Empirical Formula Molar Mass \( Molecular Formula Multiplier = \frac{184 g/mol}{46.08 g/mol} = 4 \) Since our multiplier is 4, we can now determine the molecular formula: Molecular Formula = Empirical Formula x Molecular Formula Multiplier Molecular Formula = SN x 4 = S₄N₄ Thus, the molecular formula for the given compound is S₄N₄.

Key concepts

Mole Ratio

Understanding the "Mole Ratio" is crucial when dealing with compounds and chemical reactions. A mole ratio indicates the ratio of moles of one substance to the moles of another substance in a balanced equation or compound structure. It's a tool that helps translate measurements in the laboratory into a format we can use to predict reaction yields and understand composition.

In the given exercise, the compound consists of sulfur and nitrogen. To determine its empirical formula, we first found the moles of each element. This is done by using their weights in grams and dividing by their individual molar masses (the mass of one mole of a particular element).

Once we have the moles of each element, we can determine the simplest whole number ratio between them by dividing each value by the smallest number of moles calculated. Here, both sulfur and nitrogen had moles equal to 2.17, leading directly to a simple 1:1 mole ratio. This mole ratio translates into the empirical formula, which represents the simplest form of the compound based on relative quantities of elements involved.

Molar Mass Calculation

"Molar Mass Calculation" is an essential concept, particularly when solving problems involving empirical and molecular formulas. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It reflects the combined atomic masses of all the atoms in a molecule, allowing us to equate measurable grams to invisible numbers of molecules.

In this exercise, we need to calculate the molar mass of the empirical and eventually the molecular formula. Starting with the empirical formula, SN, we add together the molar mass of sulfur (32.07 g/mol) and nitrogen (14.01 g/mol) to get 46.08 g/mol. This gives us the empirical formula’s molar mass.

Further, to find the molecular formula, we require the total molar mass of the compound, which is provided as 184 g/mol. We then divide this total molar mass by the empirical formula's molar mass to figure out how many times the empirical formula unit fits into the molecular formula. In this case, the result was a factor of 4, meaning the compound's molecular formula has four times as many atoms as indicated by the empirical formula.

Stoichiometry

"Stoichiometry" involves using quantitative relationships between reactants and products in chemical reactions. Here, it helps determine empirical formulas and the possible scale-up to the actual compound's full-size molecular formula. It's the math behind chemical reactions, ensuring that matter is neither created nor destroyed, consistent with the Law of Conservation of Mass.

In our exercise, stoichiometry first appears when converting mass percentages into moles, reflecting a move from measurable mass to countable units of particles. By establishing a mole ratio, we determine the relative number of moles of sulfur to nitrogen, thus finding the simplest "empirical" version of the formula.

The extension of stoichiometry comes when using the empirical formula to scale up to the molecular formula via molar mass calculations. It ensures that the detailed proportions align with those of larger compound samples, maintaining consistency with empirical results. By leveraging stoichiometry, chemists can predict quantitative outcomes of reactions and analyze compositions, aiding in everything from lab syntheses to industrial production.