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Chapter 3: Problem 89

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

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

Step by step solution

01

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 \( Moles of Nitrogen = \frac{30.4 g}{14.01 g/mol} = 2.17 mol \)
02

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.
03

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 \( Empirical Formula Molar Mass = 32.07 g/mol + 14.01 g/mol = 46.08 g/mol \)
04

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.

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