The mass of 6 million molecules of a diatomic gas is 5.1 × 10^-19 kg. What is the atomic mass of the element in this gas?

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Quizplus · Accepted Answer

The mass of 6 million (6 × 10^6) molecules of the diatomic gas is 5.1 × 10^-19 kg. To find the molar mass (molecular mass in grams per mole), we first convert the mass of these molecules to grams: 5.1 × 10^-19 kg = 5.1 × 10^-16 g. Since 1 mole of any substance contains Avogadro's number of molecules (approximately 6.022 × 10^23 molecules/mole), we can calculate the mass of 1 mole of this diatomic gas. The mass of 1 mole of molecules is proportional to the mass of 6 million molecules, so we set up a proportion: (5.1 × 10^-16 g) / (6 × 10^6 molecules) = (x g) / (6.022 × 10^23 molecules), solving for x gives the molar mass of the diatomic gas. Simplifying, x ≈ (5.1 × 10^-16 g/6 × 10^6 molecules) × 6.022 × 10^23 ≈ 51.2 g/mol. Since the gas is diatomic, the atomic mass of the element is half of the molar mass of the diatomic molecule, which is 51.2 g/mol ÷ 2 = 25.6 u.

The Mass of 6 Million Molecules of a Diatomic Gas