A container holds a sample of SO₂ gas and a sample of CH₄ gas. If both samples contain the exact same total number of atoms, what is the ratio of the mass of SO₂ to the mass of CH₄ in the container?

Step-by-step solution

Let the total number of atoms in each sample be x . The atomicity of SO₂ is 3 (1 S + 2 O). The number of moles of SO₂ is x 3 N_A . The atomicity of CH₄ is 5 (1 C + 4 H). The number of moles of CH₄ is x 5 N_A . The ratio of their moles is n( SO₂ ) : n( CH₄ ) = 1 3 : 1 5 = 5 : 3 . The molar mass of SO₂ is 32 + 2(16) = 64 g/mol . The molar mass of CH₄ is 12 + 4(1) = 16 g/mol . The ratio of their masses is n( SO₂ ) M( SO₂ ) n( CH₄ ) M( CH₄ ) = 5 64 3 16 = 320 48 = 20 3 . Thus, the mass ratio is 20 : 3 . Answer: 20 : 3