Two samples, one of glucose ( C ₆ H ₁₂ O ₆ ) and another of sucrose ( C ₁₂ H ₂₂ O ₁₁ ), are found to contain the exact same number of carbon atoms. What is the ratio of the mass of the glucose sample to the mass of the sucrose sample?

Step-by-step solution

Let the mass of glucose be m₁ and the mass of sucrose be m₂ . Molar mass of glucose ( C ₆ H ₁₂ O ₆ ) = 180 g mol ⁻¹ Molar mass of sucrose ( C ₁₂ H ₂₂ O ₁₁ ) = 342 g mol ⁻¹ Number of moles of carbon atoms in glucose = m₁ 180 6 = m₁ 30 Number of moles of carbon atoms in sucrose = m₂ 342 12 = m₂ 28.5 Since the number of carbon atoms is equal in both samples: m₁ 30 = m₂ 28.5 m₁ m₂ = 30 28.5 = 300 285 = 20 19 Thus, the ratio of their masses is 20 : 19 . Answer: 20 : 19