Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of 85.7% C and 14.3% H by mass. If 1.56 g of cyclopropane has a volume of 1.00 L at 99.7 kPa and 50.0 °C, what is the molecular formula of cyclopropane?

Question

23-09-2023
Chemistry

High School

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Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of 85.7% C and 14.3% H by mass. If 1.56 g of cyclopropane has a volume of 1.00 L at 99.7 kPa and 50.0 °C, what is the molecular formula of cyclopropane?

Answer :

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kashishAg78 kashishAg78 · Answer 1 · 2024-09-11T10:50:51-04:00

Final answer:

The molecular formula of cyclopropane is found by first determining the empirical formula from the percent composition and then using the Ideal Gas Law to find the molar mass. This leads us to the molecular formula, which is C3H6.

Explanation:

To find the molecular formula of cyclopropane, we first determine its empirical formula using the percent composition by mass. We assume a 100 g sample for ease of calculation: 85.7 g of carbon (C) and 14.3 g of hydrogen (H).

The number of moles of C is 85.7 g / 12.01 g/mol (which is the molar mass of C) = 7.136 moles of C. For H, it's 14.3 g / 1.01 g/mol (molar mass of H) = 14.158 moles of H. Dividing by the smaller number of moles (7.136), we get the empirical formula CH₂.

Next, we use the gas laws to find the molar mass (MM) of cyclopropane. At 99.7 kPa and 50.0 °C, which is 323.15 K after converting to Kelvin, and 1.00 L volume, we rearrange the Ideal Gas Law to solve for molar mass:

MM = (mass of gas) * (R * T) / (P * V) MM = (1.56 g) * (8.314 J/mol·K * 323.15 K) / (99.7 kPa * 1.00 L * 1000 J/kPa) MM = 42.08 g/mol (rounded to two decimal places)

The empirical formula mass (EM) of CH₂ is about 14.03 g/mol. By dividing the molar mass of the gas by the EM, we get the ratio of the molecular formula to the empirical formula, which is 3, indicating that the molecular formula is C₃H₆ (or three times the empirical formula).