Cyclopropane, a gas that when mixed with oxygen is used as a general anesthetic, is composed of 85.7\(\% \mathrm{C}\) and 14.3\(\% \mathrm{H}\) by mass. If the density of cyclopropane is 1.88 \(\mathrm{g} / \mathrm{L}\) at STP, what is the molecular formula of cyclopropane?

Based on the information provided, we know that cyclopropane is composed of 85.7% carbon (C) and 14.3% hydrogen (H) by mass. Assume we have 100 g of cyclopropane; then we would have 85.7 g of carbon and 14.3 g of hydrogen. To find the empirical formula, we can convert these masses to moles: Moles of carbon: \[\frac{85.7\, \mathrm{g}}{12.01\, \mathrm{g/mol}} = 7.14\, \mathrm{mol}\] Moles of hydrogen: \[\frac{14.3\, \mathrm{g}}{1.01\, \mathrm{g/mol}} = 14.16\, \mathrm{mol}\] Next, divide each of the mole values by the smallest mole value: \[\frac{7.14\, \mathrm{mol}}{7.14\, \mathrm{mol}} = 1.00\] \[\frac{14.16\, \mathrm{mol}}{7.14\, \mathrm{mol}} = 1.98 \approx 2\] The empirical formula is CH2.

Now that we have the empirical formula (CH2), we can calculate its molecular weight: Molecular weight of CH2: \(12.01\, \mathrm{g/mol} + 2\cdot 1.01\, \mathrm{g/mol} = 14.03\, \mathrm{g/mol}\)

With the molecular weight of the empirical formula and the density of cyclopropane at STP, we can now calculate the molecular weight of cyclopropane. Since we know the density at STP, we can use the equation \(d = \frac{PM}{RT}\), where d is the density, P is the pressure (1 atm), R is the gas constant (\(0.0821\, \mathrm{L\cdot atm/mol\cdot K}\)), and T is the temperature (273 K). Rearrange this equation for M (molecular weight): \[M = \frac{dRT}{P} = \frac{(1.88\, \mathrm{g/L})(0.0821\, \mathrm{L\cdot atm/mol\cdot K})(273\, \mathrm{K})}{1\, \mathrm{atm}} = 41.85\, \mathrm{g/mol}\] Now, to find the molecular formula, divide the molecular weight of cyclopropane by the molecular weight of the empirical formula: \[\frac{41.85\, \mathrm{g/mol}}{14.03\, \mathrm{g/mol}} = 2.98 \approx 3\] The molecular formula of cyclopropane is therefore 3 times the empirical formula CH2, which is C3H6.