Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of \(85.7 \% \mathrm{C}\) and \(14.3 \% \mathrm{H}\) by mass. \((\mathrm{a})\) If \(1.56 \mathrm{~g}\) of cyclopropane has a volume of \(1.00 \mathrm{~L}\) at 0.984 atm and \(50.0^{\circ} \mathrm{C}\), what is the molecular formula of cyclopropane? (b) Judging from its molecular formula, would you expect cyclopropane to deviate more or less than Ar from ideal-gas behavior at moderately high pressures and room temperature? Explain. (c) Would cyclopropane effuse through a pinhole faster or more slowly than methane, \(\mathrm{CH}_{4} ?\)

The empirical formula represents the simplest whole-number ratio of elements in a compound. It is a crucial first step in determining the molecular formula, which shows the actual number of atoms in a molecule. To find the empirical formula of cyclopropane, we begin by assuming a 100g sample, which simplifies the calculation of percentages to actual masses of carbon (C) and hydrogen (H).

By dividing the mass of each element by their respective molar masses, we get the number of moles, which we then use to find the simplest ratio. In the case of cyclopropane, the empirical formula turns out to be C1H2. This process reveals not only the types of atoms in the molecule but also their basic ratio, setting the stage for further analysis to determine the molecular formula.

The ideal gas law is a fundamental relationship between pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T). In this context, it helps to find the molar mass of a gaseous sample. For cyclopropane, the given conditions of pressure, volume, and temperature allow us to calculate the number of moles using the formula PV = nRT.

After finding the moles, the molar mass is determined by dividing the mass of the sample by the calculated number of moles. This step is not only vital for finding the molecular formula but also for understanding gas behavior in different conditions, which can be essential in various scientific and industrial applications.

Graham's Law of Effusion states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass. Effusion is the process by which gas escapes through a tiny opening, and this law helps us understand how quickly different gases will effuse under the same conditions.

In comparing cyclopropane to methane, we use their molar masses in the law's formula to find that cyclopropane, being the heavier gas, will effuse more slowly than methane. This principle not only aids us in predicting the behavior of gases but also has practical applications, such as in separating isotopes or in identifying unknown gases.