Propane, C3H8, liquefies under modest pressure, allowing a large amount to be stored in a container. (a) Calculate the number of moles of propane gas in a 20-L container at 709.3 kPa and 25 C. (b) Calculate the number of moles of liquid propane that can be stored in the same volume if the density of the liquid is 0.590 g/mL. (c) Calculate the ratio of the number of moles of liquid to moles of gas. Discuss this ratio in light of the kinetic-molecular theory of gases.

Verified step by step guidance

1. 1. For part (a), we can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. We need to convert the pressure from kPa to atm, the volume from L to m^3, and the temperature from Celsius to Kelvin. The ideal gas constant R is 0.0821 L·atm/(K·mol).
2. 2. For part (b), we need to calculate the mass of liquid propane that can be stored in the 20-L container first. We can do this by multiplying the volume of the container by the density of liquid propane. Then, we can convert the mass to moles by using the molar mass of propane, which is approximately 44.1 g/mol.
3. 3. For part (c), we can calculate the ratio of the number of moles of liquid propane to the number of moles of gas propane by dividing the number of moles of liquid propane by the number of moles of gas propane.
4. 4. The kinetic-molecular theory of gases assumes that the volume of individual gas molecules is negligible compared to the volume of the container. This is why gases can be compressed to a much smaller volume than liquids or solids. The ratio calculated in part (c) shows how much more propane can be stored in the same volume when it is in the liquid state compared to the gas state.
5. 5. In conclusion, by applying the ideal gas law and the concept of density, we can compare the amount of propane that can be stored in the same volume under different states of matter. This demonstrates the compressibility of gases and the efficiency of storing substances in their liquid state.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the number of moles of a gas under specific conditions, which is essential for part (a) of the question.

Density and Volume Relationship

Density is defined as mass per unit volume and is a critical concept for converting between the mass of a substance and its volume. In this context, the density of liquid propane (0.590 g/mL) allows us to determine how many grams of propane can fit into a given volume (20 L). By using the density, we can calculate the mass of liquid propane and then convert that mass into moles for part (b) of the question.

Kinetic-Molecular Theory

The Kinetic-Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that gas pressure results from collisions of gas molecules with the walls of their container. This theory helps us understand the differences in behavior between gases and liquids, particularly in how the ratio of moles of liquid to gas can reflect the intermolecular forces and kinetic energy of the molecules, which is relevant for part (c) of the question.