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Ch.10 - Gases
Chapter 10, Problem 102

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
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Textbook Question

Assume that a single cylinder of an automobile engine has a volume of 524 cm3. (a) If the cylinder is full of air at 74 C and 99.3 kPa, how many moles of O2 are present? (The mole fraction of O2 in dry air is 0.2095.) (b) How many grams of C8H18 could be combusted by this quantity of O2, assuming complete combustion with formation of CO2 and H2O?

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