Ch.10 - Gases

Problem 3

Chapter 10, Problem 3

Consider the sample of gas depicted here. What would the drawing look like if the volume and temperature remained constant while you removed enough of the gas to decrease the pressure by a factor of 2? (a) It would contain the same number of molecules. (b) It would contain half as many molecules. (c) It would contain twice as many molecules. (d) There is insufficient data to say.

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Identify the relationship between pressure, volume, and number of molecules using the ideal gas law, which is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.

Understand that if the volume (V) and temperature (T) are held constant, the equation simplifies to P ∝ n, indicating that pressure is directly proportional to the number of moles of gas.

Recognize that decreasing the pressure by a factor of 2 while keeping volume and temperature constant implies that the number of moles of gas must also decrease by a factor of 2 to maintain the proportionality (since P ∝ n).

Conclude that if the number of moles of gas is halved, the number of molecules must also be halved because the number of molecules is directly proportional to the number of moles (Avogadro's number).

Choose the correct answer based on the analysis: (b) It would contain half as many molecules.

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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 relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law helps us understand how changing one variable affects the others, assuming ideal behavior. In this scenario, if the volume and temperature are constant, a decrease in pressure must correspond to a decrease in the number of gas molecules.

Avogadro's Principle

Avogadro's Principle states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This principle is crucial for understanding how the number of gas molecules changes with pressure when volume and temperature are held constant. Thus, if the pressure is halved, the number of molecules must also decrease to maintain the relationship defined by this principle.

Pressure-Volume Relationship

The pressure-volume relationship, often described by Boyle's Law, indicates that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. In this case, since the volume is constant and the pressure is reduced by half, it implies that the number of gas molecules must also decrease, reinforcing the connection between pressure and the quantity of gas present.

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