Problem 3 - Chemistry The Central Science In Si Units

Question

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 \(2 ?\) [Section 10.3\(]\) (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.

Step-by-Step Solution

Answer

(b) It would contain half as many molecules.

Step 1: Understanding the Relationship

The pressure of a gas is related to the number of gas molecules, the volume, and the temperature. Since volume and temperature remain constant in this problem, we should consider the relationship between pressure and the number of molecules.

Step 2: Analyze the Relation between Pressure and Molecules

According to the ideal gas law, if volume and temperature are constant, pressure \(P\) is directly proportional to the number of molecules \(n\), such that \(P \propto n\). This means that if the pressure is decreased by a factor of 2, the number of molecules must also decrease by a factor of 2.

Step 3: Apply the Concept to the Options

If the pressure is decreased by a factor of 2, the number of molecules that should be removed is half of the original amount to achieve this pressure drop. Therefore, the correct depiction would involve half as many molecules as initially present.

Key Concepts

Gas Pressure

Gas pressure is a measure of the force that the gas molecules exert when they collide with the walls of their container. This force is generated by the molecules' momentum as they move rapidly and hit the surface. The more frequent and forceful these collisions are, the higher the gas pressure.

Key factors that determine gas pressure include:

• Number of molecules: More molecules mean more collisions, which leads to higher pressure.
• Volume: With a smaller volume, molecules are crowded more closely together, increasing the frequency of collisions.
• Temperature: Higher temperature causes molecules to move faster, increasing the force of collisions.

In summary, any change in these factors can alter the gas pressure in a container, which is why understanding what remains constant or changes is crucial for predicting how the system behaves.

Gas Molecules

Gas molecules are tiny particles that are in constant, random motion. They fly around at high speeds and bounce off each other as well as off the walls of their container. This random movement of gas molecules is described by the kinetic molecular theory.

Key characteristics of gas molecules include:

• Continuous Motion: They move continuously and randomly.
• No fixed position: Gas molecules do not have a fixed arrangement as factors like temperature and pressure change.
• Behavior: Their behavior can be predicted by the ideal gas law, given the right conditions.

When we decrease the number of gas molecules in a container, fewer collisions occur, leading to a decrease in gas pressure while volume and temperature remain unchanged. This foundational concept helps us understand gas behavior in different scenarios.

Volume and Temperature Relationship

The volume and temperature relationship in gases is a key concept in understanding their behavior. According to Charles's Law, when the pressure is constant, the volume of a gas is directly proportional to its absolute temperature (measured in Kelvin). This means that if the temperature of a gas increases, its volume also increases, and vice versa.

Expressed mathematically, Charles's Law can be written as: \[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]In this relationship:

• \(V\): volume of the gas.
• \(T\): absolute temperature of the gas.

An important thing to note is that this relationship holds true as long as there is no change in the gas's pressure or the number of molecules. In our specific scenario, since both volume and temperature remain constant, changes in pressure are directly linked to changes in the number of gas molecules, independent of this relationship.