Question

Will a balloon filled with the given gas rise in the air or drop to the ground? (Assume the mass of the balloon is negligible and the density of air is \(1.29 \mathrm{~g} / \mathrm{L} .)\) (a) laughing gas \((d=1.96 \mathrm{~g} / \mathrm{L})\) (b) ammonia \((d=0.759 \mathrm{~g} / \mathrm{L})\)

Short answer

The laughing gas balloon will drop, while the ammonia balloon will rise.

Step-by-step solution

Understanding the Problem

We need to determine if a balloon filled with a given gas will rise or fall. This depends on the density of the gas relative to air. If the gas is less dense than air, the balloon will rise; if it is more dense, the balloon will fall.

Density Comparison for Laughing Gas

The density of laughing gas is given as 1.96 g/L. The density of air is 1.29 g/L. Since 1.96 g/L > 1.29 g/L, laughing gas is more dense than air. Therefore, a balloon filled with laughing gas will drop to the ground.

Density Comparison for Ammonia

The density of ammonia is given as 0.759 g/L. The density of air is 1.29 g/L. Since 0.759 g/L < 1.29 g/L, ammonia is less dense than air. Therefore, a balloon filled with ammonia will rise into the air.

Key concepts

Gas Properties

Gases have distinct characteristics influenced by their molecules' behavior and interactions. The properties of gases include density, pressure, and volume. Density is a crucial aspect, as it represents the mass of the gas per unit volume. This property can differ vastly among gases due to molecular weight and intermolecular forces. For instance, helium, being a light gas, has a lower density compared to denser gases like carbon dioxide.

In the original problem, the behavior of balls filled with different gases is based on their density relative to air. Laughing gas and ammonia, for example, are chosen to demonstrate how varying densities can influence whether a balloon rises or falls.

• Density: It influences how gases react to external conditions.
• Behavior under pressure: Gases expand to fill their containers.
• Molecular composition: Determines unique properties like color and smell.

Understanding these concepts helps us observe how gases behave in real-world applications like balloon buoyancy.

Balloon Buoyancy

Buoyancy refers to the ability of an object to float in a fluid—liquid or gas—due to differences in density. For balloons, buoyancy is crucial in determining whether they ascend or not. A balloon filled with a gas less dense than the surrounding air will be buoyant and rise. This happens because the force acting upward (because of lower density) is stronger than the gravitational force acting downward.

In our exercise, we see that a balloon filled with ammonia rises, leveraging its buoyancy. Ammonia's lower density compared to air allows it to float. Conversely, laughing gas, being denser, makes its balloon descend.

• Force balance: Upward buoyant force vs. downward gravitational force.
• Density comparison: Key factor determining buoyancy.
• Applications: Hot air balloons work on similar principles.

By analyzing density and buoyancy, we can predict and manipulate the movement of objects in different environments.

Air Density Comparison

Air density is an important factor when examining the movement of gases and objects through air. Air, primarily composed of nitrogen and oxygen, has a typical density of about 1.29 g/L at sea level. When comparing this to other gases, we can predict their behavior when released into the atmosphere. If a gas has a lower density than air, like helium or ammonia, it will rise. If it is denser, like sulfur hexafluoride, it will fall.

The exercise clearly demonstrates this concept with laughing gas and ammonia. Laughing gas, denser than air at 1.96 g/L, causes balloons to descend due to a higher gravitational pull. Ammonia, however, with a density of 0.759 g/L, will float upwards.

Understanding air density comparison reveals key insights into:

• Weather patterns: Hot and cold air masses exhibit different densities.
• Engineering: Planes and jets need to consider air density for lift and navigation.
• Everyday phenomena: Balloons used in decorations or scientific experiments.

Grasping how air density operates allows us to predict and harness the power of gases in various scientific fields.