Problem 49 - Chemistry The Central Science In Si Units

Question

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Step-by-Step Solution

Answer

Statement (c) is correct; it explains the buoyancy principle with lower density of helium.

Step 1: Identify the key concept

The key concept involved in explaining why a balloon filled with helium rises in air is that objects will float if they are less dense than the fluid they are in. This concept is based on Archimedes' principle, which relates to buoyancy.

Step 2: Evaluate the options

Assess each statement: (a) Discusses helium as monatomic but doesn't address density compared to air. (b) Speaks about average speed of helium atoms affecting propulsion which isn't relevant to buoyancy. (c) Connects lower mass of helium to less density compared to air and mentions the principle of the balloon displacing more mass of air, which aligns with buoyancy. (d) Incorrectly associates faster motion with higher temperature, which isn't directly related to buoyancy.

Step 3: Select the correct statement

Based on the evaluations, statement (c) correctly emphasizes the principle of buoyancy by explaining that helium is less dense than air, making the balloon's total mass less than that of the displaced air volume. This results in the balloon rising.

Key Concepts

Archimedes' Principle

Archimedes' Principle is a fundamental law of physics that helps us understand why objects float or sink in a fluid. This principle states that any object submerged in a fluid experiences an upward buoyant force. This force is equal to the weight of the fluid that the object displaces. So, when a balloon filled with helium is in the air, it experiences an upward force. This force comes from the air pushing up on it.

According to Archimedes' Principle:

• The weight of the fluid displaced is what determines if an object will float or sink.
• If the weight of the displaced fluid is greater than the weight of the object, the object will float.
• If the weight of the displaced fluid is less than the weight of the object, the object will sink.

Helium balloons rise because they are less dense than air. This means that the weight of air displaced by the balloon is more than the weight of the balloon itself. Therefore, the buoyant force is strong enough to lift the balloon.

Buoyancy

Buoyancy refers to the ability of an object to float in a fluid, such as water or air. It plays a significant role in why certain objects, like helium balloons, can rise. Check out some key points about buoyancy:

• Buoyancy is all about the difference in density between an object and the fluid it is in.
• An object that is less dense than the fluid will float, thanks to the buoyant force.
• The buoyant force is the reason why objects can stay afloat, opposing the force of gravity.

In the context of a helium balloon floating in the air, the concept of buoyancy helps explain that because helium is less dense than air, the balloon experiences an upward force greater than its weight. That's why it floats up into the air.

It's amazing to think that such a simple principle as buoyancy can explain so much about why objects float or sink! Remember:

• Density is key in determining buoyancy, and hence, the rise of a helium balloon.

Helium Gas

Helium gas is a key player when we think about balloons floating in the air. It is a noble gas, meaning it does not react with many elements. Here are some important things to know about helium with regards to buoyancy:

• Helium is less dense than the average components of air, such as nitrogen and oxygen.
• The lower density of helium causes balloons filled with it to weigh less than the air they displace.
• Since the air supports a weight greater than the balloon, the balloon rises.

When helium is enclosed in a balloon, it takes up a unique position against the surrounding air due to these factors. Another interesting fact is that helium is often preferred for filling balloons because it is non-flammable and non-toxic.

Helium's low density is crucial in making it ideal for balloons that float. Remember, it's the difference in densities between helium and air that plays a central role in allowing a helium balloon to rise. That's the power of this light, safe, and inert gas!