Question

Four balloons are each filled with a different gas, each having a different density: $$\text { helium, } d=0.164 \mathrm{g} / \mathrm{L} \quad \text { neon, } d=0.825 \mathrm{g} / \mathrm{L}$$ $$\begin{aligned}&\text { argon, } d=1.633 \mathrm{g} / \mathrm{L}&\text { krypton, } d=4.425 \mathrm{g} / \mathrm{L}\end{aligned}$$ If the density of dry air is \(1.12 \mathrm{g} / \mathrm{L},\) which balloon or balloons float in air?

Short answer

Helium and neon will cause balloons to float in air.

Step-by-step solution

Understand the Problem

We need to determine which gases, when filled in a balloon, will cause the balloon to float in air. This is determined by comparing the density of each gas with the density of air. If a gas has a lower density than air, it will cause the balloon to float.

Compare Density of Helium with Air

The density of helium is given as \(0.164 \ \mathrm{g/L}\). The density of dry air is \(1.12 \ \mathrm{g/L}\). Since \(0.164 \ \mathrm{g/L} < 1.12 \ \mathrm{g/L}\), a balloon filled with helium will float.

Compare Density of Neon with Air

The density of neon is \(0.825 \ \mathrm{g/L}\). Since \(0.825 \ \mathrm{g/L} < 1.12 \ \mathrm{g/L}\), a balloon filled with neon will also float.

Compare Density of Argon with Air

The density of argon is \(1.633 \ \mathrm{g/L}\). Since \(1.633 \ \mathrm{g/L} > 1.12 \ \mathrm{g/L}\), a balloon filled with argon will not float.

Compare Density of Krypton with Air

The density of krypton is \(4.425 \ \mathrm{g/L}\). Since \(4.425 \ \mathrm{g/L} > 1.12 \ \mathrm{g/L}\), a balloon filled with krypton will not float.

Key concepts

Buoyancy

Buoyancy is a force exerted by a fluid that opposes the weight of an object immersed in it. In simpler terms, it is what makes objects float or sink in water or air. Imagine you are putting a balloon filled with a gas into the air. If the gas inside is lighter than the air, the balloon will rise. Here's how buoyancy works:

• When an object is in a fluid (like gas in air), the fluid exerts an upward force on the object.
• This force is equal to the weight of the fluid that the object displaces.
• If this upward force is greater than the weight of the object, the object will float.

For a balloon filled with gas, the weight of the balloon must be less than the buoyant force from the air for it to float. This is why understanding buoyancy helps us figure out why some balloons go up, while others stay down. Remember this: a lower density gas compared to air means a floating balloon.

Gas Comparison

To understand gas comparison, think about how we compare the density of different gases to figure out their properties. The density of a gas is a measure of how much mass it has in a given volume. When comparing gases like helium, neon, argon, and krypton:

• Helium: Very light with a density of 0.164 g/L, much lower than air.
• Neon: Slightly heavier but still comparatively light with a density of 0.825 g/L.
• Argon: Heavier than both air and neon with a density of 1.633 g/L, hence it does not float.
• Krypton: The heaviest among these, with a density of 4.425 g/L, making it the least buoyant in air.

Comparing these densities with air (1.12 g/L) helps us understand which gases will allow balloons to rise: - Helium and neon, having densities lower than air, float and lift balloons upward. - Argon and krypton, with higher densities, lead to balloons that sink.

Floatation

Floatation is an application of buoyancy, referring specifically to the ability of a gas-filled balloon to rise in air. As we've discussed, this depends on the relative density of the gases involved. Here’s how it relates to the problem:

• When a balloon floats, it experiences buoyant lift because it is lighter than the air around it.
• Gases with densities lower than that of air help make a balloon achieve floatation.

In your exercise:

• Balloons filled with helium and neon experience floatation as both gases have a density lower than air.
• Balloons with argon or krypton do not float, as these gases are denser than air.

In summary, floatation depends on buoyancy and the density of the gas, and by comparing densities, we can predict which balloons will rise or stay put.