Problem 68 - Chemistry and Chemical Reactivity

Question

Four balloons (each with a volume of \(10 \mathrm{L}\) and a mass of \(1.00 \mathrm{g})\) are filled with a different gas: Helium, \(d=0.164 \mathrm{g} / \mathrm{L}\) Neon, \(d=0.825 \mathrm{g} / \mathrm{L}\) Argon, \(d=1.633 \mathrm{g} / \mathrm{L}\) Krypton, \(d=4.425 \mathrm{g} / \mathrm{L}\) If the density of dry air is \(1.12 \mathrm{g} / \mathrm{L},\) which balloon or balloons float in air?

Step-by-Step Solution

Answer

The helium and neon balloons float in air.

Step 1: Balloon Mass Calculation

First, calculate the total mass of the balloons when filled with gas. Add the mass of the balloon material (1.00 g) to the mass of the gas contained in the 10 L volume. The mass of the gas is calculated by multiplying the gas density by the volume of the balloon (10 L).

Step 2: Mass of Helium Balloon

The density of Helium is 0.164 g/L. Thus, the mass of 10 L of helium is \(0.164 \ \text{g/L} \times 10 \ \text{L} = 1.64 \text{ g}\). The total mass of the helium balloon is \(1.00 \text{ g} + 1.64 \text{ g} = 2.64 \text{ g}\).

Step 3: Mass of Neon Balloon

The density of Neon is 0.825 g/L. Thus, the mass of 10 L of neon is \(0.825 \ \text{g/L} \times 10 \ \text{L} = 8.25 \text{ g}\). The total mass of the neon balloon is \(1.00 \text{ g} + 8.25 \text{ g} = 9.25 \text{ g}\).

Step 4: Mass of Argon Balloon

The density of Argon is 1.633 g/L. Thus, the mass of 10 L of argon is \(1.633 \ \text{g/L} \times 10 \ \text{L} = 16.33 \text{ g}\). The total mass of the argon balloon is \(1.00 \text{ g} + 16.33 \text{ g} = 17.33 \text{ g}\).

Step 5: Mass of Krypton Balloon

The density of Krypton is 4.425 g/L. Thus, the mass of 10 L of krypton is \(4.425 \ \text{g/L} \times 10 \ \text{L} = 44.25 \text{ g}\). The total mass of the krypton balloon is \(1.00 \text{ g} + 44.25 \text{ g} = 45.25 \text{ g}\).

Step 6: Compare Balloon Masses to Air

The density of dry air is 1.12 g/L. Therefore, the mass of air displaced by each 10 L balloon is \(1.12 \ \text{g/L} \times 10 \ \text{L} = 11.2 \text{ g}\). A balloon will float if its total mass is less than the mass of the air it displaces.

Step 7: Determine Floating Balloons

Compare the masses of the balloons: - Helium balloon: 2.64 g - Neon balloon: 9.25 g - Argon balloon: 17.33 g - Krypton balloon: 45.25 g Only the helium and neon balloons have masses less than 11.2 g and will float in air.

Key Concepts

Balloon Floatation

Understanding why balloons float begins with the basic concept of buoyancy. A balloon will float if it weighs less than the air it displaces. Each type of gas has its own density, which means some gases will make a balloon float, and others will not.
When you fill a balloon with a gas lighter than air, like helium, it rises. This is because the total weight of the balloon and gas is less than the weight of the air the balloon displaces. As per our scenario, the helium and neon balloons float because their total masses are less than the mass of air displaced by a 10-liter volume of air, which is 11.2 grams. Understanding these principles explains why parade balloons or party balloons can float effortlessly in the air.

Gas Displacement

Gas displacement plays a crucial role in buoyancy. When a balloon filled with a gas is placed in the atmosphere, it displaces an amount of air equal to its own volume. This displaced air is what determines the buoyant force on the balloon.
Say a balloon has a volume of 10 liters; it displaces 10 liters of air. If this air weighs more than the balloon and its contained gas, the balloon will float; otherwise, it will sink. The density of dry air is 1.12 g/L, implying that 10 liters of air weighs 11.2 grams. Any balloon with a total weight below this threshold will rise, demonstrating the key concept that displacement determines floating capability.

Density of Gases

The density of a gas is defined as its mass per unit volume. It's a measure of how much matter exists in a given space and is crucial for determining buoyancy. For gases, density can vary based on temperature and pressure, but at standard conditions, each gas has a unique density.
In our example, we considered four gases: helium, neon, argon, and krypton. Helium is very light with a density of 0.164 g/L, while krypton is much heavier at 4.425 g/L. The relative lightness or heaviness of these gases affects whether a balloon filled with them will float or sink. This helps students see the direct relationship between gas density and a balloon's ability to float.

Comparative Analysis of Gases

Comparing different gases provides insight into the properties affecting balloon flotation. Each gas has specific physical characteristics, one of the most important being density. This analysis helps us identify which gases will enable a balloon to float when comparing them to the air's density.

• Helium (0.164 g/L): Lightest, and therefore most buoyant gas in this scenario.
• Neon (0.825 g/L): Heavier than helium, but still lighter than air, allowing it to float.
• Argon (1.633 g/L): Heavier than air, causing balloons to sink.
• Krypton (4.425 g/L): Heaviest among the gases, leading to sinking balloons.

By considering the densities of these gases against the density of air, we can predict and explain their potential for lift in a simple, comparative manner.