Question

Use the kinetic molecular theory of gases to explain each of the following: a. A container of nonstick cooking spray explodes when thrown into a fire. b. The air in a hot-air balloon is heated to make the balloon rise.

Short answer

Higher temperature increases kinetic energy, leading to higher pressure causing the explosion in a fire and lower density making a hot-air balloon rise.

Step-by-step solution

- Understanding Kinetic Molecular Theory

The kinetic molecular theory of gases states that gas particles are in constant, random motion and their kinetic energy increases with temperature.

- Explaining the Explosion of Cooking Spray in Fire

When the container of nonstick cooking spray is thrown into a fire, the temperature increases. According to the kinetic molecular theory, as the temperature increases, the kinetic energy of the gas molecules inside the container also increases. This increases the pressure inside the container until it cannot withstand the higher pressure and explodes.

- Explaining the Rising of a Hot-Air Balloon

In a hot-air balloon, heating the air inside increases the temperature. Again, referring to the kinetic molecular theory, higher temperature leads to increased kinetic energy and faster motion of gas molecules. This causes the air to expand and become less dense than the cooler air outside the balloon, making the balloon rise.

Key concepts

Gas Particles

According to the kinetic molecular theory, gas particles are constantly moving. These particles are always in random motion, colliding with each other and the walls of their container. We can't see these tiny particles, but their motion has significant effects. For example, the pressure in a container comes from gas particles hitting the container walls.

Gas particles are also very tiny and far apart. This is why gases can be compressed, unlike liquids or solids. Despite their small size, their motion creates observable effects, such as the pressure we measure in a balloon.

Kinetic Energy

Kinetic energy is the energy of motion. In the context of gases, it refers to how fast gas particles are moving.

When you heat a gas, you increase the kinetic energy of its particles. This causes them to move faster. The faster movement leads to more collisions with the walls of the container, which increases the pressure. This is why a can of nonstick cooking spray explodes when thrown into a fire—it’s a dramatic increase in kinetic energy and pressure.

The formula for kinetic energy in gases is given by \(\text{KE} = \frac{3}{2} kT \), where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin. This equation shows a direct relationship between temperature and kinetic energy.

Temperature and Pressure Relationship

Temperature and pressure are closely related when it comes to gases. According to the kinetic molecular theory, as temperature increases, the kinetic energy of gas particles also increases. This means particles move faster and collide more often with the walls of their container.

An interesting example is when the air in a hot-air balloon is heated. When you heat the air inside, its temperature increases and so does its pressure, as explained by \(\text{Pressure} = \frac{nRT}{V} \) according to the Ideal Gas Law, where \( n \) is the number of moles, \( R \) is the gas constant, \( T \) is the temperature, and \( V \) is volume.

This concept explains why hot-air balloons rise; the increased temperature reduces the density of the air inside, making it lighter than the cooler air outside.

Gas Expansion

Gas expansion happens when gas particles spread out. This occurs if you increase the volume or decrease the pressure. Expansion can also happen with heating. According to the kinetic molecular theory, when the temperature increases, gas particles move faster and need more space.

In a hot-air balloon, as the air inside heats up, it expands. This reduces its density, allowing the balloon to rise. The principle behind this is Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is constant \( V \propto \ T \).

This law explains many everyday phenomena. For instance, on a hot day, a closed car tire pressure goes up due to the expansion of air inside. Conversely, in winter, the air contracts, causing lower tire pressure.