Question

You have a gas in a container fitted with a piston, and you change one of the conditions of the gas such that a change takes place, as shown below: State three distinct changes you can make to accomplish this, and explain why each would work.

Short answer

Three distinct changes that can be made to cause a change in the gas conditions are: 1. Adjusting Volume: By moving the piston up or down, the volume inside the container will either increase or decrease. According to Boyle's Law, the pressure of a gas is inversely proportional to its volume with constant temperature. When the volume increases, the pressure decreases, and vice versa. 2. Applying Heat: Heating or cooling the container will change the gas's conditions. When heated, the gas particles gain kinetic energy, causing them to move faster and more frequently collide with the walls of the container, thereby increasing the pressure. According to Charles's Law, the volume of a gas is directly proportional to its temperature with constant pressure. When the temperature increases, the volume will also increase, and vice versa. 3. Altering Gas Amount: Adding or removing gas from the container will change the gas's conditions. Avogadro's Law states that the volume of a gas is directly proportional to the number of moles of gas with constant temperature and pressure. When the amount of gas increases, the volume will also increase, and vice versa.

Step-by-step solution

Change 1: Adjusting Volume

If the volume of the container is changed, the gas's conditions will also change. By moving the piston up or down, the volume inside the container will either increase or decrease. According to Boyle's Law, the pressure of a gas is inversely proportional to its volume with constant temperature. So, when the volume of the gas is increased, its pressure will decrease; and when the volume is decreased, the pressure will increase.

Change 2: Applying Heat

The gas's conditions can also be altered by heating or cooling the container. By heating the container, the gas particles gain kinetic energy causing them to move faster and more frequently collide with the walls of the container, thereby increasing the pressure. According to Charles's Law, the volume of a gas is directly proportional to its temperature with constant pressure. So, when the temperature of a gas is increased, its volume will also increase. Conversely, when the temperature of a gas is decreased, its volume will decrease.

Change 3: Altering Gas Amount

Another change that could be made is to add or remove gas from the container. According to Avogadro's Law, the volume of a gas is directly proportional to the number of moles of gas with constant temperature and pressure. So, as the amount of gas inside the container increases, the volume of the gas will also increase since they are directly proportional. Conversely, when the amount of gas inside the container decreases, the volume of the gas will also decrease.

Key concepts

Boyle's Law

Boyle's Law is a fundamental principle in chemistry that relates the pressure of a gas to its volume. It states that, for a given mass of gas at constant temperature, the pressure is inversely proportional to the volume. This means that if you increase the volume of the gas by compressing it into a smaller space, the pressure will increase. Conversely, when you increase the volume by allowing the gas more space, the pressure decreases.

Imagine a syringe being used to compress air - as the plunger is pushed down, the volume decreases and the air pressure within the syringe increases. This is Boyle's Law in action. An easy way to remember this law is that pressure and volume are like a seesaw; when one goes up, the other goes down, as long as the temperature remains unchanged.

Charles's Law

When you're dealing with gases, temperature plays a massive role in how they behave. Charles's Law gives us insight into this by showing the relationship between volume and temperature. It tells us that the volume of a gas is directly proportional to its temperature (measured in Kelvins) when the pressure is held constant.

So, if you heat a balloon, the air inside expands and the balloon grows larger without bursting - this is Charles's Law in action. An easy way to visualize this is thinking about a hot day versus a cold day: on a hot day, the air inside a beach ball expands, making the ball firmer, while on a cold day, it contracts, and the ball feels softer.

Avogadro's Law

Avogadro's Law tells us about the relationship between the volume of a gas and the amount of substance present, which is measured in moles. In very simple terms, this law states that equal volumes of all gases, at the same temperature and pressure, contain an equal number of molecules.

As a real-life example, if you have two balloons of the same size, one filled with hydrogen and the other with carbon dioxide, and they are at the same temperature and pressure, they contain the same number of molecules. If we add more gas to one balloon (increase the moles of gas), its volume will increase as long as the temperature and pressure are kept the same. Avogadro's Law is key when predicting the behavior of gases during chemical reactions and other processes.

Kinetic Molecular Theory

The kinetic molecular theory is a cornerstone of understanding how gases behave. It explains the properties of gases in terms of the movement and interactions of the molecules they are comprised of. This theory assumes that gas particles are in constant, random motion and the collisions between them are perfectly elastic - meaning the particles don't lose energy when they collide with each other or the walls of their container.

The theory provides a foundation for understanding the other laws of gases. For instance, when we look at Boyle's Law from the kinetic molecular theory perspective, the increased pressure from decreased volume is due to gas particles hitting the container walls more frequently. As we take these microscopic events into account, we start to see how the macroscopic properties of gases like pressure and volume come to life.

Gas Pressure-Volume Relationship

In the context of the textbook problem, understanding the gas pressure-volume relationship is crucial. It's essentially the practical application of Boyle's Law; as you adjust the volume available to a gas in a closed space, you directly affect the pressure it exerts. This is because gas particles are always moving and bumping into each other and the container walls, which creates pressure.

For a visual example, think of a bike pump: as you decrease the volume inside the pump by pushing the handle down, the pressure increases, inflating your tire. The beauty of this relationship is in its predictability - knowing how volume changes will affect pressure allows for a wide range of applications, from industrial processes to daily tasks like cooking with a pressure cooker.