Question

Draw a highly magnified view of a sealed, rigid container filled with a gas. Then draw what it would look like if you cooled the gas significantly but kept the temperature above the boiling point of the substance in the container. Also draw what it would look like if you heated the gas significantly. Finally, draw what each situation would look like if you evacuated enough of the gas to decrease the pressure by a factor of 2 .

Short answer

Draw four sealed containers with gas particles (dots) inside to represent the following scenarios: 1. Original gas at room temperature: even distribution of particles with random movements. 2. Gas cooled above boiling point: particles closer together and moving more slowly. 3. Gas heated significantly: particles further apart and moving more quickly. 4. Original gas with reduced pressure: half the particles removed but remaining ones evenly distributed. 5. Cooled gas with reduced pressure: half the particles removed, remaining particles closer together. 6. Heated gas with reduced pressure: half the particles removed, remaining particles further apart.

Step-by-step solution

Draw the original gas at room temperature

Draw a sealed container with equally spaced gas particles (dots) to represent the original scenario. Ensure the particles are evenly distributed and moving randomly inside the container.

Draw the gas when cooled above boiling point

Draw a similar container as in Step 1 but with the gas particles closer together. This represents the gas being cooler, and the particles now have less kinetic energy. Ensure the particles are moving more slowly and are closer together than in Step 1.

Draw the gas when heated significantly

Draw a similar container as in Step 1 but with the distance between the gas particles increased. This represents the gas being hotter and now has more kinetic energy. Ensure the particles are moving more quickly and are further apart than in Step 1.

Draw the original gas with pressure reduced by a factor of 2

Draw a similar container as in Step 1 but remove half of the gas particles and ensure the remaining particles are evenly distributed. This scenario represents the original gas but with half of the pressure.

Draw the cooled gas with pressure reduced by a factor of 2

Draw a similar container as in Step 2 but remove half of the gas particles and distribute the remaining particles evenly. This scenario represents the cooled gas but with half of the pressure.

Draw the heated gas with pressure reduced by a factor of 2

Draw a similar container as in Step 3 but remove half of the gas particles and distribute the remaining particles evenly. This scenario represents the heated gas but with half of the pressure.

Key concepts

Gas Laws

Gas laws are fundamental principles understanding the behavior of gases. They describe how gases interact with changes in pressure, volume, and temperature. The most commonly known laws are Boyle's Law, Charles's Law, and Avogadro's Law.

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is constant: \[ P_1V_1 = P_2V_2 \] where \(P\) is pressure and \(V\) is volume.

Charles's Law expresses the relationship between temperature and volume, stating that the volume of a gas is directly proportional to its temperature when pressure is constant: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Here, \(T\) is in Kelvin.

Avogadro's Law tells us that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles: \[ V \propto n \] where \(n\) is the amount of substance, often measured in moles.

These principles help visualize changes when heating or cooling gases, and altering container pressures, as described in the original exercise.

Temperature and Pressure

In terms of gases, temperature and pressure are closely linked. Temperature measures the average kinetic energy of gas particles, while pressure results from collisions between particles and the container walls.

As a gas is heated, its particles gain energy and move faster, resulting in increased pressure if confined in a rigid container. Conversely, cooling gas reduces the energy and speed of particles, leading to lower pressure.

This relationship can be observed by manipulating the temperature: heating the gas significantly will increase both the speed of particles and pressure (if the volume remains constant). Cooling it will have the opposite effect, reducing pressure as depicted in cooling steps of the exercise.

Particle Distribution

Particle distribution refers to how individual gas particles are spread within a container. In a highly magnified view of a gas, particles appear to be moving randomly and, ideally, evenly distributed.

Changes in temperature and quantity can affect distribution. Cooler temperatures will reduce particle speed, causing them to cluster closer together. You end up seeing denser distributions. Conversely, heating will increase speed, making particles spread further apart within the container.

When pressure is reduced by removing particles, the remaining particles become more spaced, illustrating less dense distribution. Thus, both temperature and pressure changes play a key role in how particle distribution appears in different scenarios.

Kinetic Energy of Particles

The kinetic energy of particles in a gas is crucial in determining the overall behavior observed under different conditions. Kinetic energy is directly proportional to the temperature of the gas.

When a gas is heated, its particles absorb energy, increasing their kinetic energy. As a result, they move more rapidly and, if the volume of the container remains the same, collide with the walls with greater force, leading to higher pressure.

In contrast, cooling gas decreases kinetic energy. Particles move slower, resulting in less forceful collisions and thus, decreased pressure.

Visualizing these changes in kinetic energy helps understand the different behaviors of gases shown in various heating and cooling scenarios in the exercise. The concept of kinetic energy ties directly into changes observed in particle speed and how they contribute to variations in pressure and temperature relationships.