Question

Indicate what happens to the pressure of a gas with the following changes: (a) The volume decreases. (b) The temperature decreases. (c) The moles of gas decrease.

Short answer

(a) Pressure increases. (b) Pressure decreases. (c) Pressure decreases.

Step-by-step solution

Understand the Gas Laws

To solve this problem, recall the Ideal Gas Law, which states: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. This formula helps us understand how pressure relates to volume, temperature, and moles.

Analyze the Effect of Volume on Pressure

According to Boyle's Law, for a given mass of gas at constant temperature, pressure is inversely proportional to volume: \( P \propto \frac{1}{V} \). Therefore, if the volume decreases and temperature remains constant, the pressure will increase.

Analyze the Effect of Temperature on Pressure

According to Charles's Law, pressure is directly proportional to temperature when volume and moles are constant: \( P \propto T \). Thus, if the temperature decreases while volume and moles remain constant, the pressure will also decrease.

Analyze the Effect of Moles on Pressure

According to Avogadro's Law, pressure is directly proportional to the number of moles when volume and temperature are constant: \( P \propto n \). If the number of moles decreases with volume and temperature held constant, the pressure will decrease.

Key concepts

Boyle's Law

Boyle's Law is an essential principle in understanding how gases behave under varying conditions. It tells us that for a given quantity of gas at a constant temperature, the pressure and volume are inversely proportional. This means that if the volume of the gas decreases, its pressure increases, provided the temperature remains the same.

Imagine gas particles trapped in a container. When you compress the container, reducing its volume, the gas particles are forced closer together. This results in more frequent collisions with the container walls, which increases the pressure inside the container.

Here are some real-world examples of Boyle's Law in action:

• When you pump air into a bicycle tire, you're compressing the gas, reducing its volume and increasing its pressure.
• A syringe used by medical professionals works on this principle. When the plunger is pulled outwards, the volume increases, and the pressure inside the syringe decreases, allowing liquid to be drawn in.

Understanding Boyle's Law is vital in fields like chemistry and physics, as it helps in predicting how gases will react to changes in volume, which is crucial for safety and efficiency in many applications.

Charles's Law

Charles's Law provides insight into the relationship between temperature and pressure in gases. This law states that, for a fixed amount of gas at constant volume, the pressure is directly proportional to its temperature in Kelvin.

What does this mean? Simply put, if the temperature of the gas increases, the pressure also increases when the volume of the container is constant. Conversely, if the temperature decreases, the pressure decreases. This occurs because temperature measures the average kinetic energy of the gas particles. Higher temperatures make particles move faster, increasing the frequency and force of their collisions with the walls of the container, hence raising the pressure.

Some daily instances of Charles's Law are:

• A balloon will shrink if placed in a colder environment because the decrease in temperature leads to a decrease in pressure.
• Pressure cookers use this law to cook food more quickly. As the temperature rises, the pressure inside increases, cooking the food at a faster rate.

Knowing how temperature influences pressure through Charles's Law is essential for various scientific and cooking processes, enabling better control over experimental conditions and culinary outcomes.

Avogadro's Law

Avogadro's Law is a fundamental concept that helps us understand how the amount of gas (in moles) affects pressure, given constant temperature and volume. According to Avogadro's Law, the pressure is directly proportional to the number of moles of gas present. In simpler terms, if the amount of gas increases, the pressure will also increase, provided that all other variables are held constant.

This law is crucial when considering chemical reactions involving gases. In a closed system, adding more gas molecules will lead to more collisions with the container walls, raising the pressure.

Here are some scenarios demonstrating Avogadro's Law:

• Inflating a balloon demonstrates this law. As you add more air (moles of gas) to the balloon, its pressure and volume increase.
• Air tanks for scuba diving are carefully measured to ensure the right amount of air is present, balancing enough pressure for breathing under water without causing danger.

Understanding Avogadro's Law is imperative for chemists and engineers, as it helps predict and manipulate how changes in the quantity of gas can affect pressure, playing a crucial role in designing processes and safe handling of gases.