Question

Calculate the final volume when \(5.00 \mathrm{~L}\) of argon gas undergoes a pressure change from 1.55 atm to 6.50 atm. Assume that the temperature remains constant.

Short answer

The final volume is approximately 1.19 L.

Step-by-step solution

Identify the Given Values and Formula

We are given that the initial volume \( V_1 = 5.00 \, \mathrm{L} \), the initial pressure \( P_1 = 1.55 \, \mathrm{atm} \), and the final pressure \( P_2 = 6.50 \, \mathrm{atm} \). Since the temperature is constant, we'll use Boyle's Law, which states: \( P_1V_1 = P_2V_2 \). We need to find the final volume \( V_2 \).

Rearrange the Formula to Solve for \( V_2 \)

Rearrange Boyle's Law equation to solve for \( V_2 \): \( V_2 = \frac{P_1V_1}{P_2} \). We'll substitute the known values into this equation to solve for \( V_2 \).

Substitute the Known Values

Substitute \( P_1 = 1.55 \, \mathrm{atm} \), \( V_1 = 5.00 \, \mathrm{L} \), and \( P_2 = 6.50 \, \mathrm{atm} \) into the rearranged formula: \( V_2 = \frac{1.55 \, \mathrm{atm} \times 5.00 \, \mathrm{L}}{6.50 \, \mathrm{atm}} \).

Calculate the Final Volume

Calculate \( V_2 \): \( V_2 = \frac{1.55 \times 5.00}{6.50} \approx 1.19 \, \mathrm{L} \). So, the final volume of the argon gas is approximately \( 1.19 \, \mathrm{L} \).

Key concepts

Gas Laws

Gas laws are fundamental principles in chemistry that describe how gases behave under various conditions. They form a crucial part of introductory chemistry and are vital for understanding many scientific and real-world phenomena. Boyle's Law, Charles's Law, and Avogadro's Law are some of the main gas laws, each focusing on different aspects of gas behavior.

• Boyle's Law: Focuses on the pressure-volume relationship at a constant temperature.
• Charles's Law: Describes how a gas's volume changes with temperature when pressure is constant.
• Avogadro's Law: Explores the relationship between gas volume and the number of gas molecules at constant temperature and pressure.

Understanding gas laws involves knowing how to manipulate equations and how different variables influence each other. This is essential for calculations like determining volumes and pressures under various circumstances.

Pressure-Volume Relationship

The pressure-volume relationship described by Boyle's Law is a key concept in understanding gases. It can be expressed as: \[ P_1V_1 = P_2V_2 \]where:

• \( P_1 \) and \( V_1 \) are the initial pressure and volume of the gas.
• \( P_2 \) and \( V_2 \) are the final pressure and volume.

Boyle's Law states that the product of pressure and volume is constant when temperature is steady. This means if one increases, the other decreases proportionately to maintain balance.
For instance, in our exercise, the pressure increased, leading to a decrease in volume. This inverse relationship is pivotal in diverse fields, including engineering and environmental science. It helps us predict how gases will react when placed under different conditions without changing their temperature.

Introductory Chemistry

In introductory chemistry, students begin to explore the magical world of atoms and molecules, understanding how they interact and change. Gas laws, like Boyle's Law, are often among the first principles students encounter. They provide a hands-on way to see scientific theory applied to real life.

Essentials in learning chemistry also include:

• Atomic Structure: Understanding the building blocks of matter.
• Periodic Table: A map of elements that reveals periodic trends and properties.
• Chemical Reactions: How substances change and interact to form new products.

Grasping these core concepts sets the foundation for more complex studies in chemistry. It enables students to solve problems systematically, like calculating a gas's final volume after a pressure change. Engaging with these tools helps in sharpening analytical skills, making chemistry both a challenging and rewarding subject.