Applying the Ideal Gas Law to a Specific Problem

Oct 13, 2025 by wbrum.org 100 views

Introduction

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a crucial tool for understanding the properties and behavior of gases, and it has numerous applications in various fields, including chemistry, physics, and engineering. In this article, we will explore the ideal gas law and its applications, with a focus on a specific problem involving a gas in a rigid container.

The Ideal Gas Law

The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas. It is expressed as:

PV = nRT

where:

P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the gas constant
T is the temperature of the gas in Kelvin

Applying the Ideal Gas Law to a Specific Problem

Let's consider a specific problem involving a gas in a rigid container. We are given that the gas has a pressure of 0.96 atm at a temperature of $$25^{\circ} C$$, and that a change in temperature causes the pressure to increase to 1.25 atm. We are asked to find the new temperature of the gas.

Using the Combined Gas Law

To solve this problem, we can use the combined gas law, which is a variation of the ideal gas law that takes into account changes in pressure, volume, and temperature. The combined gas law is expressed as:

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where:

P1 is the initial pressure of the gas
T1 is the initial temperature of the gas
P2 is the final pressure of the gas
T2 is the final temperature of the gas

Solving for the New Temperature

We can now substitute the given values into the combined gas law equation:

$\frac{0.96 \text{ atm}}{298 \text{ K}}=\frac{1.25 \text{ atm}}{T_2}$

To solve for T2, we can cross-multiply and rearrange the equation:

T2 = (1.25 atm) (298 K) / (0.96 atm)

T2 = 319.79 K

Converting the Temperature to Celsius

To convert the temperature from Kelvin to Celsius, we can use the following equation:

T (°C) = T (K) - 273.15

T (°C) = 319.79 K - 273.15

T (°C) = 46.64 °C

Conclusion

In this article, we have explored the ideal gas law and its applications, with a focus on a specific problem involving a gas in a rigid container. We have used the combined gas law to solve for the new temperature of the gas, and we have converted the temperature from Kelvin to Celsius. The ideal gas law is a powerful tool for understanding the behavior of gases, and it has numerous applications in various fields.

References

Gases and Their Properties by David R. Lide
Physical Chemistry by Peter Atkins and Julio de Paula
The Ideal Gas Law by the American Chemical Society

Introduction

In our previous article, we explored the ideal gas law and its applications, with a focus on a specific problem involving a gas in a rigid container. We used the combined gas law to solve for the new temperature of the gas, and we converted the temperature from Kelvin to Celsius. In this article, we will answer some frequently asked questions (FAQs) related to the ideal gas law and its applications.

Q: What is the ideal gas law?

A: The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas. It is expressed as:

PV = nRT

where:

P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the gas constant
T is the temperature of the gas in Kelvin

Q: What is the combined gas law?

A: The combined gas law is a variation of the ideal gas law that takes into account changes in pressure, volume, and temperature. It is expressed as:

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where:

P1 is the initial pressure of the gas
T1 is the initial temperature of the gas
P2 is the final pressure of the gas
T2 is the final temperature of the gas

Q: How do I use the combined gas law to solve for the new temperature of a gas?

A: To use the combined gas law to solve for the new temperature of a gas, you can follow these steps:

Write down the combined gas law equation: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$
Substitute the given values into the equation
Cross-multiply and rearrange the equation to solve for T2

Q: What is the difference between the ideal gas law and the combined gas law?

A: The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas. The combined gas law is a variation of the ideal gas law that takes into account changes in pressure, volume, and temperature.

Q: Can I use the ideal gas law to solve for the new temperature of a gas?

A: No, you cannot use the ideal gas law to solve for the new temperature of a gas. The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas, but it does not take into account changes in pressure, volume, and temperature.

Q: What are some real-world applications of the ideal gas law and the combined gas law?

A: The ideal gas law and the combined gas law have numerous real-world applications, including:

Calculating the pressure and temperature of a gas in a container
Determining the volume of a gas in a container
Calculating the number of moles of a gas in a container
Understanding the behavior of gases in various industrial and scientific applications

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to the ideal gas law and its applications. We have also provided a brief overview of the ideal gas law and the combined gas law, and we have discussed some real-world applications of these laws. We hope that this article has been helpful in understanding the ideal gas law and its applications.

References

Gases and Their Properties by David R. Lide
Physical Chemistry by Peter Atkins and Julio de Paula
The Ideal Gas Law by the American Chemical Society