# Ideal Gas Equation Example Problems: Mastering the Application of PV = nRT

Understanding the ideal gas equation, also known as the ideal gas law, is fundamental in the study of thermodynamics and chemistry. This equation provides a powerful tool for solving a wide range of problems related to gases, from calculating pressure, volume, and temperature to determining the number of moles of a gas. In this article, we will delve into several example problems to illustrate the application of the ideal gas equation in various scenarios. By mastering these examples, you will gain a deeper understanding of how to use the ideal gas equation to solve real-world problems.

## Example 1: Calculating Pressure

Suppose we have a gas confined in a container with a volume of 5.00 liters at a temperature of 300 K. If there are 0.025 moles of gas present, what is the pressure exerted by the gas?

To solve this problem, we can use the ideal gas equation: PV = nRT. We are given the volume (V = 5.00 L), temperature (T = 300 K), and the number of moles (n = 0.025). Additionally, we can use the ideal gas constant R = 0.0821 L•atm/mol•K. Plugging these values into the equation, we get:

P(5.00 L) = (0.025 mol)(0.0821 L•atm/mol•K)(300 K)

Solving for P, we find:

**P = (0.025 mol)(0.0821 L•atm/mol•K)(300 K) / 5.00 L**

**P = 0.1238 atm**

Therefore, the pressure exerted by the gas is 0.1238 atm.

## Example 2: Determining Volume

Imagine a gas occupies a volume of 2.50 liters at a pressure of 3.00 atm and a temperature of 400 K. If there are 0.040 moles of the gas, what will be its new volume if the pressure is decreased to 2.00 atm and the temperature is kept constant?

In this scenario, we can again utilize the ideal gas equation to solve for the new volume. The initial conditions are P_{1} = 3.00 atm, V_{1} = 2.50 L, n = 0.040 moles, and T = 400 K. We need to find V_{2} when P_{2} = 2.00 atm, with T remaining constant. The ideal gas law allows us to set up the following equation:

P_{1}V_{1} = nRT = P_{2}V_{2}

Solving for V_{2}, we get:

**V _{2} = (P_{1}V_{1}) / P_{2}**

**V _{2} = (3.00 atm * 2.50 L) / 2.00 atm**

**V _{2} = 3.75 L**

Therefore, the new volume of the gas will be 3.75 liters.

## Example 3: Finding the Number of Moles

Let's consider a scenario where a gas occupies a volume of 10.0 liters at a pressure of 2.00 atm and a temperature of 500 K. If the gas constant R = 0.0821 L•atm/mol•K, how many moles of gas are present in the container?

To determine the number of moles in this situation, we can rearrange the ideal gas equation to solve for n:

**n = (PV) / RT**

Substituting the given values, we find:

**n = (2.00 atm * 10.0 L) / (0.0821 L•atm/mol•K * 500 K)**

**n = 0.487 moles**

Thus, there are 0.487 moles of the gas present in the container.

## Frequently Asked Questions

### What are the units of the ideal gas constant R?

The ideal gas constant R can be expressed in various sets of units. Common units for R include 0.0821 L•atm/mol•K, 8.314 J/mol•K, and 62.364 L•Torr/mol•K.

### When can the ideal gas equation be applied?

The ideal gas equation is most accurate for low pressures and high temperatures. At low temperatures and high pressures, the behavior of real gases deviates from that predicted by the ideal gas equation due to intermolecular forces becoming significant.

### What are some real-world applications of the ideal gas equation?

The ideal gas equation is widely used in various fields, including chemistry, physics, engineering, and environmental science. It is applied in studies of gas behavior, industrial processes, air quality monitoring, and the design of thermodynamic systems.

## Reflection

In conclusion, the ideal gas equation serves as a valuable tool for solving a myriad of problems related to the behavior of gases. By understanding the examples discussed in this article, you have gained insight into how the ideal gas equation can be applied to calculate various gas properties. Whether it's determining pressure, volume, temperature, or the number of moles, the ideal gas equation offers a versatile approach to addressing gas-related problems with confidence.

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