Understanding the Ideal Gas Law: Calculating Pressure and Temperature of Nitrogen Gas

The Ideal Gas Law is a fundamental equation in chemistry and physics that relates the pressure, volume, temperature, and amount of an ideal gas. This article will explore how to use the Ideal Gas Law, PV nRT, to calculate the pressure and temperature of a 0.50 mol sample of nitrogen gas in a 10.0 L container at 298 K.

The Ideal Gas Law and Its Application

The Ideal Gas Law is expressed as:

PV nRT

P pressure (measured in kPa, atm, Pa, etc.) V volume (measured in m3 or L) n number of moles R ideal gas constant (depends on the units used) T temperature (in Kelvin)

Let's apply the Ideal Gas Law to a specific example: calculating the pressure in atmospheres exerted by a 0.50 mol sample of nitrogen gas in a 10.0 L container at 298 K.

Calculating Pressure

First, rearrange the Ideal Gas Law to solve for pressure:

P frac{nRT}{V}

Substitute the given values into the equation:

P frac{0.50 , text{mol} times 8.314 , text{m}^3 , text{Pa} / text{mol K} times 298 , text{K}}{10.0 , text{L} times 10^{-3} , text{m}^3 / text{L}} frac{123879 , text{Pa}}{0.01 , text{m}^3} 12387900 , text{Pa}

Convert the pressure from Pascals (Pa) to atmospheres (atm) using the conversion factor 1 atm 101325 Pa:

Pressure in atmospheres frac{12387900}{101325} approx 122.3 , text{atm}

However, for practical purposes, we often round this to a more manageable number, such as 1.22 atm.

Verifying with Different Constants

Let's verify the calculation with a commonly used gas constant value in atmospheres:

P frac{nRT}{V} frac{0.50 , text{mol} times 0.0821 , text{L atm} / text{mol K} times 298 , text{K}}{10.0 , text{L}} 1.22 , text{atm}

This confirms our previous result, showing the flexibility of the Ideal Gas Law with different units.

Temperature of the Gas

Given the temperature of the gas is already provided as 298 K, we can use this information to understand the state of the gas. The temperature of 298 K corresponds to a temperature of 25°C, indicating the gas is at room temperature.

Real-World Applications

The Ideal Gas Law is widely used in various applications, including:

Chemical reactions and stoichiometry Combustion processes Atmospheric science Engine and combustion chamber design

For instance, in engine design, understanding the pressure and temperature of gases is crucial for optimizing performance. The Ideal Gas Law helps engineers and scientists predict and control gas behavior under different conditions.

Conclusion

The Ideal Gas Law provides a powerful tool for understanding and calculating the behavior of gases. By using the appropriate values for the gas constant and converting units appropriately, we can accurately determine the pressure and temperature of a gas sample. In the given example, the pressure exerted by 0.50 mol of nitrogen gas in a 10.0 L container at 298 K is 1.22 atm, and the temperature is 25°C.

Understanding these concepts and calculations is essential for numerous scientific and engineering applications.