Calculating the Volume of Nitrogen Gas at N.T.P. Using the Ideal Gas Law

When dealing with gases, the Ideal Gas Law is a fundamental tool for determining various properties such as volume. This article explains how to use the Ideal Gas Law, PVnRT, to determine the volume occupied by 0.5 moles of nitrogen gas at N.T.P. (Normal Temperature and Pressure).

Understanding the Ideal Gas Law (PVnRT)

The Ideal Gas Law, represented as PVnRT, is a mathematical equation that describes the relationship between the pressure (P), volume (V), amount of substance (n), and temperature (T) for an ideal gas. In this law, R is the universal gas constant, which is approximately 8.314 J/(mol·K) or 0.08206 L·atm/(mol·K).

Given Parameters and Conversion

In our scenario, we have the following given parameters:

P 760 mmHg (which is equivalent to 1 atmosphere, or 1 atm)

n 0.5 moles of nitrogen gas

T 273.15 K (since we are at N.T.P., which is 0°C or 273.15 K)

R 0.08206 L·atm/(mol·K) (the ideal gas constant for the appropriate units)

Step-by-Step Calculation

To calculate the volume (V) of 0.5 moles of nitrogen gas at N.T.P., we use the Ideal Gas Law formula:

V nRT/P

Substituting the given values into the formula:

V (0.5 mol) times; (0.08206 L·atm/(mol·K)) times; (273.15 K) / 1 atm

V (0.5 times; 0.08206 times; 273.15) L

V 11.21957 L

Therefore, the volume occupied by 0.5 moles of nitrogen gas at N.T.P. is approximately 11.22 liters.

Alternative Approach Using Avogadro's Law

Alternatively, using Avogadro's Law, which states that equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules, we can determine the volume more simply. Avogadro's Law can be expressed as:

1 mole of nitrogen gas occupies 22.4 liters at N.T.P.

Therefore, 0.5 moles of nitrogen gas will occupy half the volume:

Volume 0.5 times; 22.4 L 11.2 L

This confirms our previous calculation using the Ideal Gas Law.

Conclusion

The volume occupied by 0.5 moles of nitrogen gas at N.T.P. is 11.2 liters. This calculation aligns with both the Ideal Gas Law and Avogadro's Law, providing a consistent and accurate result. Understanding these principles is crucial for any professional or student involved in physical chemistry, engineering, or related fields.

References

For a more in-depth understanding, refer to this source and this article.