Calculating Molar Mass of a Gas Using the Ideal Gas Law: A Practical Example

The ideal gas law, PV nRT, provides a useful framework for understanding and calculating various properties of gases. This article will walk you through the process of determining the molar mass of a gas when provided with specific parameters such as pressure, volume, and temperature. Let's delve into a detailed example and the corresponding calculations.

Detailed Example: Finding the Molar Mass of a Gas

Consider a 0.529 g sample of an unknown gas that occupies a volume of 125 mL at a pressure of 60 cm of Hg and a temperature of 25°C. Our goal is to determine the molar mass of this gas. To do so, we will employ the ideal gas law.

Step 1: Convert Given Values to the Appropriate Units

First, we need to ensure all given values are in the correct units. The pressure is in centimeters of mercury (cm Hg), the volume in milliliters (mL), and the temperature in degrees Celsius (°C). Let's convert these to atmospheres (atm), liters (L), and Kelvin (K), respectively.

Pressure: 60 cm Hg 60 * 10 mm Hg 600 mm Hg
1 atm 760 mm Hg
Thus, P 600 mm Hg / 760 mm Hg/atm 0.7895 atm Volume: 125 mL 0.125 L Temperature: 25°C 25 273.15 298.15 K

Step 2: Calculate the Number of Moles

The ideal gas law equation is PV nRT, where:

P 0.7895 atm V 0.125 L R 0.0821 L?atm/(mol?K) T 298.15 K

First, rearrange the formula to solve for n (number of moles):

n PV/RT

Substitute the values:

n (0.7895 atm) * (0.125 L) / (0.0821 L?atm/(mol?K)) * (298.15 K)

Calculate:

n 0.0986875 / 24.475515 ≈ 0.00403 mol

Step 3: Calculate the Molar Mass

The molar mass M is given by the formula:

M mass / moles

Given that the mass m is 0.529 g, we can now calculate the molar mass:

M 0.529 g / 0.00403 mol ≈ 131.2 g/mol

Thus, the molar mass of the gas is approximately 131.2 g/mol.

Conclusion

Using the ideal gas law, we were able to determine the molar mass of a gas given its pressure, volume, and temperature. This process can be applied to a variety of gases and conditions. Understanding the ideal gas law and its derivatives is crucial in chemical and physical research and analysis.

Further Reading and Related Keywords

For further insights into gas laws and thermodynamics, you may find these resources useful:

Keyword 1: Ideal Gas Law - Explore the fundamental principles behind the ideal gas law. Keyword 2: Molar Mass Calculation - Learn how to calculate molar masses using different methods and formulas. Keyword 3: Gas Composition - Understand how the composition of gases affects their properties and behavior.

By mastering these concepts, you will be better equipped to tackle complex problems in chemistry and physics.