Calculating the Molar Volume of Chlorine Gas: A Step-by-Step Guide

Understanding the molar volume of gases is a fundamental concept in chemistry and physics. In this article, we will delve into the calculation of the molar volume of a 25 g sample of chlorine gas (Cl2) at 273 K and 1 atm. This process involves several key steps and the use of the ideal gas law. Let's explore this in detail.

Introduction to Molar Volume

Molar volume is the volume occupied by one mole of any gas at a specific temperature and pressure. For an ideal gas, under standard temperature and pressure (STP), one mole of any gas occupies 22.4 liters. However, when dealing with a specific mass of a gas, the calculation involves determining the number of moles and subsequently the volume.

Calculating Moles of Chlorine Gas

To begin our calculation, we first need to determine the number of moles of chlorine gas (Cl2) in the given sample. The molar mass of chlorine (Cl) is 35.45 g/mol. Therefore, the molar mass of Cl2 (dichlorine) is:

[ text{Molar mass of } Cl_2 2 times 35.45 , g/mol 70.9 , g/mol ]

Given a 25 g sample of Cl2, we can calculate the number of moles:

[ text{Number of moles} frac{25.0 , g}{70.9 , g/mol} 0.353 , mol ]

Using the Ideal Gas Law to Determine the Volume

The ideal gas law, represented by the formula [ PV nRT ] where:

P is the pressure (1 atm) V is the volume (L) n is the number of moles (0.353 mol) R is the ideal gas constant (0.0821 L·atm/mol·K) T is the temperature (273 K)

At STP, the molar volume of any ideal gas is 22.4 liters per mole. However, we need to use the ideal gas law to verify this for our specific sample. Solving for V:

[ V frac{nRT}{P} ]

Substituting the values:

[ V frac{0.353 , mol times 0.0821 , L·atm/mol·K times 273 , K}{1 , atm} ]

[ V 0.353 times 0.0821 times 273 7.90 , L ]

Conclusion

The molar volume of a 25 g sample of chlorine gas (Cl2) at 273 K and 1 atm is 7.90 liters. This calculation confirms that the molar volume of an ideal gas at STP is consistent with the ideal gas law, even when dealing with a specific mass of gas. Understanding these concepts is crucial for various applications in chemistry and physics, from stoichiometry to practical gas volume measurements.

Related Keywords

Calculation of molar volume Chlorine gas properties Ideal gas law application Mole concept in chemistry

Further Reading and Resources

For more detailed information on the ideal gas law and related calculations, please refer to ideal gas law calculators and online chemistry textbooks.