Understanding the Vapour Density of a Mixture of Methane and Ethane at STP

Molecular weight and vapour density are crucial concepts in physical chemistry and gas behavior. Understanding these concepts, particularly for mixtures of gases at standard temperature and pressure (STP), is essential for various scientific and industrial applications. This article delves into the calculation of the vapour density of a mixture containing 11.2 liters of methane (CH4) and 22.4 liters of ethane (C2H6) at STP.

Introduction to STP and Ideal Gases

Standard Temperature and Pressure (STP) is a reference point widely used in chemistry. At STP, the temperature is 0°C (273.15 K) and the pressure is 1 atmosphere (101.325 kPa). Under these conditions, one mole of any ideal gas occupies exactly 22.4 liters, a value known as the molar volume at STP.

Methane (CH4) and Ethane (C2H6) at STP

Methane (CH4) and ethane (C2H6) are both hydrocarbon gases with well-defined molecular weights. Methane has a molar mass of approximately 16 g/mol, while ethane has a molar mass of approximately 30 g/mol.

Calculating Vapour Density

The vapour density (VD) of a gas is given by the ratio of its molecular weight to half the molecular weight of hydrogen (1 g/mol). Therefore, we have the formula:

VD (Average molecular weight) / 2

To calculate the vapour density of a mixture of methane and ethane at STP, we need to determine the average molecular weight of the mixture. Here's how it's done:

Given Data

Volume of CH4 11.2 liters Volume of C2H6 22.4 liters

At STP, 22.4 liters of any gas contain one mole. Therefore, 11.2 liters of CH4 and 22.4 liters of C2H6 each represent half a mole.

Step-by-Step Calculation

Calculate the molecular weight contribution for CH4: 11.2 liters of CH4 0.5 moles of CH4 Molecular weight of CH4 16 g/mol Weight of CH4 0.5 * 16 8 grams Calculate the molecular weight contribution for C2H6: 22.4 liters of C2H6 1 mole of C2H6 Molecular weight of C2H6 30 g/mol Weight of C2H6 1 * 30 30 grams Calculate the total molecular weight: Total molecular weight 8 grams (CH4) 30 grams (C2H6) 38 grams Calculate the average molecular weight per 0.5 moles of the mixture (since the total volume is the sum of 0.5 and 1 moles): Average molecular weight (38 grams) / (1.5 moles) 25.33 g/mol Calculate the vapour density: Vapour density (25.33 g/mol) / 2 12.665

Application of Vapour Density in Gas Behavior

The vapour density is a useful parameter in the study of gas behavior, particularly in the design of gas storage tanks and the understanding of gas reactions. It provides insights into the density of the gas relative to hydrogen, which is a common reference point.

Conclusion

Understanding the calculation of vapour density for mixtures of gases like methane (CH4) and ethane (C2H6) at STP is pivotal for various scientific and industrial applications. The vapor density of the mixture in question is 12.665, providing a specific measure that can be used in further calculations and real-world applications.

Keywords: vapour density, methane, ethane, molecular weight, STP