Calculating the Volume Occupied by Marsh Gas (CH4) at STP

To determine the volume occupied by marsh gas (CH4) at standard temperature and pressure (STP) containing (4.8 times 10^{24}) molecules, we can follow a series of logical steps based on the ideal gas laws and Avogadro's number. This article will explore the process in detail, ensuring clarity and understanding of the concept.

Understanding the Ideal Gas Law and Avogadro’s Number

At standard temperature and pressure (STP), defined as 0°C (273.15 K) and 1 bar (100 kPa), one mole of any ideal gas occupies a volume of 22.71 liters, as recommended by the International Union of Pure and Applied Chemistry (IUPAC). However, it is important to note that this volume can also be approximated as 22.4 liters for simplicity, especially in younger educational contexts. Additionally, Avogadro’s number, which is the number of particles (atoms, molecules, etc.) in one mole of a substance, is approximately (6.022 times 10^{23}) particles per mole.

Calculating the Molar Quantity of Marsh Gas (CH4)

Given that there are (4.8 times 10^{24}) molecules of CH4, we can calculate the molar quantity (number of moles) by dividing the number of molecules by Avogadro’s number:

( frac{4.8 times 10^{24}}{6.022 times 10^{23}} 7.97) moles

This calculation shows that 4.8 billion trillion molecules of CH4 are present in 7.97 moles of the gas.

Calculating the Volume Occupied by Marsh Gas at STP

Now, using the knowledge that 1 mole of an ideal gas occupies 22.71 liters at STP, we can find the total volume occupied by 7.97 moles of CH4:

( 7.97 text{ moles} times 22.71 text{ L/mole} 181 text{ L} )

Therefore, 4.8 billion trillion molecules of marsh gas (CH4) occupy about 181 liters at STP conditions.

Conclusion

This detailed step-by-step calculation demonstrates the process of determining the volume occupied by marsh gas (CH4) at STP, given the number of molecules. Understanding these fundamental concepts of gas behavior is crucial in various scientific and engineering applications.

References

1. International Union of Pure and Applied Chemistry (IUPAC), Standard Temperature and Pressure (STP).

2. Avogadro's Number - Applications in Chemistry and Physics.

3. Ideal Gas Law and Its Practical Applications in Chemical Engineering.