Understanding Effective Volume Occupied by Gas Molecules
To find the fraction of effective volume occupied by molecules in 1 mole of a gas at STP, we will follow a systematic approach.
1. Volume of 1 Mole of Gas at STP
- At Standard Temperature and Pressure (STP), 1 mole of an ideal gas occupies approximately 22.4 liters.
- This is equivalent to 22.4 x 10^3 cm³ or 22.4 x 10^-3 m³.
2. Volume of a Single Molecule
- The diameter of the molecule is given as 2 x 10^-10 m.
- The radius is therefore 1 x 10^-10 m.
- The volume of a single molecule (considering it as a sphere) can be calculated using the formula: V = (4/3)πr³.
- This results in a volume of approximately 4.19 x 10^-30 m³ per molecule.
3. Total Volume of Molecules in 1 Mole
- The number of molecules in 1 mole is Avogadro's number, which is approximately 6.022 x 10^23.
- Thus, the total volume occupied by 1 mole of molecules is:
Total Volume = Number of Molecules x Volume per Molecule
= 6.022 x 10^23 x 4.19 x 10^-30 m³ = approximately 2.52 x 10^-6 m³.
4. Fraction of Volume Occupied by Molecules
- To find the fraction of the effective volume occupied:
Fraction = (Total Volume of Molecules) / (Volume of 1 Mole of Gas at STP)
= (2.52 x 10^-6 m³) / (22.4 x 10^-3 m³) = approximately 0.000112.
5. Conclusion
- The fraction of the effective volume occupied by the molecules in 1 mole of gas at STP is very small, approximately 0.000112, indicating that most of the volume is empty space in the gas phase.