Avogadro’s law application: If 1 Nm³ of O2 contains N molecules at given conditions, how many molecules are present in 2 Nm³ of SO2 at the same T and P?

Introduction / Context:
Avogadro’s law states that equal volumes of any gases at the same temperature and pressure contain equal numbers of molecules, regardless of chemical identity. This principle allows direct proportionality between gas volume and number of molecules, forming the basis for molar volume and normal-cubic-meter calculations in industry.

Given Data / Assumptions:

• Both gases compared at the same temperature and pressure.
• Volumes are “normal” cubic meters (Nm³), i.e., referenced to standard conditions.
• Ideal-gas approximation holds sufficiently well at these conditions.

Concept / Approach:
Number of molecules is proportional to volume at fixed T and P: n ∝ V. If 1 Nm³ contains N molecules, then any gas occupying 2 Nm³ at the same T and P contains 2N molecules, independent of its chemical composition (O2 vs. SO2).

Step-by-Step Solution:

Verification / Alternative check:
At standard conditions, one kilomole of any ideal gas occupies ~22.414 Nm³. Thus, molecules per Nm³ are fixed by Avogadro’s number, independent of gas species; doubling volume doubles molecules.

Why Other Options Are Wrong:

• N implies equal volumes, but here volume is doubled.
• N/2 or N/4 contradict the direct proportionality to volume.
• 4N would require quadrupling the volume, not doubling.

Common Pitfalls:
Thinking heavier gases contain fewer molecules at the same volume; mass differs, but molecule count per volume at fixed T and P is the same for all gases under ideal behavior.

Final Answer:
2N