Ideal-gas mixing in a fixed 1.0 L vessel: 500 c.c. H2 at 700 mm Hg and 500 c.c. O2 at 600 mm Hg are combined in a 1.0 L container at the same temperature. What is the final total pressure (mm Hg)?

Introduction / Context:This problem illustrates Dalton’s law of partial pressures and the ideal-gas scaling of pressure with volume at constant temperature and moles. It is common in gas handling, reaction stoichiometry before ignition, and laboratory blending operations.

Given Data / Assumptions:

• Initial gases: 0.5 L H2 at 700 mm Hg; 0.5 L O2 at 600 mm Hg.
• They are mixed into a 1.0 L vessel.
• Temperature is the same before and after; no reaction occurs (inert mixing).
• Ideal-gas behavior; volumes add; pressures scale inversely with volume at constant T and n.

Concept / Approach:Each gas’s partial pressure after expansion/compression to 1.0 L equals its initial pressure multiplied by the ratio Vi/Vtotal (at constant T). The final total pressure equals the sum of the new partial pressures, per Dalton’s law.

Step-by-Step Solution:For H2: P_H2,final = 700 mm Hg * (0.5 L / 1.0 L) = 350 mm Hg.For O2: P_O2,final = 600 mm Hg * (0.5 L / 1.0 L) = 300 mm Hg.Total pressure: P_total = 350 + 300 = 650 mm Hg.Select 650 mm Hg.

Verification / Alternative check:Using n = PV/RT separately: n_H2 = 7000.5/(R T); n_O2 = 6000.5/(R T). After mixing in 1.0 L at same T, P_total = (n_total R T)/V = [(7000.5 + 6000.5)/(R T)] * (R T)/1.0 = 650 mm Hg.

Why Other Options Are Wrong:700 or 600 mm Hg ignore one of the component contributions and the volume scaling.375 mm Hg is an arithmetic error (e.g., averaging after dividing by 2 twice).

Common Pitfalls:Forgetting to scale each gas by its volume change; averaging initial pressures incorrectly; assuming reaction occurs.

Final Answer:650