Ideal Gas Law at Constant Temperature for Mixing Gases

Steps:

• Calculate the initial amount of gas in each flask using PV (proportional to moles since T is constant): Flask O = 12 kPa × 5 dm³ = 60 kPa·dm³; Flask R = 6 kPa × 10 dm³ = 60 kPa·dm³.
• Add the amounts: total = 60 + 60 = 120 kPa·dm³.
• Determine total volume after connection: 5 dm³ + 10 dm³ = 15 dm³.
• Compute final pressure: P_f = total amount / total volume = 120 / 15 = 8 kPa.

Why A is correct:

• The formula P_f = (P₁V₁ + P₂V₂) / (V₁ + V₂) from the ideal gas law (PV ∝ n at constant T) yields exactly 8 kPa for the mixed gases.

Why the others are wrong:

• B: Ignores equal contributions from both flasks, underestimating total moles.
• C: Assumes average pressure without volume weighting, like (12 + 6)/2 × something incorrect.
• D: Overestimates by possibly averaging volumes instead of using PV totals.

Final answer: A