Mixed ideal gases and basic solution concepts: Identify the single incorrect statement among the following (assume ideal-gas behavior and standard molar volume 22.4 L/mol at N.T.P., so that 1 kmol occupies 22.4 Nm^3).

Introduction / Context:
This problem checks fluency with multiple foundational ideas: normality and dilution in solutions, Dalton’s law for gas mixtures, Avogadro’s law for gas volumes at N.T.P., and mole-to-volume conversions. Mastering these enables quick screening of statements for consistency.

Given Data / Assumptions:

• N.T.P. molar volume: 22.4 L/mol; therefore 1 kmol occupies 22.4 Nm^3.
• Ideal-gas behavior and Dalton’s law for partial pressures.
• Equal weights of O2 and CH4 are mixed with no reaction.
• Ozone O3 contains three oxygen atoms per molecule.

Concept / Approach:
For gases, partial pressure fraction equals mole fraction (at fixed T,V). For solutions, normality scales inversely with dilution factor. At N.T.P., volume is proportional to moles; converting “atoms” in O3 to “molecules” divides the atom count by 3 before using the molar volume.

Step-by-Step Solution:
(a) Dilution: dividing solute per liter by 10 reduces normality to N/10 → correct.(b) Equal weights of O2 and CH4: molar masses are 32 (O2) and 16 (CH4). If masses are equal, n_O2 : n_CH4 = (m/32):(m/16) = 1:2. Hence y_O2 = 1/3, not 1/2; oxygen contributes one-third of total pressure → statement is incorrect.(c) 9.034 × 10^23 oxygen atoms in O3 correspond to 9.034e23/3 = 3.011e23 molecules ≈ 0.5 mol; volume = 0.5 × 22400 c.c = 11200 c.c → correct.(d) 1 kmol occupies 22.4 Nm^3 at N.T.P. → correct by definition.

Verification / Alternative check:
Compute mole fractions explicitly for part (b) to reaffirm y_O2 = 0.333… and y_CH4 = 0.666…, so the oxygen partial pressure is one-third of the total.

Why Other Options Are Wrong:
They are not wrong; each is consistent with basic definitions and calculations.

Common Pitfalls:
Equating equal masses with equal moles; misreading N.T.P. molar volume as 22400 Nm^3 instead of 22.4 Nm^3; forgetting to divide by 3 when converting oxygen atoms to O3 molecules.

Final Answer:
When equal weights of O2 and CH4 are mixed at room temperature, oxygen exerts one-half of the total pressure.