Ideal-gas mixture laws:\nWhich of the following ideal-gas relations are not directly applicable to a mixture as a mixture property (without referencing components)?

Introduction / Context:
Mixture behavior for ideal gases is built from component contributions. Two cornerstone mixture rules are Dalton’s law for pressures and Amagat’s law for volumes. In contrast, Boyle’s and Charles’s laws describe how a single ideal gas varies when one state variable changes, not a “mixture-as-a-single-species” without component resolution.

Given Data / Assumptions:

• Ideal-gas behavior of each component.
• No interactions beyond ideal mixing.
• Mixture properties are sums of component partial properties.

Concept / Approach:
Dalton’s law: p = Σpi with each pi = yi p. Amagat’s law: V = ΣVi with Vi = yi,V V at common T, p. These are mixture-specific relations. Boyle’s and Charles’s laws apply to a single species’ p–V–T variation; applying them to a mixture without specifying composition or partial properties is not meaningful as a standalone “mixture law.”

Step-by-Step Solution:
Identify mixture laws: Dalton and Amagat are designed for mixtures.Recognize Boyle/Charles are single-component relations.Therefore, the items “not applicable to mixture (as mixture laws)” are Boyle’s & Charles’s laws.

Verification / Alternative check:
Standard thermodynamics texts present Dalton and Amagat under “ideal-gas mixtures,” but treat Boyle/Charles as single-gas limiting behaviors.

Why Other Options Are Wrong:
Dalton and Amagat explicitly apply to mixtures; “none of these” is false; Graham’s law concerns rates of effusion, not a mixture property law.

Common Pitfalls:
Assuming “ideal gas” automatically makes the mixture obey every single-gas formula without composition awareness.

Final Answer:
Boyle's law & Charles's law (as pure-gas relations for the mixture)