Gas-mixture volumes:\n“The total volume of a gas mixture equals the sum of the pure-component volumes at the mixture pressure and temperature.” This statement corresponds to which law?

Introduction / Context:
Two additive laws describe ideal gas mixtures: Dalton’s law of additive partial pressures and Amagat’s law of additive partial volumes. Correctly distinguishing them is crucial for multicomponent gas calculations and mixture property estimates.

Given Data / Assumptions:

• Ideal or near-ideal gas behavior.
• Same temperature and pressure for components and mixture.
• Statement explicitly refers to additivity of volumes.

Concept / Approach:
Amagat’s law states that the total volume of a gas mixture equals the sum of the partial volumes that each component would occupy alone at the mixture temperature and pressure. Dalton’s law, in contrast, states that total pressure equals the sum of partial pressures at the mixture temperature and volume. Gay-Lussac’s and Avogadro’s laws concern proportionalities for pure gases, not mixture additivity rules.

Step-by-Step Solution:
Identify key phrase: “sum of pure component volumes.”Match with Amagat’s law of additive volumes.Select Amagat’s law as the correct option.

Verification / Alternative check:
For ideal gases, Amagat’s and Dalton’s laws can be shown to be consistent and lead to the same mixture relationships because PV = nRT applies component-wise.

Why Other Options Are Wrong:
Dalton’s law refers to pressures, not volumes; Gay-Lussac’s and Avogadro’s are single-gas proportionalities; Boyle’s is P–V inverse relationship for a pure gas at constant temperature.

Common Pitfalls:
Swapping Dalton’s and Amagat’s because both are “additive” statements; always note whether the additive variable is pressure or volume.

Final Answer:
Amagat's law