Dalton’s Atomic theory could not explain which of the following?

The correct option is Law of gaseous volume (also known as Gay-Lussac's Law of Gaseous Volumes).

Step-by-Step Explanation:

1. Understanding Dalton's Atomic Theory:
John Dalton formulated his atomic theory based on the laws of chemical combination. The theory states that matter consists of indivisible atoms, and chemical reactions involve the reorganization of these atoms in simple whole-number ratios.

2. Laws explained by Dalton's Theory:
Dalton's atomic theory successfully explained the laws of chemical combination based on mass, including:
- Law of conservation of mass: Since atoms are indivisible and cannot be created or destroyed in a chemical reaction, the total mass remains constant.
- Law of constant/definite proportion: Compounds are formed by the combination of atoms of different elements in a fixed ratio by mass.
- Law of multiple proportion: When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.

3. Why it could not explain the Law of Gaseous Volumes:
Gay-Lussac's Law of Gaseous Volumes states that when gases combine or are produced in a chemical reaction, they do so in a simple ratio by volume, provided all gases are at the same temperature and pressure.
Dalton's theory did not distinguish between the ultimate particle of an element (atom) and the ultimate particle of a compound (which we now call a molecule). According to Dalton, atoms of the same element combine to form compounds, but he did not support the idea of diatomic gaseous molecules (like $H_2$ or $O_2$).
Because Dalton's theory was strictly based on mass relations of indivisible atoms and did not account for gaseous volumes or molecular existence under Avogadro's hypothesis, it could not explain Gay-Lussac's law of gaseous volumes.