Avogadro made the distinction between atoms and molecules, which today seems clear. However, Dalton rejected Avogadro's hypothesis because Dalton believed that atoms of the same kind could not combine. Since it was believed that atoms were held together by an electrical force, only unlike atoms would be attracted together, and like atoms should repel. Therefore it seemed impossible for a molecule of oxygen, O2, to exist. Avogadro's work, even if it was read appears not to have been understood, and was pushed into the dark recesses of chemistry libraries and ignored. Avogadro continued to teach at the university of Turin, when it was not closed because of the political upheavals going on in Italy at the time, and died in 1854, an unknown figure. 

Avogadro's Law:
Avogadro's Law, proposed by Amedeo Avogadro in 1811, states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. This law was crucial in understanding the distinction between atoms and molecules.

Explanation:
- Dalton's Atomic Theory: Dalton's atomic theory, proposed by John Dalton in the early 19th century, laid the foundation for modern chemistry by stating that all matter is composed of indivisible particles called atoms. This theory helped in understanding the existence of atoms as the building blocks of matter.
- Laws of Chemical Combination: The laws of chemical combination, including the law of definite proportions and the law of multiple proportions, helped in understanding how atoms combine to form molecules and compounds. These laws provided insight into the composition and behavior of different substances.
- Avogadro's Law: Avogadro's Law specifically addressed the distinction between atoms and molecules by highlighting that equal volumes of gases contain the same number of molecules. This law helped in quantifying the relationship between the volume of a gas and the number of molecules present, leading to a better understanding of molecular composition.
- Gay-Lussac's Law: Gay-Lussac's Law, also known as the Law of Combining Volumes, states that when gases react, they do so in volumes that are in simple ratios to each other. This law further supported the concept of molecular composition and the relationship between different gases in chemical reactions.
In conclusion, Avogadro's Law played a crucial role in distinguishing between atoms and molecules by providing a quantitative relationship between the volume of gases and the number of molecules present. This law, along with other fundamental principles in chemistry, helped in shaping our understanding of the composition and behavior of matter at the molecular level.