According to Avogadro's hypothesis, two samples of gas of equal volume, at the same temperature and pressure, contain the same number of molecules. But is there any proof of this? We can't possibly count the total molecules in two different gases of equal volumes at equal temperature and pressure. Then how did we arrive at this hypothesis? If not experemental, is there any Mathematical proof of this statement?

Even the exact number of atoms or molecules in 1 mole of any substance is known and is termed as Avogadro's Number. How was is found? How did we know the exact number of molecules present in 1 mole of a substance? Please provide the derivation if any.

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Solution

1 mole =602,214,150,000,000,000,000,000 Avogadro's Number

Avogadro's number, the number of particles in a mole, can be experimentally determined by first "counting" the number of atoms in a smaller space and then scaling up to find the number of particles that would have a mass equal to the atomic or molecular mass in grams. Here is some real data from which Avogadro's number can be determined.
X-Ray diffraction studies show that gold consists of a repeating atomic arrangement where the repeating unit (called a cell unit) is a cube containing 4 gold atoms. Each side of the cube has a length of 4.08x10-8 cm. The density of gold is 19.3 g / cm3 and its atomic mass is 197.

v= side3= (4.08 x 10-8cm)3= 6.79 x 10-23cm3
197g
X 1 cm3 X 4 atoms=6.013 x 1023 atoms/mole (pretty close)
mol
19.3g6.79 x 10-23cm3
The History of the Term"Mole"
The Avogadro constant is named after the early nineteenth century Italian scientist Amedeo Avogadro, who is credited (1811) with being the first to realize that the volume of a gas (strictly, of an ideal gas) is proportional to the number of atoms or molecules. The French chemist Jean Baptiste Perrin in 1909 proposed naming the constant in honor of Avogadro. American chemistry textbooks picked it up in the 1930's followed by high school textbooks starting in the 1950s.
The unit "mole" was introduced into chemistry around 1900 by Ostwald, and he originally defined this unit in terms of gram. Gram is a unit of mass; but what is the mole a unit of? Ostwald did not say; however, several years later, he did make it clear that the concept of mole should be linked to the ideal gas.

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Similar questions

According to Avogadro's Law, "Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules". But how is this statement correct? How do we know that equal number of molecules are present in two gases taken in equal volumes?

Even if we consider equal volumes of any two gases(let's consider two gases for example) contain equal number of molecules, if we have the two gases in two containers of same volumes, we can add more gas to any one container and increase the density of the gas inside the container. In that case, the volume of the gas remains equal to the volume of the container but the number of gas molecules inside the container has increased and there is no chage to the number of molecules of the other gas we took inside a similar container. So now we have equal volumes of two gases but we have increased the number of molecules of one gas so now how can we say that the equal volumes of these two gases contain equal number of molecules?

If we take equal number of molecules of two gases and contain one of the gas in a container of some volume and the other gas in a container of a different volume, we will have unequal volumes of two gases having equal number of particles.

So how is Avogadro's Law explained?

Q. 'Equal volumes of all gases at the same temperature and pressure contain equal number of molecules'. This law is called as

Read the given statements carefully.

(i) Equal volumes of gases contain equal number of molecules at the same temperature and pressure.
(ii) 273 K and $1.015 \times 10^{5}$ Pa are considered as standard temperature and pressure.
(iii) Equal volumes of gases contain unequal number of molecules at the same temperature and pressure.
(iv) At STP, one mole of any gas will have a volume of 22.4 L.

Which of the following statements are correct?

Q. The proposition 'equal volumes of different gases contain equal numbers of molecules at the same temperature and pressure' is known as _____.

Q. Equal volumes of all gases, at the same temperature and pressure, have equal number of molecules. Which law states this?

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