Why is Amount of Mole in Grams Equal to Atomic Mass?

[batballbat]

Why is the amount of mole in gms. of an element the same as the its atomic mass. Is it just because $N_a X 1 u = 1$. Am i missing some simple reasoning behind this? Or was the carbon 12 taken exactly to make this valid?

 

[Borek]

Simple answer - atomic unit was selected to make it happen.

N_a X 1 u = 1

Or was the carbon 12 taken exactly to make this valid?

In a way you listed the same reason twice. Note what happens when you list units:

$$N_a[\frac{atom}{mole}] \times u[\frac{g}{atom}] = 1[\frac{g}{mole}]$$

 

[morrobay]

You can also take a numerical example :

1 atomic mass unit = 1.6605655 x 10^-24 grams
Once it is determined that 1 gram Hydrogen contains :
1 g. H / 1.6605655 x 10^-24 g = 6.02 x 10²³
1 mole H = Avogadro's number. Then it follows for 1 mole of any other element.
Take 40 grams of Zr :
40 g. Zr/ 40 * 1.660565 x 10^-24 g. =
40 g. Zr / 6.642 x 10^-23 g = 6.02 x 10 ²³

 

[morrobay]

You can also take a numerical example :

1 atomic mass unit = 1.6605655 x 10^-24 grams
Once it is determined that 1 gram Hydrogen contains :
1 g. H / 1.6605655 x 10^-24 g = 6.02 x 10²³
1 mole H = Avogadro's number. Then it follows for 1 mole of any other element.
Take 40 grams of Zr :
40 g. Zr/ 40 * 1.660565 x 10^-24 g. =
40 g. Zr / 6.642 x 10^-23 g = 6.02 x 10 ²³

This should be 91 grams Zr :
so : 91 grams Zr / 91 * 1.66 x 10 ^ -24 g
= 91 g Zr / 15.1 x 10^-23 g = 6.02 x 10^23

 

[LudusRex]

The amount of mole in grams being equal to the atomic mass of an element is a fundamental concept in chemistry and is known as Avogadro's law. This law states that equal volumes of different gases at the same temperature and pressure contain the same number of molecules. In other words, the amount of substance in moles is directly proportional to the mass of that substance in grams.

The reason for this relationship is due to the definition of a mole. A mole is defined as the amount of a substance that contains the same number of particles as there are atoms in 12 grams of carbon-12. This means that one mole of any element will always contain the same number of atoms, which is known as Avogadro's number (6.022 x 10^23).

Since the atomic mass of an element is the mass of one mole of that element in grams, it follows that the amount of mole in grams will be equal to the atomic mass. This can also be seen in the equation you mentioned, where the number of atoms (represented by Avogadro's number) multiplied by the atomic mass in unified atomic mass units (u) will equal one gram.

Therefore, the relationship between the amount of mole in grams and the atomic mass is not just a coincidence, but rather a result of the definition of a mole and Avogadro's law. The use of carbon-12 as the standard for atomic mass is simply a convention and does not affect the validity of this relationship.