Question

Why does $1amu = 1g/mol$?

Answer 1

We have to know that the mass of a single atom of an element [amu] is numerically equal to the mass [g] of 1 mol of that element, regardless of the element. A mole is defined as the amount of substance of a system that contains as many elementary entities as there are atoms in 12 g of carbon-12.

Complete answer:
We need to remember that Avogadro’s number is a proportion that relates molar mass on an atomic scale to physical mass on a human scale. Avogadro’s number is defined as the number of elementary particles (molecules, atoms, compounds, etc.) per mole of a substance. It is equal to $6.022 \times {10^{23}}mo{l^{ - 1}}$and is expressed as the symbol ${N_A}$.
The mole is defined as the number of particles in $12g$ of carbon$- 12$, known as ${}^{12}C$. So, we say that in one mole of carbon$- 12$, the sample has a mass of $12g$.
In other words,
Mass of carbon $- 12 = 12g/mol$
Now, we also know that the mass of a single carbon-12 atom is exactly $12amu$, as it is an isotope.
And so, Mass of carbon$- 12 = 12amu/atom$
Combining, we have:
$12amu/atom = 12g/mol$
$\Rightarrow 1amu/atom = 1g/mol$
Avogadro’s number is that the mass of one mole of a substance is equal to that substance’s molecular weight. For example, the mean molecular weight of water is $18.015$ atomic mass units (amu), so one mole of water weighs $18.015$ grams. This property simplifies many chemical computations.

Note:
We need to know that each ion, or atom, has a particular mass; similarly, each mole of a given pure substance also has a definite mass. The mass of one mole of atoms of a pure element in grams is equivalent to the atomic mass of that element in atomic mass units (amu) or in grams per mole (g/mol). Although mass can be expressed as both amu and g/mol, g/mol is the most useful system of units for laboratory chemistry.