Question

What is a unified atomic mass unit$?$ How is it equivalent to $1\,g\,mo{l^{ - 1}}\,?$

Answer 1

Hint: Unified mass unit also known as Dalton $($represented by Da or u$)$is a unit to represent atomic and molecular mass wildly used in the field of chemistry and physics. Try to represent it in terms of mass of unbound $^{12}C$ atoms and from there express the unified atomic mass unit in terms of $g\,mo{l^{ - 1}}$.

Complete step-by-step answer:
The dalton or unified atomic mass unit $($generally represented by Da or u$)$ is a unit of mass widely used in physics and chemistry to represent atomic or molecular mass. Da is defined as ${\dfrac{1}{{12}}^{th}}$ the mass of an unbound neutral atom of $^{12}C$ in its nuclear and electronic ground state and at rest.

The relationship of the unified atomic mass unit to the macroscopic SI base unit of mass, $kg$, is given by Avogadro's number ${N_A}$. By the definition of Avogadro's number, the mass of ${N_A}$ $^{12}C$ atoms, at rest and in their ground state, is $12\,g\, = \,\left( {12 \times {{10}^{ - 3}}} \right)\,kg$. From the latest value of ${N_A}$ follows the latest value of the unified atomic mass unit:
$1\,u\, \approx 1.660538782 \times {10^{ - 27}}\,kg$.

The mole is a unit of substance, which was originally defined so that the mass of one mole of a substance measured in grams would be numerically equal to the average mass of one of its constituent particles measured in daltons. That is, the molar mass of a chemical compound was meant to be numerically equal to its average molecular mass, i.e. $1\,Da\, \approx \,1\,g\,mo{l^{ - 1}}$.

Note: We should not get confused between the unified atomic mass unit or Dalton with the unit of mass in the atomic units systems, which is instead the electron rest mass $\left( {{m_e}} \right)$. Also remember that $1\,Da\, \approx \,1\,g\,mo{l^{ - 1}}$ is perfectly true for $^{12}C$, it varies accordingly for others.