Question

What is the mass of $3.011\times {10}^{20}$molecules of mercury? Given: Atomic weight of mercury is 200.

Answer 1

Hint: A molecule is a chemically bound collection of two or more atoms that are electrically neutral. Molecules differ from ions in that they do not have an electrical charge. In quantum physics, organic chemistry, and biochemistry, the difference between ions and molecules is typically omitted, and polyatomic ions are referred to as molecules.

Complete answer:
The atomic mass of an element is a weighted average of all its isotopes, where the mass of each isotope is multiplied by the abundance of that isotope. (Atomic mass is also known as atomic weight, but "mass" is a more precise phrase.)
The Avogadro constant is a proportionality factor that links the number of component particles in a sample (typically molecules, atoms, or ions) to the amount of material in that sample. The reciprocal mole is its SI unit, and it is defined as $N_a=6.023\times {10}^{23}$ . It is named after Amedeo Avogadro, an Italian physicist. Although Avogadro's constant (or number) is named after him, he was not the scientist who discovered its value. At the Karlsruhe Congress in 1860, Stanislao Cannizzarro explained this figure four years after Avogadro's death.
We know that
${\displaystyle \frac{\text{Given mass}}{\text{Atomic Mass}}}\text{ = }{\displaystyle \frac{\text{Given number of molecules}}{\text{Avagadro number}}}$
Upon substitution we get
${\displaystyle \frac{x}{200}}={\displaystyle \frac{3.011\times {10}^{20}}{6.023\times {10}^{23}}}$
We need to find x
$x={\displaystyle \frac{3.011\times {10}^{20}}{6.023\times {10}^{23}}}\times 200$
x = 0.01 g

Note:
The relative isotopic mass and the atomic mass of an isotope relate to a specific isotope of an element. Because most substances are not isotopically pure, the elemental atomic mass, which is the average (mean) atomic mass of an element, weighted by the quantity of the isotopes, is a handy measurement. The weighted mean relative isotopic mass of a (typical naturally-occurring) combination of isotopes is the dimensionless (standard) atomic weight. Due to binding energy mass loss, the atomic mass of atoms, ions, and atomic nuclei is somewhat less than the total of the masses of their component protons, neutrons, and electrons.