Question

If one atom of an element ‘ $x$ ’ weighs $6.643 \times {10^{ - 23}}G$ . What will be the number of moles in $20Kg$ ?

Answer 1

A mole of a substance is equivalent to $6.023 \times {10^{23}}$ units of the substance (such as atoms, molecules, or ions).The quantity $6.023 \times {10^{23}}$ is known as the Avogadro number or Avogadro constant. The definition of the mole can be used to convert mass and number of particles.

Complete Step By Step Answer:
Given:
Mass of one atom $=$ $6.643 \times {10^{ - 23}}G$
Mass of ‘ $x$ ’ atom $=$ $20Kg$ or $20000g$
Therefore, $x = \dfrac{{20000}}{{6.643 \times {{10}^{ - 23}}}}$
$x = 3 \times {10^{ - 26}}g$
Using the above formula, we can find the number of moles
$Number{\text{ }}of{\text{ }}moles = \dfrac{{3 \times {{10}^{ - 26}}}}{{6.023 \times {{10}^{23}}}}$
On solving, we get
Number of moles $= 0.498 \times {10^{ - 3}}$
Number of moles $\Rightarrow 500$
Therefore, the number of moles is $= 500$ moles.

Note:
Avogadro's constant, or Avogadro number, is the number of units in one mole of any substance. Depending on the nature of the reaction and the type of product, the units may be ions, electrons, atoms, or molecules. Avogadro's number is represented by the symbol ${N_A}$ . Understanding the constitution of molecules, as well as their interactions and combinations, requires an understanding of Avogadro's number. Avogadro's number also has the property that the mass of one mole of a material is equal to the molecular weight of that substance.