Question

Avogadro number is equal to:
A. \[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{21 }}}}\]
B. \[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{22 }}}}\]
C. \[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23 }}}}\]
D. \[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{24 }}}}\]

Answer 1

Hint: Avogadro number is the number of atoms present in 1 mole of an atom. It is also defined as the number of molecules present in 1 mole of a substance.

Complete step by step answer:
>A mole of a substance is the mass of a substance that contains exactly the same number of fundamental units, as in 12.0 g of ${\text{C}}$.
>So, Avogadro’s number is the number of atoms present in 12.0 g of ${\text{C}}$ or a number of atoms present in 1 mole of atom.
>Similarly, Avogadro’s number also represents the number of molecules present in 1 mole of a substance.
Eg. Molecular weight of \[{\text{N}}{{\text{H}}_{\text{3}}}\] is 17 g/mol
So, 1 mole of \[{\text{N}}{{\text{H}}_{\text{3}}}\] that is 17g of \[{\text{N}}{{\text{H}}_{\text{3}}}\] contains Avogadro’s number of \[{\text{N}}{{\text{H}}_{\text{3}}}\] molecules.
Avogadro’s number is estimated using the charge of 1 mole of electrons and charge of 1 electron.
Charge of 1 mole of electrons = \[96485.3383{\text{ Coulombs}}\]
Charge of 1 electron = \[{\text{1}}{\text{.60217653}} \times {\text{1}}{{\text{0}}^{{\text{ - 19}}}}{\text{ Coulombs}}\]

Avogadro's number = $\dfrac {Charge\, of \,1 mol \,electron}{Charge\, of \,1 electron}$

Avogadro's number = $\dfrac {96485.3383}{1.60217653\times 10^{-19}}$

Avogadro's number = $6.023\times 10^{-19}$

Thus, the correct answer is an option (C) \[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23 }}}}\]

Additional Information: \[{{\text{H}}_{\text{2}}}\] Italian scientist Amedo Avogadro proposed Avogadro's law. The law states that the volume of gas is directly proportional to the number of moles of gas. French physicist Jean Baptiste Perrin in 1909 first estimated the Avogadro number. Avogadro number is used to calculate the number of particles (atoms/molecules) in a given mass of the substance.


Note: Avogadro number is a constant value. 1 mole of any substance always contains an Avogadro number of molecules (\[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23 }}}}\]). Like 1 mole of \[{\text{C}}{{\text{O}}_{\text{2}}}\](44.0g), 1 mole of (2.0g) and 1 mole of \[{{\text{N}}_{\text{2}}}\](28g) contain Avogadro number of molecules (\[{\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{{\text{23 }}}}\]).