Question

How many atoms are there in ${\text{1}}\,{\text{kg}}$ of silver
A) ${\text{2}}{\text{.03}} \times {{\text{10}}^{{\text{23}}}}$ atoms
B) ${\text{5}}{\text{.57}}\times {{\text{10}}^{{\text{24}}}}$ atoms
C) ${\text{4}}{\text{.27}}\times {{\text{10}}^{{\text{ - 23}}}}$ atoms
D) ${\text{6}}{\text{.23 }} \times {{\text{10}}^{{\text{23}}}}$ atoms

Answer 1

Hint:A mole is a collection of \[{\text{6}}{\text{.023}}\times {{\text{10}}^{{\text{23}}}}\] particles, ions, atoms etc.
Avogadro Number \[{{\text{N}}_{\text{A}}}\]: The number of carbon atoms present in one gram-atom (1 mole atom) of \[{\text{C-12}}\] isotope is called Avogadro’s number. One gram-atom (\[{\text{12 grams}}\]) of \[{\text{C-12}}\] contains \[6.023 \times {10^{23}}\] atoms. Thus the numerical value of Avogadro’s number (\[{{\text{N}}_{\text{A}}}\]) is \[{\text{6}}{\text{.023}}\times {{\text{10}}^{{\text{23}}}}{\text{ per mol}}\].
It should be noted that
\[\;1{\text{ }}a.m.u. = \dfrac{1}{{12}}th{\text{ }}of{\text{ }}mass{\text{ }}of{\text{ }}a{\text{ }}{C^{12}}\;atom\]

Complete answer:
Number of moles = \[\dfrac{{{\text{Mass}}\;{\text{of}}\;{\text{substance}}\;{\text{in}}\;{\text{grams}}}}{{{\text{Molecular}}\;{\text{weight}}\;{\text{in}}\;{\text{grams}}}}\]
One mole of every gas occupies \[{\text{22}}{\text{.4 lit}}{\text{.}}\]of volume at STP.
i.e. 1 mole of ${{\text{O}}_{\text{2}}}$ occupies \[{\text{22400 ml}}\] of volume at STP.
 1 mole of He occupies \[{\text{22400 ml}}\] of volume at STP.
Number of moles = \[\dfrac{{'V'\;of\;gas\;in\;litres\;at\;STP\;}}{{22.4}}\]
Silver atomic weight \[{\text{ = 108}}\]
Therefore, \[{\text{108 grams}}\] of silver contains \[6.023{\text{ }} \times {\text{ }}{10^{23}}\] atoms of silver
1kg of silver contains how much of atoms
\[\Rightarrow {\text{1000 gms}}\] of silver contains $ = \dfrac{{1000}}{{108}} \times 6.023 \times {10^{23}}$ atoms of silver
 ${\text{ = 5}}{\text{.57}} \times {{\text{10}}^{{\text{24}}}}{\text{ atoms}}$

Option B is correct

Note:
\[{\text{6}}{\text{.023}}\times {{\text{10}}^{{\text{23}}}}\] atoms of Na constitute one mole atom of Na.
One mole of every substance weighs equal to the gram atomic weight of the substance or to the gram molecular weight of the substance.
\[{\text{No}}{\text{. of moles = }}\dfrac{{{\text{Number}}\;{\text{of}}\;{\text{particles}}}}{{{\text{6}}{\text{.023}}\times {{\text{10}}^{{\text{23}}}}}}\]
A mole of any substance is related to :
a. number of particles
b. mass of a substance
c. volume of the gaseous substance