Question

A copper plate of \[20cm \times 10cm\] is to be plated with silver of \[1{\text{ }}mm\] thickness. The number of silver atoms required for the plating is: (density of silver = \[{\mathbf{10}}.{\mathbf{8}}{\text{ }}{\mathbf{g}}/{\mathbf{c}}.{\mathbf{c}})\]
a)$1.2 \times {10^{24}}$
b)$2.4 \times {10^{24}}$
c)$1.2 \times {10^{13}}$
d)$2.4 \times {10^{23}}$

Answer 1

Hint: A mole is defined as the quantity of substance containing the same number of entities (atoms, molecules or ions) as that present in \[12grams\] of ${}^{12}C$ isotope. As a gram molecular weight or gram atomic weight of a substance contains Avogadro's number of particles ($6.023 \times {10^{23}}$ atoms, molecules or ions)
The number of moles in “g” grams of a substance whose molar mass is ‘M’, $n = \dfrac{g}{{GMW}}$ or $n = {\dfrac{g}{M}_0}$ i.e. \[Number{\text{ }}of{\text{ }}molecules = \dfrac{{weight}}{{gram{\text{ }}molecular{\text{ }}weight}}\]

Complete step by step solution:
Number of molecules in $'n'\,moles = \dfrac{g}{{{M_0}}} \times {N_0}$
Volume of copper plate $ = $ $20 \times 10 \times 0.1cc$ $(l \times b \times h)$
As volume $ = $ $length \times breadth \times height$
$\therefore $ Volume of silver required to plate the copper plate $ = $ $20cc$
Given density of silver $ = 10.8g/cc$
Mass of silver required for copper plating $ = volume \times density = 20 \times 10.8gms$
$\therefore $Number of molecules of silver required for plating $ = \dfrac{g}{{{M_0}}} \times {N_0}$
Thus number of molecules $ = \dfrac{{20 \times 10.8}}{{108}} \times {N_0}$ $ = \dfrac{{20 \times 10.8}}{{108}} \times 6.023 \times {10^{23}}$
$ =2 \times 6.023 \times {10^{23}}\,molecules$
$ = 12.046 \times {10^{23}} = 1.2 \times {10^{24}}\,molecules$

Hence, option “A” is correct

Note:
Density is a measure of mass per unit of volume. Density is a measure of mass per volume. The average density of an object equals its total mass divided by its total volume.
Mass: mass is a physical property of a body. It arises due to acceleration due to gravity. An object’s mass determines the strength of its gravitational attraction to other bodies.
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.