Question

The number of silver atoms present in a $90\%$ pure silver wire weighing $10{\text{g}}$ is:
A.$5.57 \times {10^{22}}$
B.$0.62 \times {10^{23}}$
C.$5.0 \times {10^{22}}$
D.$6.2 \times {10^{29}}$

Answer 1

:Hint: Try to find the number of moles of silver in the given mass of substance. Use the number of moles of silver to find the number of atoms present in that amount of silver using the Avogadro’s number $6.022 \times {10^{23}}$ .

Complete step by step answer:
First we will calculate the number of moles of silver present in the given amount of substance. As it is given in the question that the silver wire is $90\%$ pure which means $100{\text{g}}$ of pure wire contains only $90{\text{g}}$ of silver by mass in it. Since, the mass of given wire is $10{\text{g}}$ , thereby it contains $9{\text{g}}$ pure silver and $1{\text{g}}$ other substance in it. Now, to calculate number of moles of silver in $9{\text{g}}$ of pure silver, we can use the formula:
${\text{number of moles}} = \dfrac{{{\text{given mass}}\left( {{\text{in gram}}} \right)}}{{{\text{molar mass}}\left( {{\text{gmo}}{{\text{l}}^{ - 1}}} \right)}}$ , putting the given mass of silver which is $9{\text{g}}$ and as we know molar mass or mass of 1 mole of silver equals to $108{\text{gmo}}{{\text{l}}^{ - 1}}$ , we get: ${\text{number of moles}} = \dfrac{9}{{108}} = 0.083$ .
Now 1 mole of substance contains ${{\text{N}}_{\text{A}}}$ entities or $6.022 \times {10^{23}}$ entities, as we have $0.083{\text{mol}}$ of silver, the number of atoms of silver in $0.083{\text{mol}}$ can be given as:
${\text{number of atom}} = {\text{number of moles}} \times 6.022 \times {10^{23}}$ , ${\text{number of atom}} = 0.083 \times 6.022 \times {10^{23}}$ .
On solving, we get number of atoms in $0.083{\text{mol}}$ of silver or we can say in $90\%$ pure silver wire weighing $10{\text{g}}$ equals to $0.5 \times {10^{23}}$ atoms.

Thus, the correct option is C. As $0.5 \times {10^{23}}$ equals to $5.0 \times {10^{22}}$ .
Note:
Mole is the SI unit of amount of substance. It is defined as the amount of a substance that contains as many entities as there are atoms present in exactly $12{\text{g}}$ of carbon $\left( {{{\text{C}}^{12}}} \right)$. Mole is a concept of quantity in terms of number, mass and volume. For a given balanced equation, information of reactant or product can be determined if information of one of the species is given either in terms of moles, molecules or weight. 1 mole is equivalent to ${{\text{N}}_{\text{A}}}$ atoms, molecules, ion, or electrons. 1 mole is equivalent to molecular weight or atomic weight of a substance. 1 mole is equivalent to the volume of $22.4{\text{L}}$ of any gas occupied at NTP condition.