Question

Common salt obtained from sea-water contains $95\% {\text{NaCl}}$ by mass. The approximate number of molecules present in $10{\text{g}}$ of salt is:
A. ${10^{21}}$
B. ${10^{22}}$
C. ${10^{23}}$
D. ${10^{24}}$

Answer 1

Hint: A mole is simply a unit of measurement. One mole of a molecule has $6.02 \times {10^{23}}$ atoms. This particular number is called Avogadro number. Relative atomic mass of an element in the periodic table is the mass of one mole of that atom. In the case of molecules, composition is given by its molecular formula.

Complete step by step answer:
Concentration is the amount of solute dissolved in a given amount of solution. There are different types of concentration units. Formula and molecular mass deal with individual atoms and molecules. Mole is the unit that relates the number of particles and mass.
One mole of an element contains $6.022 \times {10^{23}}$ particles. This absolute number is called Avogadro’s number. Mass of one mole of substance is called molar mass. Or molar mass of an element is equal to the molecular weight.
It is given that the percentage of ${\text{NaCl}}$ by mass, $\% {\text{NaCl = 95\% }}$
And mass of salt, ${{\text{m}}_{{\text{salt}}}} = 10{\text{g}}$
$\% {\text{NaCl}}$ value indicates that in $100{\text{g}}$ of common salt $95{\text{g}}$ is ${\text{NaCl}}$
Amount of ${\text{NaCl}}$ in $10{\text{g}}$ of salt, ${{\text{m}}_{{\text{NaCl}}}} = \dfrac{{95{\text{g}}}}{{100{\text{g}}}} \times 10{\text{g = 9}}{\text{.5g}}$
We have to calculate the number of molecules in $10{\text{g}}$ of salt. For that initially we have to calculate the number of moles of ${\text{NaCl}}$ which is obtained by dividing the mass of ${\text{NaCl}}$ in $10{\text{g}}$ of salt by the molar mass of ${\text{NaCl}}$.
i.e. Number of moles of ${\text{NaCl}}$, ${{\text{n}}_{{\text{NaCl}}}} = \dfrac{{{{\text{m}}_{{\text{NaCl}}}}}}{{{{\text{M}}_{{\text{NaCl}}}}}}$
Molar mass of ${\text{NaCl}}$, ${{\text{M}}_{{\text{NaCl}}}} = 58.5{\text{gmo}}{{\text{l}}^{ - 1}}$
Substituting the values in the equation, we get
${{\text{n}}_{{\text{NaCl}}}} = \dfrac{{9.5{\text{g}}}}{{58.5{\text{gmo}}{{\text{l}}^{ - 1}}}} = 0.1623{\text{mol}}$
One mole of ${\text{NaCl}}$ contains $6.022 \times {10^{23}}$ molecules.
Thus $0.1623{\text{mol}}$ of ${\text{NaCl}}$ contains $0.1623{\text{mol}} \times \left( {6.022 \times {{10}^{23}}} \right)$ molecules.
Therefore the number of molecules of ${\text{NaCl}}$ in $10{\text{g}}$ of salt $ = 9.7 \times {10^{22}}$
So option B is correct.

Note:
Moles relate the mass of a single atom in ${\text{amu}}$ to the mass in grams. Moles to atoms or molecules conversions can be done by multiplying with Avogadro number. Atoms or molecules to moles conversions can be done by dividing by Avogadro number. Moles to grams conversion is moles times molar mass.