Question

A 120 grams ${\text{NaCl}}$ is equal to how many molecules of ${\text{NaCl}}$?

Answer 1

Hint: The mole concept is used to determine the amount of the substance which is obtained by taking the ratio of the mass of the substance to the molecular mass of the substance.
One mole of the substance contains the Avogadro’s numbers of the particles that are atoms, ions, or molecules of the substance.
Avogadro’s number is represented as \[{{\text{N}}_{\text{A}}}\]. The value of Avogadro’s number is \[{\text{6}}{{.023 \times 1}}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}\].

Formula used: The mole of the substance contains Avogadro’s numbers of molecules.
\[{\text{1mole}}\,{\text{ = }}\,{{\text{N}}_{\text{A}}}{\text{ = 6}}{{.023 \times 1}}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}\]

Complete step by step answer:
Here, the molecular weight of the ${\text{NaCl}}$ given is \[{\text{58}}{\text{.44}}\,{\text{g/mol}}\] and the weight of the ${\text{NaCl}}$ is 120 grams.
We have to determine the first moles of the ${\text{NaCl}}$in 120 gram as follows:
\[ \Rightarrow {\text{moles = }}\dfrac{{{\text{weight}}}}{{{\text{Molecular}}\,{\text{weight}}}}\]

Substitute, \[{\text{58}}{\text{.44}}\,{\text{g/mol}}\] for molecular weight and 120 gram for weight.
\[ \Rightarrow {\text{moles = }}\dfrac{{120\,{\text{g}}}}{{{\text{58}}{\text{.44}}\,{\text{g/mol}}}}\]
\[{\text{moles = 2}}{\text{.0534}}\,{\text{mol}}\]

Thus, the moles of the ${\text{NaCl}}$ in 120 gram are \[{\text{2}}{\text{.0534}}\,{\text{mol}}\].
Now, determine the molecules of the ${\text{NaCl}}$ in the o120 gram as follows:
As we know that one mole of the substance contains Avogadro’s numbers of molecules.
\[ \Rightarrow {\text{1mol}}\,{\text{ = }}\,{{\text{N}}_{\text{A}}}{\text{ = 6}}{{.023 \times 1}}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}\]
\[ \Rightarrow {\text{2}}{\text{.0534}}\,{\text{mol = }}\dfrac{{{\text{2}}{\text{.0534}}\,{{mol \times 6}}{{.023 \times 1}}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}}}{{{\text{1mol}}\,}}\]
\[ \Rightarrow {\text{2}}{\text{.0534}}\,{\text{mol = 1}}{{.2367 \times 1}}{{\text{0}}^{{\text{24}}}}\,{\text{molecules}}\]

Thus, the molecules of ${\text{NaCl}}$in 120 gram are \[{\text{1}}{{.24 \times 1}}{{\text{0}}^{{\text{24}}}}\].

Note: Molecular weight is the average mass of the molecules and it is deferrable from molecule to molecule. In the case of the atom, it is called atomic mass while in the case of the molecular mass it is calculated by taking the sum of the atomic masses of all the atoms in the molecule. Here, we have to use the molecular weight of the ${\text{NaCl}}$. The SI unit of the molecular weight is gram per mole. Its unit itself indicates the ratio of the mass of the substance to the molar molecular mass of the substance.