Question

1 gram of iron (Fe) contains ----atoms.
(Molecular Weight of Fe=\[{\text{56}}\,{\text{g/mol}}\])
A) \[{\text{1}}{\text{.075}} \times {10^{25}}\]
B) \[{\text{1}}{\text{.075}} \times {10^{22}}\]
C) \[{\text{1}}{\text{.075}} \times {10^{26}}\]
D) \[{\text{1}}{\text{.075}} \times {10^{27}}\]

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 \[{\text{6}}{.023 \times 1}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}\].

Complete answer:
Here, the molecular weight of the iron given is \[{\text{56}}\,{\text{g/mol}}\] and the weight of the iron is one gram.
We have to determine the first moles of the iron in one gram as follows:
\[{\text{moles = }}\dfrac{{{\text{weight}}}}{{{\text{Molecular}}\,{\text{weight}}}}\]
Substitute, \[{\text{56}}\,{\text{g/mol}}\] for molecular weight and 1 gram for weight.
\[{\text{moles = }}\dfrac{{1\,{\text{g}}}}{{{\text{56}}\,{\text{g/mol}}}}\]
\[{\text{moles = 0}}{\text{.0178571}}\,{\text{mol}}\]
Thus, the moles of the iron in one gram are \[{\text{0}}{\text{.0178571}}\,{\text{mol}}\].
Now, determine the molecules of the Fe in the one gram as follows:
As we know that one mole of the substance contains Avogadro’s numbers of molecules.
\[{\text{1mol}}\,{\text{ = }}\,{{\text{N}}_{\text{A}}}{\text{ = 6}}{.023 \times 1}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}\]
\[{\text{0}}{\text{.0178571}}\,{\text{mol = }}\dfrac{{{\text{0}}{\text{.0178571}}\,{mol \times 6}{.023 \times 1}{{\text{0}}^{{\text{23}}}}\,{\text{molecules}}}}{{{\text{1mol}}\,}}\]
\[{\text{0}}{\text{.0178571}}\,{\text{mol = 1}}{.07553 \times 1}{{\text{0}}^{{\text{22}}}}\,{\text{molecules}}\]
Thus, the molecules of Fe in one gram are \[{\text{1}}{\text{.075}} \times {10^{22}}\].
Here, option(A) \[{\text{1}}{\text{.075}} \times {10^{25}}\] is incorrect.
Option (C) \[{\text{1}}{\text{.075}} \times {10^{26}}\] is incorrect.
Now, option(D) \[{\text{1}}{\text{.075}} \times {10^{27}}\] is incorrect.
Option(B) \[{\text{1}}{\text{.075}} \times {10^{22}}\] is the correct answer to the question.

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.In the question,the molecular weight of the iron is given which is the atomic mass of the iron. 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.