Question

How many ${\text{Fe}}$ atoms are contained in $787{\text{ g}}$ of ${\text{Fe}}$?

Answer 1

Hint:We are given the mass of a substance i.e. ${\text{Fe}}$. To solve this first calculate the number of moles of ${\text{Fe}}$ in $787{\text{ g}}$ of ${\text{Fe}}$. We know that ${\text{1 mol}}$ of any substance contains $6.022 \times {10^{23}}$ atoms. $6.022 \times {10^{23}}$ is Avogadro's number. Then calculate the number of atoms of ${\text{Fe}}$ in $787{\text{ g}}$ of ${\text{Fe}}$.

Complete answer:
We are given the mass of a substance i.e. ${\text{Fe}}$. The number of moles of any substance is the ratio of mass (in grams) to the molar mass (in gram per mol).
Thus, the equation to calculate the number of moles is as follows:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}$
Substitute $787{\text{ g}}$ for the mass, $55.84{\text{ g/mol}}$ for the molar mass. Thus,
Number of moles of ${\text{Fe}}$ $ = \dfrac{{787{\text{ g}}}}{{55.84{\text{ g/mol}}}}$
Number of moles of ${\text{Fe}}$ $ = 14.09{\text{ mol}}$
Thus, moles of ${\text{Fe}}$ in $787{\text{ g}}$ of ${\text{Fe}}$ is $14.09{\text{ mol}}$.
We know that the amount of substance having exactly the same number of atoms as are present in $12{\text{ g}}$ of ${{\text{C}}^{{\text{12}}}}$ is known as mole. Moles is the ratio of the mass of substance in g to the molar mass of the substance in \[{\text{g/mol}}\]. ${\text{1 mol}}$ of any substance contains $6.022 \times {10^{23}}$ atoms. $6.022 \times {10^{23}}$ is Avogadro's number.
We know that ${\text{1 mol}}$ of any substance contains $6.022 \times {10^{23}}$ atoms. We have $14.09{\text{ mol}}$ of ${\text{Fe}}$. Thus,
Number of ${\text{Fe}}$ atoms $ = 14.09{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}}$
Number of ${\text{Fe}}$ atoms $ = 84.84 \times {10^{23}}{\text{ atoms}}$
Thus, $787{\text{ g}}$ of ${\text{Fe}}$ contains $84.84 \times {10^{23}}$ atoms of ${\text{Fe}}$.

Note: Amount of substance having exactly the same number of atoms as are present in 12 grams of ${{\text{C}}^{{\text{12}}}}$ is known as mole. The number of molecules in one mole of a compound is Avogadro’s number. The number $6.022 \times {10^{23}}$ is known as Avogadro’s number.