Question

$80{\text{ g}}$ of oxygen contains as many atoms as in
A. $80{\text{ g}}$ of hydrogen
B. $1{\text{ g}}$ of hydrogen
C. $10{\text{ g}}$ of hydrogen
D. $5{\text{ g}}$ of hydrogen

Answer 1

Hint: 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 \[{\text{g/mol}}\].

Formula Used:
${\text{Number of moles}}\left( {{\text{mol}}} \right){\text{ = }}\dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}$

Complete step by step solution:
First we will calculate the number of moles of oxygen in $80{\text{ g}}$ of oxygen using the formula for the number of moles.
The molar mass of oxygen is $16{\text{ g/mol}}$. Thus,
${\text{Number of moles of oxygen = }}\dfrac{{{\text{80 g}}}}{{{\text{16 g/mol}}}}$
${\text{Number of moles of oxygen}} = 5{\text{ mol}}$
Thus, the number of moles of oxygen in $80{\text{ g}}$ of oxygen is $5{\text{ mol}}$.
We know that ${\text{1 mol}}$ of oxygen contains $6.022 \times {10^{23}}$ atoms. Thus,
${\text{Number of oxygen atoms}} = 5{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 30.11 \times {10^{23}}{\text{ atoms}}$
Thus, $80{\text{ g}}$ of oxygen contains $30.11 \times {10^{23}}{\text{ atoms}}$ of oxygen.

a. Now, we have to calculate the moles of hydrogen in $80{\text{ g}}$ of hydrogen. The molar mass of hydrogen is $1{\text{ g/mol}}$. Thus,
${\text{Number of moles of hydrogen = }}\dfrac{{{\text{80 g}}}}{{{\text{1 g/mol}}}} = 80{\text{ mol}}$
Thus, the number of moles of hydrogen in $80{\text{ g}}$ of hydrogen is $80{\text{ mol}}$.
We know that ${\text{1 mol}}$ of hydrogen contains $6.022 \times {10^{23}}$ atoms. Thus,
${\text{Number of hydrogen atoms}} = 80{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 481.76 \times {10^{23}}{\text{ atoms}}$
Thus, $80{\text{ g}}$ of hydrogen contains $481.76 \times {10^{23}}{\text{ atoms}}$ of hydrogen.

b. Now, we have to calculate the moles of hydrogen in $1{\text{ g}}$ of hydrogen. The molar mass of hydrogen is $1{\text{ g/mol}}$. Thus,
${\text{Number of moles of hydrogen = }}\dfrac{{1{\text{ g}}}}{{{\text{1 g/mol}}}} = 1{\text{ mol}}$
Thus, the number of moles of hydrogen in $1{\text{ g}}$ of hydrogen is $1{\text{ mol}}$.
We know that ${\text{1 mol}}$ of hydrogen contains $6.022 \times {10^{23}}$ atoms.
Thus, $1{\text{ g}}$ of hydrogen contains $6.022 \times {10^{23}}$ of hydrogen.

c. Now, we have to calculate the moles of hydrogen in $10{\text{ g}}$ of hydrogen. The molar mass of hydrogen is $1{\text{ g/mol}}$. Thus,
${\text{Number of moles of hydrogen = }}\dfrac{{10{\text{ g}}}}{{{\text{1 g/mol}}}} = 10{\text{ mol}}$
Thus, the number of moles of hydrogen in $10{\text{ g}}$ of hydrogen is $10{\text{ mol}}$.
We know that ${\text{1 mol}}$ of hydrogen contains $6.022 \times {10^{23}}$ atoms. Thus,
${\text{Number of hydrogen atoms}} = 10{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 60.22 \times {10^{23}}{\text{ atoms}}$
Thus, $10{\text{ g}}$ of hydrogen contains $60.22 \times {10^{23}}{\text{ atoms}}$ of hydrogen.

d. Now, we have to calculate the moles of hydrogen in $5{\text{ g}}$ of hydrogen. The molar mass of hydrogen is $1{\text{ g/mol}}$. Thus,
${\text{Number of moles of hydrogen = }}\dfrac{{5{\text{ g}}}}{{{\text{1 g/mol}}}} = 5{\text{ mol}}$
Thus, the number of moles of hydrogen in $5{\text{ g}}$ of hydrogen is $5{\text{ mol}}$.
We know that ${\text{1 mol}}$ of hydrogen contains $6.022 \times {10^{23}}$ atoms. Thus,
${\text{Number of hydrogen atoms}} = 5{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 30.11 \times {10^{23}}{\text{ atoms}}$
Thus, $5{\text{ g}}$ of hydrogen contains $30.11 \times {10^{23}}{\text{ atoms}}$ of hydrogen.
Thus,
$80{\text{ g}}$ of oxygen contains $30.11 \times {10^{23}}{\text{ atoms}}$ of oxygen. And, $5{\text{ g}}$ of hydrogen contains $30.11 \times {10^{23}}{\text{ atoms}}$ of hydrogen.
Thus,
$80{\text{ g}}$ of oxygen contains as many atoms as in $5{\text{ g}}$ of hydrogen.

Thus, the correct option is (D) $5{\text{ g}}$ of hydrogen.

Note:
The number of atoms of a compound is Avogadro’s number for 1 mole of compound. The number $6.022 \times {10^{23}}$ is known as Avogadro’s number.