Chapter 2, Problem 2.77QA

Interpretation Introduction

To find:

Which substance contains more moles of oxygen?

Answer to Problem 2.77QA

Solution:

a) Both contain same mol of O.

b) N₂O₄

c) CO₂.

Explanation of Solution

Calculations:

A mole is the SI unit of amount chemical substance. When writing units, it is written as “mol”.

a) $1$ mol Al₂O₃ or $1$ mol of Fe₂O₃

In one molecule of Al₂O₃, there are three atoms of oxygen. So we can say, the mole ratio between Al₂O₃ and O is $1:3$. Now we have the mole to mole ratio and moles of Al₂O₃ so we can calculate the moles of oxygen by using dimensional analysis as below,

$1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3\times \frac{3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3}=3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}$

In one molecule of Fe₂O₃, there are three atoms of oxygen. So we can say, the mole ratio between Fe₂O₃ and O is $1:3$. Now we have the mole to mole ratio and moles of Fe₂O₃ so we can calculate the moles of oxygen by using dimensional analysis as below,

$1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3\times \frac{3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3}=3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}$

So $1$ mole Al₂O₃ and $1$ mole of Fe₂O₃ both contains same $3$ moles of oxygen

b) $1$ mol of SiO₂ or $1$ mol N₂O₄.

In one molecule of SiO₂, there are two atoms of oxygen. So we can say, the mole ratio between SiO₂ and O is $1:2$. Now we have the mole to mole ratio and moles of SiO₂ so we can calculate the moles of oxygen by using dimensional analysis as below,

$1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{S}\mathrm{i}\mathrm{O}}_2\times \frac{2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{S}\mathrm{i}\mathrm{O}}_2}=2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }O$

In one molecule of N₂O₄, there are four atoms of oxygen. So we can say, the mole ratio between N₂O₄ and O is $1:4$. Now we have the mole to mole ratio and moles of N₂O₄ so we can calculate the moles of oxygen by using dimensional analysis as below,

$1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{{\mathrm{N}}_2\mathrm{O}}_4\times \frac{4\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}\mathrm{ }}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{{\mathrm{N}}_2\mathrm{O}}_4}=4\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }O$

So $1$ mole of N₂O₄ contains more moles of oxygen than $1$ mole SiO₂.

c) $3$ mol of CO or $2$ mol of CO₂.

In one molecule of CO, there is one atom of oxygen. So we can say, the mole ratio between CO and O is $1:1$. Now we have the mole to mole ratio and moles of CO so we can calculate the moles of oxygen by using dimensional analysis as below,

$3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{C}\mathrm{O}\times \frac{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}\mathrm{ }}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{C}\mathrm{O}}=3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }O$

In one molecule of CO₂, there are two atoms of oxygen. So we can say, the mole ratio between CO₂ and O is $1:2$. Now we have the mole to mole ratio and moles of CO₂ so we can calculate the moles of oxygen by using dimensional analysis as below,

$2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{C}\mathrm{O}}_2\times \frac{2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{C}\mathrm{O}}_2}=4\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{O}$

So, $2$ mole of CO₂ contains more number of moles of oxygen than $3$ moles of CO.

Conclusion:

The number of moles of the oxygen calculated from the number of moles of compounds and mole ratio between them.