Chapter 4, Problem 4.10PAE

4.10 How many moles of oxygen can be obtained by the decomposition of 7.5 mol of reactant in each of the following reactions?

1. ${\text{2KClO}}_{\text{3}}\to \text{2KCl }+{\text{ 3O}}_{\text{2}}$

${\text{2H}}_{\text{2}}{\text{O}}_{\text{2}} \to {\text{2H}}_{\text{2}}\text{O }+{\text{ O}}_{\text{2}}$

$\text{2HgO} \to \text{2Hg }+{\text{ O}}_{\text{2}}$

${\text{2NaNO}}_{\text{3}} \to {\text{2NaNO}}_{\text{2}}+{\text{ O}}_{\text{2}}$

${\text{KClO}}_{\text{4}} \to \text{KCl }+{\text{ 2O}}_{\text{2}}$

Interpretation Introduction

Interpretation:

The moles of oxygen that is obtained by the decomposition of 7.5 moles of reactant in each of the following reactions have to be calculated.

Concept Introduction:

• The molar ratio can be used to relate:
• The moles of product formed from certain moles of reactant.
• The moles of reactant needed to form certain moles of a product.
• The moles of a reactant needed to react with certain moles of a second reactant.

Given:

$\begin{array}{l}{\text{2 KClO}}_{\text{3}}\to {\text{2 KCl + 3O}}_{\text{2}}\\ {\text{2 H}}_2{\text{O}}_2\to {\text{2 H}}_2{\text{O + O}}_{\text{2}}\\ \text{2 HgO}\to {\text{2 Hg + O}}_{\text{2}}\\ {\text{2 NaNO}}_3\to {\text{2 NaNO}}_2{\text{ + O}}_{\text{2}}\\ {\text{KClO}}_4\to {\text{KCl+ 2 O}}_{\text{2}}\end{array}$

(a) To determine:

The moles of oxygen that is obtained by the decomposition of 7.5 moles of reactant ${\text{2 KClO}}_{\text{3}}\to {\text{2 KCl + 3O}}_{\text{2}}$.

Answer to Problem 4.10PAE

Solution:

a) 11.25 moles of O₂.

Explanation of Solution

Write the molar ratio between the ${\text{KClO}}_{\text{3}}\text{and}{\text{O}}_{\text{2}}$

2 moles of ${\text{KClO}}_{\text{3}}$ reacting with 3 moles of ${\text{O}}_{\text{2}}$.

So that, the molar ratio is:

$\frac{{\text{3 mol O}}_{\text{2}}}{{\text{2 moles KClO}}_{\text{3}}}$

Calculate the moles of ${\text{O}}_{\text{2}}$ produced

${\text{moles of O}}_2\text{ produced= 7}{\text{.5 moles KClO}}_{\text{3}}\times \frac{{\text{3 moles O}}_{\text{2}}}{{\text{2 moles KClO}}_{\text{3}}}=11.2{\text{5 moles of O}}_{\text{2}}$

Conclusion

a) 11.25 moles of ${\text{O}}_{\text{2}}$.

Interpretation Introduction

(b) To determine:

The moles of oxygen that is obtained by the decomposition of 7.5 moles of reactant of ${\text{2 H}}_2{\text{O}}_2\to {\text{2 H}}_2{\text{O + O}}_{\text{2}}$.

Answer to Problem 4.10PAE

Solution:

b) 3.75 moles of O₂.

Explanation of Solution

Write the molar ratio between the ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\text{and}{\text{O}}_{\text{2}}$

2 moles of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$ react with 1 mol of ${\text{O}}_{\text{2}}$

So that, the molar ratio is:

$\frac{{\text{1 mol O}}_{\text{2}}}{{\text{2 moles H}}_2\text{O}}$

Calculate the moles of ${\text{O}}_{\text{2}}$ produced

${\text{moles of O}}_2\text{ produced= 7}{\text{.5 moles H}}_2{\text{O}}_2\times \frac{{\text{1 mol O}}_{\text{2}}}{{\text{2 moles H}}_2\text{O}}=3.75{\text{ moles of O}}_{\text{2}}$

Conclusion

b) 3.75 moles of ${\text{O}}_{\text{2}}$.

Interpretation Introduction

(c) To determine:

The moles of oxygen that is obtained by the decomposition of 7.5 moles of reactant of $\text{2 HgO}\to {\text{2 Hg + O}}_{\text{2}}$.

Answer to Problem 4.10PAE

Solution:

c) 3.75 moles of O₂.

Explanation of Solution

Write the molar ratio between the $\text{HgO }\text{and}{\text{O}}_{\text{2}}$

2 moles of $\text{HgO}$ react with 1 mol of ${\text{O}}_{\text{2}}$

So that, the molar ratio is:

$\frac{{\text{1 mol O}}_{\text{2}}}{\text{2 moles HgO}}$

2-Calculate the moles of ${\text{O}}_{\text{2}}$ produced

${\text{moles of O}}_2\text{ produced= 7}\text{.5 moles HgO}\times \frac{{\text{1 mol O}}_{\text{2}}}{\text{2 moles HgO}}=3.75{\text{ moles of O}}_{\text{2}}$

Conclusion

c) 3.75 moles of ${\text{O}}_{\text{2}}$.

Interpretation Introduction

(d) To determine:

The moles of oxygen that is obtained by the decomposition of 7.5 moles of reactant of ${\text{2 NaNO}}_3\to {\text{2 NaNO}}_2{\text{ + O}}_{\text{2}}$.

Answer to Problem 4.10PAE

Solution:

d) 3.75 moles of O₂.

Explanation of Solution

Write the molar ratio between the ${\text{NaNO}}_{\text{3}}\text{and}{\text{O}}_{\text{2}}$

2 moles of ${\text{NaNO}}_{\text{3}}$ react with 1 mol of ${\text{O}}_{\text{2}}$

So that, the molar ratio is:

$\frac{{\text{1 mol O}}_{\text{2}}}{\text{2 moles NaNO}}$

Calculate the moles of ${\text{O}}_{\text{2}}$ produced

${\text{moles of O}}_2\text{ produced= 7}{\text{.5 moles NaNO}}_3\times \frac{{\text{1 mol O}}_{\text{2}}}{\text{2 moles NaNO}}=3.75{\text{ moles of O}}_{\text{2}}$

Conclusion

d) 3.75 moles of ${\text{O}}_{\text{2}}$.

Interpretation Introduction

(e) To determine:

The moles of oxygen that is obtained by the decomposition of 7.5 moles of reactant of ${\text{KClO}}_4\to {\text{KCl+ 2 O}}_{\text{2}}$.

Answer to Problem 4.10PAE

Solution:

e) 15 moles of O₂.

Explanation of Solution

Write the molar ratio between the ${\text{KClO}}_{\text{4}}\text{and}{\text{O}}_{\text{2}}$

1 mol of ${\text{KClO}}_{\text{4}}$ react with 2 moles of ${\text{O}}_{\text{2}}$

So that, the molar ratio is:

$\frac{{\text{2 moles O}}_{\text{2}}}{\text{1 moles KClO}}$

Calculate the moles of ${\text{O}}_{\text{2}}$ produced

${\text{moles of O}}_2\text{ produced= 7}{\text{.5 moles KClO}}_4\times \frac{{\text{2 moles O}}_{\text{2}}}{\text{1 moles KClO}}=15{\text{ moles of O}}_{\text{2}}$

Conclusion

e) 15 moles of ${\text{O}}_{\text{2}}$.