Chapter 4, Problem 4.7PAE

For the following reactions, write the ratios that can be established among molar amounts of the various compounds.

1. ${\text{2H}}_{\text{2}}+{\text{ O}}_{\text{2}} \to {\text{2H}}_{\text{2}}\text{O}$
2. ${\text{2H}}_{\text{2}}{\text{O}}_{\text{2}} \to {\text{2H}}_{\text{2}}\text{O }+{\text{ O}}_{\text{2}}$
3. ${\text{P}}_{\text{4}}+{\text{ 5O}}_{\text{2}} \to {\text{P}}_{\text{4}}{\text{O}}_{\text{1}0}$
4. ${\text{2KClO}}_{\text{3}}\to \text{2KCl }+{\text{ 3O}}_{\text{2}}$

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Interpretation Introduction

To write:

The ratios that can be established among molar amounts of the various compounds in ${\text{2 H}}_2+{\text{O}}_{\text{2}}\to 2{\text{H}}_{\text{2}}\text{O}$.

Explanation of Solution

2 moles of H₂ react with 1 mol of O₂. So that, the molar ratio is,

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

2 moles of H₂ produce 2 mol of H₂O. So that, the molar ratio is,

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

1 mole of O₂ produces 2 mol of H₂O. So that, the molar ratio is,

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

Interpretation Introduction

To write:

The ratios that can be established among molar amounts of the various compounds in ${\text{2H}}_2{\text{O}}_{\text{2}}\to 2{\text{ H}}_{\text{2}}{\text{O + O}}_2$.

Explanation of Solution

2 moles of H₂O₂ decompose in 2 moles of H₂O and 1 mol of O₂. So that, the molar ratios are,

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

Interpretation Introduction

To write:

The ratios that can be established among molar amounts of the various compounds in ${\text{P}}_4{\text{ + 5 O}}_{\text{2}}\to {\text{P}}_4{\text{O}}_{10}$.

Explanation of Solution

1 mol of P₄ reacts with 5 moles of O₂. So that, the molar ratio is,

$\frac{{\text{5 moles O}}_{\text{2}}}{{\text{1 mol P}}_4}\text{ or }\frac{{\text{1 mol P}}_4}{{\text{5 moles O}}_2}$

1 mol of P₄ produces 1 mol of P₄O₁₀. So that, the molar ratio is,

$\frac{{\text{1 mol P}}_4{\text{O}}_{10}}{{\text{1 mol P}}_4}$

5 moles of O₂ produce 1 mol of P₄O₁₀. So that, the molar ratio is,

$\frac{{\text{1 mol P}}_4{\text{O}}_{10}}{{\text{5 moles O}}_2}$

Interpretation Introduction

To write:

The ratios that can be established among molar amounts of the various compounds in ${\text{2KClO}}_3\to 2{\text{KCl + 3 O}}_2$.

Explanation of Solution

2 moles of KClO₃ decompose in 2 moles of KCl and 3 moles of O₂. So that, the molar ratios are,

$\frac{\text{2 moles KCl}}{{\text{2 moles KClO}}_3}\text{ and }\frac{{\text{3 moles O}}_2}{{\text{2 moles KClO}}_3}\text{and }\frac{{\text{3 moles O}}_2}{\text{2 moles KCl}}$

Conclusion

a)

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

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

b)

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

c)

$\frac{{\text{5 moles O}}_{\text{2}}}{{\text{1 mol P}}_4}\text{ or }\frac{{\text{1 mol P}}_4}{{\text{5 moles O}}_2}$

$\frac{{\text{1 mol P}}_4{\text{O}}_{10}}{{\text{1 mol P}}_4}$ and $\frac{{\text{1 mol P}}_4{\text{O}}_{10}}{{\text{5 moles O}}_2}$

d)

$\frac{\text{2 moles KCl}}{{\text{2 moles KClO}}_3}\text{ and }\frac{{\text{3 moles O}}_2}{{\text{2 moles KClO}}_3}\text{and }\frac{{\text{3 moles O}}_2}{\text{2 moles KCl}}$