Chapter 5.10, Problem 5.15WE

(a)

Interpretation Introduction

Interpretation:

Number of water molecules and the numbers of hydrogen and oxygen atoms in 3.26 g of water should be identified.

Answer to Problem 5.15WE

1. (1) Number of ${\text{H}}_{\text{2}}\text{O}$ molecules is $\text{1}\text{.09×}{\text{10}}^{\text{23}}\text{molecules of }{\text{H}}_{\text{2}}\text{O}$
2. (2) Number of hydrogen and oxygen atoms in 3.26 g of water is $\text{ 2}\text{.18×}{\text{10}}^{\text{23}}\text{Hydrogen atoms}$ and $\text{ 1}\text{.09×}{\text{10}}^{\text{23}}\text{Oxygen atoms}$

Explanation of Solution

Molar mass of water is given below

Molar mass of hydrogen = $\text{1}\text{.00794 g/mol}$.

Molar mass of oxygen = $\text{15}\text{.999 g/mol}$.

$\begin{array}{l}\text{Water molecule is }\\ \text{2 (1}\text{.00794}\text{g/mol) + 15}\text{.999 g/mol }\\ \text{18}\text{.02 g/mol}\text{.}\end{array}$

$\begin{array}{l}\text{Number of water molecule is }\\ \text{3}\text{.26g of water × }\frac{\text{1 mol water}}{\text{18}\text{.02 g water}}\text{ × }\frac{\text{6}\text{.022×}{\text{10}}^{\text{23}}\text{molecules}}{\text{1 mol water}}\\ \text{= 1}\text{.09×}{\text{10}}^{\text{23}}\text{molecules of }{\text{H}}_{\text{2}}\text{O }\end{array}$

Number of ${\text{H}}_{\text{2}}\text{O}$ molecules is $\text{1}\text{.09×}{\text{10}}^{\text{23}}\text{molecules of }{\text{H}}_{\text{2}}\text{O}$

Number of hydrogen and oxygen atoms

Number of hydrogen and oxygen atoms in 3.26 g of water is given below,

$\begin{array}{l}\text{The number of hydrogen atoms}\\ \text{1}\text{.09×}{\text{10}}^{\text{23}}\text{molecules of }{\text{H}}_{\text{2}}\text{O × }\frac{\text{2 Hydrogen atoms}}{{\text{1 H}}_{\text{2}}\text{O molecules}}\\ \text{= 2}\text{.18×}{\text{10}}^{\text{23}}\text{Hydrogen atoms}\end{array}$

$\begin{array}{l}\text{The number of oxygen atoms}\\ \text{1}\text{.09×}{\text{10}}^{\text{23}}\text{molecules of }{\text{H}}_{\text{2}}\text{O × }\frac{\text{1 Oxygen atoms}}{{\text{1 H}}_{\text{2}}\text{O molecules}}\\ \text{= 1}\text{.09×}{\text{10}}^{\text{23}}\text{Oxygen atoms}\end{array}$

Conclusion

Number of water molecules and the numbers of hydrogen and oxygen atoms in 3.26 g of water was found.

(b)

Interpretation Introduction

Interpretation:

Mass of $\text{7}{\text{.92 × 10}}^{\text{19}}$ carbon dioxide molecules should be identified.

Answer to Problem 5.15WE

Mass of $\text{7}{\text{.92 × 10}}^{\text{19}}$ carbon dioxide molecules is $\text{5}\text{.79×}{\text{10}}^{\text{-3}}{\text{CO}}_{\text{2}}\text{molecule}$.

Explanation of Solution

Molar mass of carbon dioxide is given below

Molar mass of carbon = $\text{12}\text{.0107g/mol}$.

Molar mass of oxygen = $\text{15}\text{.999 g/mol}$.

$\begin{array}{l}\text{Carbon dioxide molecule is }\\ \text{12}\text{.0107}\text{g/mol + 2(15}\text{.999 g/mol) }\\ \text{44}\text{.01g/mol}\text{.}\end{array}$

$\begin{array}{l}\text{Mass of carbon dioxide molecule is }\\ \text{7}{\text{.92 × 10}}^{\text{19}}{\text{CO}}_{\text{2}}\text{molecule × }\frac{{\text{1 CO}}_{\text{2}}\text{molecule}}{\text{6}\text{.022×}{\text{10}}^{\text{23}}{\text{CO}}_{\text{2}}\text{molecule}}\text{ × }\frac{\text{44}\text{.01g of}{\text{CO}}_{\text{2}}\text{molecule}}{{\text{1 mol CO}}_{\text{2}}\text{molecule}}\\ \text{=5}\text{.79×}{\text{10}}^{\text{-3}}{\text{CO}}_{\text{2}}\text{molecule }\end{array}$

Conclusion

Mass of $\text{7}{\text{.92 × 10}}^{\text{19}}$ carbon dioxide molecules was calculated