Chapter 2, Problem 2.20P

2-20 Calculate the percentage of hydrogen and oxygen in water, H₂O, and hydrogen peroxide, H₂O₂.

Interpretation Introduction

Interpretation:

The percentage of hydrogen and oxygen in water, ${\text{H}}_{\text{2}}\text{O}$, and hydrogen peroxide, ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$ should be identified.

Concept Introduction:

The same element combined together to form a chemical compound. The elements present in the compounds are in the fixed proportion by mass.

Answer to Problem 2.20P

H − 5.88%, O − 94.12% in hydrogen peroxide and H-11.11%, O-88.89% in water.

Explanation of Solution

The percentage of an element in a given compound is calculated using the mass of that element in the compound and the total mass of the compound.

$\text{\% of an element = }\frac{\text{mass of the element in the compound}}{\text{total mass of the compound}}\text{×100}$

A water molecule (H₂ O) consists of two atoms of hydrogen and one atom of oxygen. The mass numbers of hydrogen and oxygen are 1 and 16 respectively.

Therefore, the mass of hydrogen in water is calculated using the mass number of hydrogen atoms in water.

$\text{Mass of hydrogen = mass number of hydrogen }\times \text{ 2}$

$\begin{array}{l} =1\times 2\hfill \\ =2\hfill \\ \hfill \end{array}$

Similarly, the mass of oxygen in water is calculated using the mass number of oxygen and the number of oxygen atoms in water.

$\begin{array}{l}Massofoxyg\text{e}n=massnumb\text{e}rofoxyg\text{e}n\times 1\hfill \\ =16\times 1\hfill \\ =16\hfill \end{array}$

Now, the total mass of water is calculated using the mass of hydrogen and the mass of oxygen.

Total mass of water = mass of hydrogen + mass of oxygen.

= 2 + 16.

= 18.

Now the percentage of oxygen and hydrogen in water are calculated as below:

$\begin{array}{l}\text{\% of hydrogen in water = }\frac{\text{mass of hydrogen}}{\text{total mass of water}}\times \text{100}\hfill \\ \hfill \\ \text{ =}\frac{\text{ 2}}{\text{18}}\times \text{100}\hfill \\ \text{ = 11}\text{.11\%}\hfill \\ \text{\% of oxygen in water = }\frac{\text{mass of hydrogen}}{\text{ total mass of water}}\times \text{100}\hfill \\ \text{ = }\frac{\text{16}}{\text{18}}\times \text{100}\hfill \\ \text{ = 88}\text{.89\%}\hfill \end{array}$

So, it contains 11.11% hydrogen and 88.89% oxygen.

A hydrogen peroxide contains two hydrogen and two oxygen atoms. And their masses are 1 and 16 respectively.

So, the total masses of hydrogen and oxygen are as below:

Mass of hydrogen $1\times 2=2$

Mass of oxygen $16\times 2=32$

And total mass of H₂ O₂ = 32 + 2 = 34.

Now the calculation of percentage of hydrogen and oxygen in H₂ O₂

$\begin{array}{l}{\text{\% of hydrogen in H}}_2{\text{O}}_2\text{ = }\frac{\text{mass of hydrogen}}{\text{total mass of water}}\times \text{100}\hfill \\ \hfill \\ \text{ =}\frac{\text{ 2}}{34}\times \text{100}\hfill \\ \text{ = 5}\text{.88\%}\hfill \\ {\text{\% of oxygen in H}}_2{\text{O}}_2\text{ = }\frac{\text{mass of hydrogen}}{\text{ total mass of water}}\times \text{100}\hfill \\ \text{ = }\frac{32}{34}\times \text{100}\hfill \\ \text{ = 94}\text{.12\%}\hfill \end{array}$.

Conclusion

H − 5.88%, O − 94.12% in hydrogen peroxide and H-11.11%, O-88.89% in water.