Question

Hydrogen and oxygen are combined in the ratio $1:16$ by mass in hydrogen peroxide. Calculate the percentage of hydrogen and oxygen in hydrogen peroxide.

Answer 1

To determine the answer we should know what percentage means and how to determine it. Here, we have a molecule of hydrogen peroxide which is formed by hydrogen and oxygen elements. The percentage of hydrogen or oxygen means how much of the total amount, the hydrogen or oxygen, in percent is. The percentage of the hydrogen or oxygen can be determined by dividing the mass of hydrogen or oxygen by the total mass of hydrogen peroxide and then multiplying with hundred. For this we have to determine the empirical formula of hydrogen peroxide by using mole formula.

Complete step-by-step solution:
It is given that the hydrogen and oxygen are combining in the ratio $1:16$ by mass. It means one gram of hydrogen is combined with sixteen gram of oxygen to form hydrogen peroxide.
We will determine the molar mass of hydrogen and oxygen as follows:
${\text{mole}}\, = \dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
For hydrogen,
Molar mass of the hydrogen is $1$ g/mol.
On substituting $1$ g for mass and $1$ g/mol of molar mass,
${\text{mole}}\, = \dfrac{{\text{1}}}{{\text{1}}}$
${\text{mole}}\, = 1$
For oxygen,
Molar mass of the oxygen is $16$ g/mol.
On substituting $16$ g for mass and $16$ g/mol of molar mass,
${\text{mole}}\, = \dfrac{{{\text{16}}}}{{{\text{16}}}}$
${\text{mole}}\, = 1$
So, one mole of hydrogen is combined with one mole of oxygen to give one mole of hydrogen peroxide. So, the empirical formula of hydrogen peroxide is ${\text{HO}}$.
The mass of hydrogen peroxide is the sum of mass of hydrogen and oxygen so,
Mass of HO = mass of H+ mass of O
${\text{mass}}\,{\text{of}}\,{\text{HO}}\,{\text{ = }}\,{\text{1 + 16}}$
${\text{mass}}\,{\text{of}}\,{\text{HO}}\,{\text{ = }}\,17$
Now, the mass percent of hydrogen is,
${\text{mass}}\,\,{\text{percent}}\,\,{\text{H}}\,{\text{ = }}\,\dfrac{{{\text{mass}}\,{\text{of}}\,{\text{H}}}}{{{\text{Mass}}\,{\text{of}}\,\,{\text{HO}}}}{\times }\,{\text{100}}$
On substituting $17$ for mass of hydrogen and $17$ for mass of hydrogen peroxide,
${\text{mass}}\,\,{\text{percent}}\,\,{\text{H}}\,{\text{ = }}\,\dfrac{{\text{1}}}{{{\text{17}}}}{\times }\,{\text{100}}$
${\text{mass}}\,\,{\text{percent}}\,\,{\text{H}}\,{\text{ = }}\,{\text{5}}{\text{.8}}$%
Now, the mass percent of oxygen is,
${\text{mass}}\,\,{\text{percent}}\,\,{\text{O}}\,{\text{ = }}\,\dfrac{{{\text{mass}}\,{\text{of}}\,{\text{O}}}}{{{\text{Mass}}\,{\text{of}}\,\,{\text{HO}}}}{ \times }\,{\text{100}}$
On substituting $16$ for mass of oxygen and $17$ for mass of hydrogen peroxide,
${\text{mass}}\,\,{\text{percent}}\,\,{\text{O}}\,{\text{ = }}\,\dfrac{{{\text{16}}}}{{{\text{17}}}}{{ \times }}\,{\text{100}}$
${\text{mass}}\,\,{\text{percent}}\,\,{\text{O}}\,{\text{ = }}\,{\text{94}}{\text{.1}}$%

Therefore, the percentage of hydrogen and oxygen in hydrogen peroxide is ${\text{5}}{\text{.8}}$% and ${\text{94}}{\text{.1}}$% respectively.

Note: By dividing the mass of hydrogen or oxygen with total mass of hydrogen peroxide we get the fraction of hydrogen or oxygen. To determine any amount in percent we multiply the amount with hundred. Empirical formulas represent the simplest ratio of atoms. The molecular formula of hydrogen peroxide is ${{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}$ and the empirical formula is HO. To determine the percent amount of any element in a molecule, the empirical formula of the molecule is necessary.