Question

Water is $11.2$ % by mass hydrogen (H). How many kilograms of water would contain $4.8$g of hydrogen?

Answer 1

First we will determine the moles of hydrogen by using mole formula. Then we will determine the mole of water from the formula of water. By using the mole formula we will convert the mole of water into mass. Then by using the conversion factor we can answer in kilograms.

Formula used: ${\text{mole}}\,\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,\,{\text{mass}}}}$

Complete step by step answer:
We will use the mole formula to determine the moles of hydrogen as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
The molar mass of hydrogen is $1.00$ g/mol.
On substituting $4.8$g for the mass of hydrogen and $1.00$for molar mass of hydrogen,
$\Rightarrow {\text{mole}}\,{\text{ = }}\,\dfrac{{4.8}}{{1.00}}$
$\Rightarrow {\text{mole}}\,{\text{ = }}\,4.8$
So, the mole of hydrogen is $4.8$mol.

The chemical formula of water is ${{\text{H}}_{\text{2}}}{\text{O}}$.
According to the formula of water, two moles of hydrogen is present in one mole of water then $4.8$moles of hydrogen be present in,
$\Rightarrow 2$mole H = $1$ mole ${{\text{H}}_{\text{2}}}{\text{O}}$
$\Rightarrow 4.8$mole H = $2.4$ mole${{\text{H}}_{\text{2}}}{\text{O}}$
So, $4.8$ mole hydrogen is present in $2.4$ mole water.

Now, we will calculate the mass of water as follows:
$\Rightarrow {\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
The molar mass of water is $18.01$ g/mol.

On substituting $2.4$mol for the mole of water and $18.01$for molar mass of water,
$\Rightarrow {\text{2}}{\text{.4}}\,{\text{mol}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{18}}{\text{.01}}}}$
$\Rightarrow {\text{mass}}\, = \,\,{\text{2}}{\text{.4}}\,{\text{mol}}\,\, \times \,{\text{18}}{\text{.01}}$
$\Rightarrow {\text{mass}}\, = \,\,{\text{43}}{\text{.24}}\,{\text{g}}$
So, the mass of water is ${\text{43}}{\text{.24}}$gram.

We know,
$\Rightarrow 1000\,{\text{g}}\,{\text{ = }}\,{\text{1}}\,{\text{Kg}}$
$\Rightarrow {\text{43}}{\text{.24}}\,{\text{g}}\,{\text{ = }}\,0.04324\,{\text{Kg}}$
So, the mass of water is$0.04324$ Kg.

Therefore, $0.04324$ kilograms of water would contain $4.8$g of hydrogen.

Note: The molar mass is determined by adding the atomic mass of each constituting atom of the molecule. The unit of molar mass is gram per mole. During calculation of mass by using mole formula we get an answer in gram. We have to determine the answer in kilograms, so we have to use the conversion factor. The comparison of moles to get the moles of a species is known as stoichiometric comparison.