Question

The ratio of hydrogen and oxygen in water is \[1:8\] . Find the ratio of the number of atoms in one molecule of water.

Answer 1

Hint: The given ratio of hydrogen and oxygen is the ratio of their molar masses. This ratio can be used to determine the number of atoms of hydrogen and oxygen that are present in water. The ratio of molar masses of the elements will be the same as atomic masses multiplied by the stoichiometric numbers.

Complete answer:
The given ratio of molar masses of hydrogen and oxygen atoms is \[1:8\] . The mass of one atom of hydrogen is approximately \[1u\]and that of an oxygen atom is \[16u\] .
Let the total mass of water be \[x\] then according to ratio of molar masses the total mass of hydrogen atoms will be \[\dfrac{1}{9}x\] and that of oxygen will be \[\dfrac{8}{9}x\] .
The molar mass of hydrogen is \[1g\] and that of oxygen is \[16g\] . The moles of both hydrogen and oxygen atoms in water can be determined by taking the ratio of masses calculated in terms of \[x\] and the molar masses.
\[moles(H) = \dfrac{{\dfrac{1}{9}x}}{{1g}} = \dfrac{1}{9}x\]
\[moles(O) = \dfrac{{\dfrac{8}{9}x}}{{16g}} = \dfrac{1}{{18}}x\]
Now the ratio of moles of hydrogen and oxygen will be the same as the ratio of their atoms:
\[H:O = \dfrac{{\dfrac{1}{9}x}}{{\dfrac{1}{{18}}x}} = 2:1\]
Thus, the ratio of atomic masses can be \[1:8\] only when the mass of a hydrogen atom is multiplied by a stoichiometric factor of two and the ratio reduces to \[1:8\] in the simplest form. This tells us that each molecule of water actually contains two hydrogen atoms for every one oxygen atom.
\[ \Rightarrow \] Hence the ratio of hydrogen and oxygen atoms in water is \[2:1\].

Note:
The formula of water is known and can simply be used to calculate the ratio of number of atoms of hydrogen and water but in this question we aim to use the ratio of masses and establish a relation between the ratios involved for the same formula.