Question

What is the mass of a mole of water containing 50 % of heavy water (\[{{\text{D}}_{\text{2}}}{\text{O}}\])?
(A) 19 g
(B) 18 g
(C) 20 g
(D) 21 g

Answer 1

Hint: A mole of any substance contains Avogadro’s number of molecules. Avogadro’s number of molecules is \[6.023 \times {10^{23}}{\text{ molecules/mol}}\]. The mass of one mole of a substance is equal to its molecular weight.

Complete step by step answer:
Isotopes are the atoms of the same element, having the same atomic number but different mass number. They have the same number of electrons and same number of protons, but they have different numbers of neutrons. They have the same chemical properties but different physical properties.
Hydrogen, deuterium and tritium are three isotopes. They have the same atomic number of 1, but different mass numbers. The mass numbers of hydrogen, deuterium and tritium are 1, 2 and 3 respectively.
The molecular weight of atomic oxygen is 16 g/mol. The molecular weight of hydrogen and deuterium atoms is 1 g/mol and 2 g/mol respectively.
Calculate the molecular weight of \[{{\text{H}}_{\text{2}}}{\text{O}}\] molecule.
\[2\left( 1 \right) + 16 = 2 + 16 = 18\]
Calculate the molecular weight of \[{{\text{D}}_{\text{2}}}{\text{O}}\] molecule.
\[2\left( 2 \right) + 16 = 4 + 16 = 20\]
Calculate the molecular weight of mixture containing 50 % of \[{{\text{H}}_{\text{2}}}{\text{O}}\] and 50 % of \[{{\text{H}}_{\text{2}}}{\text{O}}\] .
\[\dfrac{{18 + 20}}{2} = \dfrac{{38}}{2} = 19{\text{g/mol}}\]
Hence, the mass of a mole of water containing 50 % of heavy water (\[{{\text{D}}_{\text{2}}}{\text{O}}\]) is 19g.

So the option (A) is the correct option.

Note: This calculation is similar to the calculation involving the average atomic mass of an element containing isotopes. For example, the average atomic mass of chlorine is 35.5. Chlorine contains two isotopes with atomic masses of 35 and 37 with natural abundance of 3:1
\[\dfrac{{3\left( {35} \right) + 1\left( {37} \right)}}{4} = 35.5{\text{g/mol}}\]