Question

The molar mass of normal water $ ({H_2}O) $ is ___ as compared to heavy water $ {D_2}O $ .
(A) $ 10\% $ less
(B) $ 10\% $ high
(C) $ 2\% $ less
(D) Zero $ \% $ less

Answer 1

Hint: Isobars: Those elements which have the same atomic mass but different atomic numbers. For example: argon and calcium. The atomic number of argon is $ 18 $ and that of calcium is $ 20 $ but the atomic mass of both the elements is the same i.e. $ 40 $ .

Complete step by step solution:
First of all let us read about molecular formulas.
Molecular mass of an element: It is the atomic mass of an element.
Molecular weight of the substance: It is defined as the sum of the molecular masses of all elements present in the substance.
Number of moles: It is defined as the ratio of mass of the substance to the molecular mass of the substance.
Molecular formula: The molecular composition in the compound is known as molecular formula. For example: the molecule of water is $ {H_2}O $ i.e. two atoms of hydrogen with oxygen.
Isobars: Those elements which have the same atomic mass but different atomic numbers. For example: argon and calcium. The atomic number of argon is $ 18 $ and that of calcium is $ 20 $ but the atomic mass of both the elements is the same i.e. $ 40 $ . And here we are given with the elements hydrogen and deuterium. They are isobars of each other.
Now here we are given the molecular formula of the compound i.e. water as $ {H_2}O $ and $ {D_2}O $ .
Now we already know that the molecular mass of hydrogen is $ 1 $ and the molecular mass of deuterium $ D $ is $ 2 $ molecular mass of oxygen is $ 16 $ . In compound $ {H_2}O $ there is one atom of oxygen and two atoms of hydrogen atoms are present. So the molecular mass of the compound will be $ 1 \times 2 + 16 = 18 $ . Hence the molecular mass of water i.e. $ {H_2}O $ is $ 18u $ . $ u $ is used for the unit of molecular mass. And similarly the molecular mass of $ {D_2}O $ will be $ 2 \times 2 + 16 = 20u $ . Hence the difference in the mass of normal water and heavy water is $ 20 - 18 = 2u $ . So the $ \% $ increase (because the mass of heavy water is higher than that of normal water) in the mass of heavy water is $ \dfrac{2}{{20}} \times 100 = 10\% $ . Hence option b is correct.

Note:
Isotopes: Those elements which have the same atomic number but different atomic mass. For example: $ C - 12 $ and $ C - 13 $ . They both have the same atomic number i.e. $ 6 $ but different atomic mass i.e. in $ C - 12 $ mass is $ 12 $ and in $ C - 13 $ mass is $ 13 $ .