Question

The weight of one molecule of a compound of molecular formula \[{C_{60}}{H_{122}}\] is:
(A) \[1.2 \times {10^{ - 20}}g\]
(B) \[5.025 \times {10^{ - 20}}g\]
(C) \[1.4 \times {10^{ - 20}}g\]
(D) \[6.023 \times {10^{ - 20}}g\]

Answer 1

Hint: The molecular weight of a compound is equivalent to the sum of all the masses of its constituent atoms. In simpler terms, it is a sum of the product each constituent atom’s atomic weight to the number of atoms of that element present in the compound

Complete Step-by-Step answer:
The atomic mass number of carbon is 12, while the atomic mass number of hydrogen is 1.
In the given compound, we can see that there are 60 atoms of carbon and 122 atoms of hydrogen present. Now the total mass of all these atoms can be calculated as:
Molecular mass of \[{C_{60}}{H_{122}}\]= 60(12) + 122(1)
= 720 + 122
= 844 \[gmo{l^{ - 1}}\]
Hence the molecular mass of \[{C_{60}}{H_{122}}\] is 844 \[gmo{l^{ - 1}}\].
Now this is the weight of one mole of \[{C_{60}}{H_{122}}\]. We know that one mole of any substance contains \[6.022 \times {10^{23}}\] atoms / molecules of the given substance. This number is also known as Avogadro’s Number. From this, we can calculate the mass of one molecule of \[{C_{60}}{H_{122}}\]. Let the mass of one molecule of \[{C_{60}}{H_{122}}\] be ‘x’.
Hence, x = = \[\dfrac{{844}}{{6.022 \times {{10}^{23}}}}\] = \[140.15 \times {10^{23}}\] = \[1.4 \times {10^{ - 20}}g\]

Hence, Option C is the correct option.

Note: Avogadro constant (Avogadro number) The number of molecules, atoms, or ions in one mole of a substance: $6.02252 \times 10^{23}$. It is derived from the number of atoms of the pure isotope 12C in 12 grams of that substance and is the reciprocal of atomic mass in grams.