Question

The weight of one molecule of \[{C_{60}}{H_{122}}\] is:
A. \[\;1.2 \times {10^{ - 20}}g\]
B. \[5.025 \times {10^{23}}g\]
C. \[1.4 \times {10^{ - 21}}g\]
D. \[6.023 \times {10^{23}}g\]

Answer 1

Hint: A mole is a standard unit of measurement of an amount of a substance. Calculating the molar mass of the substance results in the grams of the substance contained in that particular mole. Atomic weight when multiplied to the number of moles results in its gram weight.

Complete step by step answer:
Substances react in the simple ratios of their moles. One mole consists of Avogadro number of atoms i.e. \[6.022 \times {10^{23}}\] atoms. The number of atoms in 12.0 grams of Carbon-12 is the same as Avogadro’s number as it is for 1 mole of carbon i.e. a sample of 12 grams of carbon is equal to its one mole. It is similar to a dozen.
The molar mass is the number of grams present in one mole of a substance. It is also the average atomic weight of a substance. For example, carbon has an atomic weight of 12 amu, so its molar mass is 12 grams per mole. The formula for converting moles to gram is written as-
Grams = moles \[ \times \]atomic weight
Now, the molecular weight of the given molecule is, \[{C_{60}}{H_{122}}\] , where the atomic weight of the carbon is 12. The atomic weight of hydrogen is 1. Therefore, the molecular weight is
  \[
  60 \times 12 + \left( {122 \times 1} \right) \\
  720 + 122 \\
  842gm/mol \\
 \]
Now, we know \[{\text{1 mole = atomic weight = 6}}{\text{.023 \times 1}}{{\text{0}}^{{\text{23}}}}{\text{no}}{\text{.of atoms}}\] . Therefore, the weight of one molecule \[{C_{60}}{H_{122}}\] is:
 \[
  \dfrac{{842}}{{6.023 \times {{10}^{23}}}} \\
   = 139.79 \times {10^{ - 23}} \\
   = 1.39 \times {10^{ - 23}} \\
   = 1.39 \times {10^{ - 21}} \\
   = 1.4 \times {10^{ - 21}}gm \\
 \]

So, the correct option is C.

Note:
Calculating mass like this is known as gram atomic mass. It is the mass of one mole of that element. For example, the gram atomic mass of hydrogen is 1 gram for one mole of hydrogen. It is the same as the atomic weight of a hydrogen atom.