Question

One gross : One mole : : 144 : ?
A.$6.023 \times {10^{23}}$
B.$6 \times {10^{23}}$
C.${10^{23}}$
D.None of the above

Answer 1

In this question, we have to relate that ratio of given moles to one gross. We shall simply use the unitary method to find the answer to this question. $6.023 \times {10^{23}}$ is Avogadro's number and represents the number of atoms/molecules present in one mole of the substance.

Complete step by step answer:
Another property of mole concept that we should know is that the mass of one mole of a substance is equal to that substance’s molecular weight. An amount of 1 dozen of anything = 12 units of that thing.
Similarly in the question, we have 1 gross of anything = 144 units of that thing.
Hence, 1 mole of anything = $6.023 \times {10^{23}}$ units of that thing.

Hence, the correct answer is option A.

Note: The concept that a mole of any substance contains the same number of particles was formed out of research which was conducted by Italian physicist Amedeo Avogadro. Avogadro constant can be defined as the number of molecules, atoms, or ions in one mole of a substance: $6.022 \times {10^{23}}$ per mol. It is derived from the number of atoms of the pure isotope $^{{\text{12}}}{\text{C}}$in 12 grams of that substance and is the reciprocal of atomic mass in grams. Now the mole concept can be applied to ions and formula units.
a)1 mole of ${O_2}$means Avogadro's number of oxygen molecules and it will be equal to 2 times Avogadro's number of oxygen atoms.
b)1 g-molecule of ${O_2}$ is the same as one mole of the oxygen molecule and contains Avogadro's number of nitrogen molecules and twice this number of atoms.
c)1 g-atom of Nitrogen means 1 mole of nitrogen atoms and contains Avogadro's number of nitrogen atoms. The mass of 1 mole of any species is equal to its molar mass.
The formulae for the mole concept can be summarized as:
${\text{No}}{\text{. of moles = }}\dfrac{{{\text{Mass of the Substance in grams}}}}{{{\text{Molar mass of a Substance}}}} = \dfrac{{{\text{Number of Atoms or Molecules}}}}{{6.022 \times {{10}^{23}}}}$