Question

Find the number of atoms present in 100 grams of sodium:
(A) $2.6182 \times {10^{23}}$
(B) $0.6182 \times {10^{24}}$
(C) $2.6182 \times {10^{24}}$
(D) $2.6182 \times {10^{20}}$

Answer 1

Hint: One mole of any particle is equal to $6.022 \times {10^{23}}$ particles. This number is called the Avogadro’s number.

Complete step-by-step answer: The given mass of sodium (Na) in grams ${\text{ = 100g}}$
We need to find the number of atoms in 100 grams of sodium (Na).
We know that the atomic mass of sodium (Na) is equal to 23 grams. Now from the mole concept, we know that Gram atomic mass = 1 gm atom $ = 6.022 \times {10^{23}}$ atoms.
So, according to the mole concept, 23 grams of sodium (Na) contains $6.022 \times {10^{23}}$ number of atoms. Thus, 1 g of sodium (Na) will contain $ = \dfrac{{6.022 \times {{10}^{23}}}}{{23}}$ atoms.
Therefore, 100 g of sodium will contain $ = \dfrac{{6.022 \times {{10}^{23}}}}{{23}} \times 100$ number of atoms.
                                                                        $ = 2.6182 \times {10^{24}}$ number of atoms.
Therefore, option (A), option (B) and option (D) are not correct. So, the correct option is (C).

Additional information: (1) Molecular weight refers to the average relative weight of an element or a molecule as compared to the weight of a ${{\text{C}}^{{\text{12}}}}$carbon atom taken as 12 on the atomic mass unit scale. The molecular weight of any substance can be calculated by adding the atomic weights of all its constituent atoms.
(2) Gram molecular weight of a substance refers to the molecular weight of that substance (in amu) in grams, i.e., it is the weight in grams which is numerically equal to its molecular weight.
(3) According to the mole concept, a mole represents $6.022 \times {10^{23}}$ particles irrespective of their nature. The amount of matter having this Avogadro’s number of particles represents one mole of that species.

Note: The mole concept can also be applied to calculate the number of molecules in the given mass of a substance. According to the mole concept, gram molecular mass will be equal to the Avogadro’s number of molecules. So the number of molecules in 1 g of the substance can be calculated and from this, the number of molecules in the given mass of that substance can also be determined.