Question

The ratio of the mass of 1 mole of sodium and 1 atom of sodium is:
A. \[6.02 \times {10^{23}}\]
B. 23
C. \[\dfrac{{23}}{{6.02}}{\text{ }}\]
D. \[23 \times 6.02\]

Answer 1

Hint: The number of atoms in one mole of any substance is equal to Avogadro’s Number i.e. \[6.02 \times {10^{23}}\] atoms per mole. On multiplying the molar mass of the substance to the number of moles, we can get the grams of the substance contained in that particular mole of the substance. Atomic weight when multiplied to the number of moles results in its gram weight.
Formula used: Grams = moles \[ \times \] atomic weight.

Complete step by step answer:
A mole is a standard unit of measurement of an amount of a substance. 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 amount 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
We are given 1 mole of sodium atoms
Therefore, grams = 1-mole \[ \times \] atomic weight of sodium atom
The atomic weight of sodium atom is 23 (number of neutrons + number of protons)
\[\therefore \]grams = 1 mole \[ \times \] 23
                = 23 grams
Therefore, the mass of 1-mole sodium is 23 grams.
Now for one atom sodium, the mass is \[\dfrac{{23}}{{6.02 \times {{10}^{23}}}}{\text{ gm }}\]
Now the ratio of the mass of 1 mole of sodium and 1 atom of sodium is:
 \[
  23:\dfrac{{23}}{{6.02 \times {{10}^{23}}}} \\
   = \dfrac{{23 \times 6.02 \times {{10}^{23}}}}{{23}} \\
  {\text{ = }}6.02 \times {10^{23}}{\text{ }} \\
 \]

So, the correct answer is A.

Note:
 Molecular mass means the weight of the 1-mole amount of a compound. According to the mole concept, we know 1 mole of any substance is equal to its molecular weight. And 1 mole is equal to Avogadro’s number of atoms i.e. .. .