Question

For \[3.00mol\] of carbon dioxide is equal to how many atoms?

Answer 1

Hint:The concept of number of molecules present in a mole of a substance is given by Avogadro. According to this \[6.023 \times {10^{23}}\] number of molecules is present in one mole of a compound.

Complete step by step answer:
The Avogadro constant ($N_A$) or Avogadro number is the factor which is used to express the relation between the numbers of constituent molecules with the amount of the substance taken. The name of the constant is given by Stanislao Cannizzarro after the death of Italian scientist Amedeo Avogadro.
According to the concept a numeric value of the Avogadro constant is assigned which is a dimensionless number, is called the Avogadro number. It states that the number of particles which are contained in one mole of a substance is equal to\[6.023 \times {10^{23}}\]. As the Avogadro number is related to the mole of a compound so it is related to the molar mass of a compound.
As an example a mole of water contains \[18.0153grams\]. Also one mole of water contains \[6.023 \times {10^{23}}\] numbers of molecules. So the mass of one molecule present in \[18.0153g\] of water is equal to \[\dfrac{{18}}{{6.023 \times {{10}^{23}}}}\] . Thus, the Avogadro constant $N_A$ relates the molar mass of a substance to the average mass of one molecule.
So, \[1\] mole of carbon dioxide contains \[6.023 \times {10^{23}}\] number of molecules. The number of moles of carbon dioxide given is \[3moles\] .
Thus \[3moles\] of carbon dioxide contains = \[3 \times 6.023 \times {10^{23}} = 18.069 \times {10^{23}}molecules\]
Further one molecule of carbon dioxide contains three atoms in the form of one carbon atom and two oxygen atoms. Thus the number of atoms present in \[3moles\] of carbon dioxide is
$ = 3 \times 18.069 \times {10^{23}} = 54.207 \times {10^{23}}atoms$ .

Note:
The above relation is also applied in case of molar volume. The Avogadro constant also relates the molar volume of a substance to the average volume one particle.