Question

Calculate the mass of one atom of nitrogen

Answer 1

We know that one mole of any substance comprises $6.022 \times {10^{23}}$ particles. We can call the value of $6.022 \times {10^{23}}$ as Avogadro number (or) Avogadro constant and is represented by the symbol ${N_A}.$ We can calculate the mass of atom by the moles of one atom and Avogadro number.

Complete step by step answer: We know that molar mass of nitrogen is $14\,g\,mo{l^{ - 1}}$.
Let us now write the mass for one mole of nitrogen atom.
The mass of one mole of nitrogen atom will be $14\,g$.
We know that one mole of a particle will contain Avogadro number of atoms.
$1\,mole = 6.022 \times {10^{23}}\,atoms$
Therefore, the mass of Avogadro number of atoms of nitrogen will contain $14\,g$.
Mass of $6.022 \times {10^{23}}\,atoms$ of nitrogen=$14\,g$
Now let us calculate the mass of one atom of nitrogen.
We can calculate the mass of one atom of nitrogen by dividing the mass of one mole of nitrogen to the Avogadro number of atoms.
We can write the formula as,
Mass of one atom of nitrogen=$\dfrac{{{\text{Mass}}\,{\text{of}}\,\,{\text{1}}\,{\text{mole}}}}{{{\text{Avogadro's}}\,\,{\text{number}}}}$
Mass of one atom of nitrogen=$\dfrac{{14\,g}}{{6.022 \times {{10}^{23}}\,atoms}}$
Mass of one atom of nitrogen=$\dfrac{{{\text{Mass}}\,{\text{of}}\,\,{\text{1}}\,{\text{mole}}}}{{{\text{Avogadro's}}\,\,{\text{number}}}}$
Mass of one atom of nitrogen=$2.32 \times {10^{ - 23}}\,g$
Therefore, we have calculated the mass of one atom of nitrogen as $2.32 \times {10^{ - 23}}\,g$.

Note:
We know that the number of constituent particles such as molecules, atoms or ions present in a sample is related with mass of the substance in the sample using the proportionality factor called as Avogadro constant/Avogadro number. We must remember the SI of Avogadro number is reciprocal mole $\left( {{\text{mol}}{{\text{e}}^{{\text{ - 1}}}}} \right)$. We know that the Avogadro number is dimensionless. We can also relate the molar volume of a substance to the average volume occupied by one of the particles, when the units of volume are in the same quantity using Avogadro constant/number.