Question

Calculate the mass of one molecule of water

Answer 1

Hint: 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 one molecule of water using the molar mass of water and Avogadro number.

Complete step by step answer:
We know that molar mass of water is $18\,g\,mo{l^{ - 1}}$.
Let us now write the mass for one mole of water atom.
The mass of one mole of water atom will be $18\,g$.
We know that one mole of a particle will contain Avogadro number of atoms.
$1\,mole = 6.022 \times {10^{23}}\,atoms$
Now let us calculate the mass of a molecule of water.
We can calculate the mass of one molecule of water by dividing the mass of one mole of water to the Avogadro number of atoms.
We can write the formula as,
Mass of one atom of water=$\dfrac{{{\text{Mass}}\,{\text{of}}\,\,{\text{1}}\,{\text{mole}}}}{{{\text{Avogadro's}}\,\,{\text{number}}}}$
Mass of one atom of water=$\dfrac{{18\,g/mol}}{{6.022 \times {{10}^{23}}\,molecules\,}}$
Mass of one atom of water=$2.989 \times {10^{ - 23}}\,g$
we have calculated the mass of one molecule of water as $2.989 \times {10^{ - 23}}\,g$.

Note:
We also remember 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. 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.