Question

How many molecules are in a sample of water with a mass of \[44.99{\text{ }}grams\] ?

Answer 1

Hint: Water is denoted with the symbols of \[{H_2}O\] having the molecular mass \[{\text{18 }}g/mol\] . A mole is defined as \[6.02214076 \times {10^{23}}\] of a chemical unit in the terms of ions, atoms, molecules, etc. A mole is a unit measurement for the amount of substance in the international system of units i.e., SI unit. A mole of a particle or a mole of a substance is defined as \[6.02214076 \times {10^{23}}\] of a chemical unit, that can be ions, atoms, molecules, etc. Originally it was defined as the number of atoms in \[12{\text{ }}g\] of carbon-12.

Complete step-by-step answer:
First, we need to calculate the number of moles of water;
As we know, the number of moles will be equal to the given mass divided by the molecular mass of a compound.
Hence, the formula will be as follows,
\[n\,\, = \,\,\dfrac{{mass}}{{molar\,mass}}\]
Where,
\[n\, = \] the amount in moles \[(mol)\]
Mass will be in the terms of\[\;(g)\]
Molar mass will be in the terms of \[\;(g/mol)\]
Now, the given values are;
Mass of the water\[ = \,\,44.99{\text{ }}grams\]
Molar mass of the water\[{\text{ = }}\,\,{\text{18 }}g/mol\]
So, the number of moles of water will be,
\[n\,\, = \,\,\dfrac{{44.99\,g}}{{18\,g/mol}}\]
We get,
\[ = \,2.5\,\,moles\] of water
Since a mole of any substances will be \[ = \,6.02214076 \times {10^{23}}\] molecules
Therefore, a mole of water is having \[6.02214076 \times {10^{23}}\] molecules.
So, we have to multiply the moles with the Avogadro’s number to get the number of molecules.
Now, let’s calculate the number of molecules present in \[44.99{\text{ }}grams\] of water
\[ = \,6.022 \times {10^{23}}\,mo{l^{ - 1}}\, \times \,2.50\,mol\]
\[ = 15.04\, \times \,{10^{23}}\] molecules

Therefore, in \[44.99{\text{ }}grams\] of water there is \[15.04\, \times \,{10^{23}}\] molecules

Note: In one mole of substance there contains an Avogadro’s number (\[{N_A}\] ) of atoms
So, the equation will be;
\[1\,mole\, = \,6.022\, \times \,{10^{23}}\,atoms\]
Now let’s calculate for \[1\] atom;
So, we get;
\[1\,atom\, = \,\dfrac{1}{{6.022\, \times \,{{10}^{23}}}}\,moles\]
Therefore, the answer will be;
\[1\,atom\, = 1.66\, \times \,{10^{ - 24}}\,\,moles\]
One atom contains \[1.66\, \times \,{10^{ - 24}}\] number of moles