Question

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

Answer 1

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