Question

How many water molecules are present in $54$ gram of water?

Answer 1

To solve this question first we will calculate the number of moles of ${H_2}O$ present. After that we will multiply the number of moles with Avogadro’s number by which we will get the number of molecules.
$number\;of\;moles\;of\,{H_2}O = \dfrac{{Weight\;of\;the\;given\;sample}}{{molecular\;weight\,of\,{H_2}O}}$ .

Complete answer:
To solve this question we have to know about the concept of moles and molecular weight. Moles are the basic unit of the SI, i.e. International System of Units. It has exactly $6.022 \times {10^{23}}$ particles which can be atoms, molecules, ions or electrons. Molecular weight is the total mass of the atoms present in the molecule.
As we know that one mole contains $6.022 \times {10^{23}}$ molecules. Moreover we also know that one mole of water weighs $18gm$ as the molecular mass of water is $18$ . Thus, $18gm$ of water has $6.022 \times {10^{23}}$ molecules of water.
It is given that mass of water is $54gm$
Now we know that one mole of water weighs $18gm$ , so according to the question, moles of given of $54gm$ water is:
$number\;of\;moles\;of\,{H_2}O = \dfrac{{Weight\;of\;the\;given\;sample}}{{molecular\;weight\,of\,{H_2}O}}$
$\Rightarrow number\;of\;moles = \dfrac{{54}}{{18}}$
$\Rightarrow number\;of\;moles = 3$
As these are in moles and we have to find the number of molecules of water and we also know that one mole has $6.022 \times {10^{23}}$ molecules. So we will multiple the calculated amounts with it then we get:
$number\,of\,molecules = \;number\,of\,moles \times 6.022 \times {10^{23}}$
$\Rightarrow number\,of\,molecules = 3 \times 6.022 \times {10^{23}}$
$\Rightarrow number\,of\,molecules = 1.8066 \times {10^{24}}$
$\Rightarrow number\,of\,molecules \approx 1.8 \times {10^{24}}$
Thus there are $1.8 \times {10^{24}}$ molecules in $54$ grams of water.

Note:
In this question we can also use that one mole of water has $18.0152gm$ . In the above solution, we have taken a round off of this value. So the number of moles of water we have will be:
$\Rightarrow number\,of\,moles = \dfrac{{54}}{{18.0152}}$
$\Rightarrow number\,of\,moles = 2.997$
Thus the number of molecules will be:
$\Rightarrow number\,of\,molecules = 2.997 \times 6.022 \times {10^{23}}$
$\Rightarrow number\,of\,molecules = 1.805 \times {10^{24}}$
$\Rightarrow number\,of\,molecules \approx 1.8 \times {10^{24}}$
Thus, you can find the answer in this way too.