Question

Given $5.0\times {{10}^{24}}$ molecules is equal to how many litres?

Answer 1

Hint: The answer to this question is based on the Avogadro number of molecules concept and by taking an example of one substance or chemical compound, you can deduce the complete required answer.

Complete step by step solution:
In the previous classes, we have come across the simple concepts of conversion of one unit of the physical quantity like pressure, volume, temperature and so on to the other units of that particular quantity.
Let us now see in detail about the conversion of molecules into litres.
- Let us cite an example of a water molecule so that it can be converted into litres.
- In the first step let us determine the number of moles present in the water molecules. We have studied the Avogadro concept that 1 mole of any substance consists of Avogadro number of atoms and that is $6.022\times {{10}^{23}}$ atoms.
- To determine the number of moles we have from the number of molecules, we have to divide the number of molecules by Avogadro number that is,
\[\dfrac{5.0\times {{10}^{24}}}{6.022\times {{10}^{23}}}=8.3mol\]
Let us now determine the total amount in grams of water based on the molar mass of the compound.
- Here, water has the molar mass equal to$2\times 1+1\times 16=18.02g/mol$
Now to determine the number of grams of water, we have to multiply the molar mass of water by the number of total moles and that will be,
\[18.02\times 8.3=149.57g\]
Now, for water 1g = 1mL and thus,149.57g will be equal to 149.57mL which is nothing but $149.57\times 1000=0.149\approx 0.15L$
Hence, $5.0\times {{10}^{24}}$ molecules of water is equal to 0.15L

Note:
Note that the conversion factor in this particular form is dependent on the particular compound given and is different for every compound based on the molecular mass of the compound.