Question

Molar‌ ‌volume‌ ‌is‌ ‌the‌ ‌volume‌ ‌occupied‌ ‌by‌ ‌1‌ ‌mol‌ ‌of‌ ‌any‌ ‌(idea)‌ ‌gas‌ ‌at‌ ‌standard‌ ‌temperature‌ ‌and‌ ‌pressure‌ ‌(S‌ ‌T‌ ‌P:‌ ‌1‌ ‌atmospheric‌ ‌pressure,‌ ‌${{0}^{0}}\,C$).‌ ‌Show‌ ‌that‌ ‌it‌ ‌is‌ ‌22.4‌ ‌litres.‌ ‌

Answer 1

Hint: In order to answer the following question, we need to will acquainted with the features of modern periodic table and the following formula the maximum number of electrons present in shell = $2{{n}^{2}}$
Where n = shell number
To prove that the molar volume at standard pressure and temperature is 224.4 litres can be proved using the ideal gas law \[PV=nRt\],where R is the universal gas constant

Complete step-by-step answer:It is given to us that Molar volume is the volume occupied by 1 mole of any (ideal) gas at standard pressure and temperature (S T P: 1 atmosphere pressure, \[={{O}^{o}}C\] )
As it is given in the question, molar volume is basically the volume occupied by 1 mole of any (ideal) gas at standard pressure and temperature.
So, from it we can conclude that the standard pressure is 1 atmosphere (ATM) while standard temperature is \[{{0}^{o}}C\]
Now, in order to show that the molar volume at S T P is 22.4 litres we will use the ideal gas equation.
Now, we know that the ideal gas equation relating pressure (P), volume (V) and absolute temperature (T) is given as follows-
\[PV=nRT\]
Where 'R' is the universal gas constant with value \[R=8.314Jmo{{l}^{-1}}{{K}^{-1}}\]
n = number of moles
here, n = 1
T = standard temperature
\[={{O}^{o}}C\]
= 273 K
\[\text{P = standard pressure = 1 atm = 1}\text{.013}\times \text{1}{{\text{0}}^{5}}N{{m}^{-2}}\]
In order to find the volume we need to rearrange the ideal gas equation as depicted below.
Thus, we can write
\[V=nRT/P\]
Now substituting the values of $n,\,R,\,T,\,P$ in the above equation and solving it we will get volume as,
\[\Rightarrow \,V\,=\dfrac{1\times 8.314\times 273}{1.013\times {{10}^{5}}}\]
\[\therefore V=0.0224{{m}^{3}}\]
Now, we know that
\[{{\operatorname{Im}}^{3}}=1000\text{ Liters}\]
So on converting the meter cube unit to liters we get,
\[\therefore V=0.224\times 1000\text{ litres}\]
$V=22.4$ liters
Hence, We can see that the molar volume of a gas at S T P is 22.4 litres. Therefore, it is proved that one mole of a gas occupies $22.4L$ of the volume at STP.

Note: Students should note that for real gases the molar volume at S T P does not equal to 22.4 litres. Which leads us to questioning the accuracy of \[PV=nRT\] and this can only be judged by comparing the actual volume of 1 mole of gas to the molar this is given by the compressibility factor.