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**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.

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