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What is gram molecular volume prove that gram molecular volume is equal to \[22.4d{m^3}\]?

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Last updated date: 16th May 2024
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Answer
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Hint: We need to know the gram molecular volume which is also called molar volume. For an ideal gas at standard temperature and pressure, the gram molecular volume is fixed or constant and it will not change. And the gram molecular volume of a compound can be calculated by using an ideal gas equation and that is, \[PV = nRT\].

Complete answer:
The gram molecular volume is defined as, it is the volume of one mole of a gas which is occupied at a standard temperature and pressure, STP. And it is always fixed at STP which means, the gram molecular mass of an ideal gas mainly depends on temperature and pressure. The standard pressure is equal to 1atm and standard temperature is \[273K\]. And the molar volume of an ideal gas can be calculated by using the ideal gas equation, \[PV = nRT\].
For 1 mole,
\[PV = nRT\] …….. (1)
Where, P is pressure, V is the volume, n is the number of molecules, R is universal gas constant and T is equal to temperature.
By rearranging the equation one, will get
\[V = \dfrac{{nRT}}{P}\]
Applying the values of n, R, T and P
\[V = \dfrac{{n \times 0.0821 \times 273}}{{1atm}}\]
On simplification we get,
\[V = 22.4L\]
Hence, the gram molecular volume is equal to \[22.4L\].

Note:
We have to remember that the volume of one mole of a gas which is occupied at a standard temperature and pressure, STP is known as gram molecular volume. And it mainly depends on standard temperature and pressure. The standard pressure and temperature is equal to $1atm$ and \[273K\]respectively. The gram molecular volume is calculated by using the ideal gas equation and it is equal to \[22.4L\].
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