Question

The number of moles of a gas in $1{{m}^{3}}$ of volume at NTP is:
(A) 4.46
(B) 0.446
(C) 1.464
(D) 44.6

Answer 1

Hint: Recollect the mole concept and Avogadro’s law. We know, 1mole of gas occupies a volume of 22.4L at NTP. So, cross-multiply and find out how many moles of gas are present in 1L.

Complete step by step solution:
- According to Avogadro’s law, equal volumes of gases under identical conditions of temperature and pressure contain equal numbers of molecules. This is combination of Gay Lussac’s law of combining volumes of gas and Dalton’s atomic theory.
- According to mole concept, one mole of a substance is defined as the amount of substance that contains the number of particles, atoms, molecules, ions or electrons, etc. as present in 0.012g of Carbon-12. This number of particles is equal to $6.022\times {{10}^{23}}$ particles. The number $6.022\times {{10}^{23}}$ is called Avogadro’s number.
- So, $6.022\times {{10}^{23}}$ of atoms, molecules, ions, electrons are present in 1 mole of a substance.
- $6.022\times {{10}^{23}}$ electrons make one Faraday of charge.
- One mole of different gases having different molar masses occupy the same volume of 22.4L at STP and contain $6.022\times {{10}^{23}}$ molecules.
- 1mole = 22.4L
So, ‘x’ moles = $1{{m}^{3}}$ = ${{10}^{3}}L$
By cross-multiplication we get, $x=\dfrac{{{10}^{3}}}{22.4}=44.6$
Therefore, the number of moles of a gas in $1{{m}^{3}}$ of volume at NTP is 44.6 moles.
Therefore, the correct answer is option (D) 44.6.


Note: Remember one mole is equal to $6.022\times {{10}^{23}}$ molecules or atoms or electrons or ions which occupies 22.4L volume irrespective of its molar masses. $6.022\times {{10}^{23}}$ electrons make one Faraday of charge.