Question

The volume of a gas in a discharge tube is $1.12\times {{10}^{-7}}$ ml at STP. Then the number of molecules of gas in the tube is:
A. $3.01\times {{10}^{4}}$
B. $3.01\times {{10}^{15}}$
C. $3.01\times {{10}^{12}}$
D. $3.01\times {{10}^{16}}$

Answer 1

Hint: At standard temperature and pressure (STP) one mole of gas occupies 22400 ml of volume. At the time of calculation of number of molecules of a gas at STP we should consider the Avogadro number also.
Avogadro number = $6.023\times {{10}^{23}}$ atoms or molecules

Complete Solution :
- In the question it is given that to calculate the number of molecules of a gas present with a volume of $1.12\times {{10}^{-7}}$ ml at STP in a discharge tube.
- We know that one mole of gas occupies 22400 ml of volume.
- Therefore the number of moles in a volume of $1.12\times {{10}^{-7}}$ ml will be calculated as follows.
Number of moles of the gas = \[\dfrac{1.12\times {{10}^{-7}}}{22400}\]
- We should calculate the number of molecules present in the volume of $1.12\times {{10}^{-7}}$ ml and it is as follows.
- Number of molecules in $1.12\times {{10}^{-7}}$ ml volume of the gas is
\[\begin{align}
  & =\frac{1.12\times {{10}^{-7}}}{22400}\times {{N}_{A}} \\
 & =\frac{1.12\times {{10}^{-7}}}{22400}\times 6.023\times {{10}^{23}} \\
 & =3.01\times {{10}^{12}} \\
\end{align}\]
Here ${{N}_{A}}$ = Avogadro number = $6.023\times {{10}^{23}}$ atoms or molecules.
- Therefore the number of molecules in a gas which is present in a discharge tube with a volume of $1.12\times {{10}^{-7}}$ ml is $3.01\times {{10}^{12}}$ .
So, the correct answer is “Option C”.

Note: At the time of calculation of the number of molecules for gas we should consider the volume of a one mole of gas at standard temperature and pressure (STP). The volume of one mole of gas at STP is equal to 22400 ml.