Question

One mole of a light gas (Mol. mass $= 32$) occupies a volume of 20 lit under certain conditions. Under the same conditions, two moles of a heavy gas (Mol. mass $= 64$) occupies a volume of:
A.80 lit
B.40 lit
C.10 lit
D.20 lit

Answer 1

In this question, we have to find the volume occupied by 2 moles of heavy gas. Gas is one of the states of matter where the molecules move freely and are associated with three types of motion. Avogadro’s law states that keeping the pressure and temperature constant, the volume of the gas is directly proportional to the number of molecules or moles. $V \propto n$ (P and T constant)

Complete step by step answer:
Now we will find out the volume occupied by two moles of heavy gas:
Using Avogadro’s Law we will find the volume occupied by the two moles of heavy gas.
Avogadro’s law $V \propto n$ (P and T constant)
Removing the proportionality with a constant K,
$\Rightarrow V = K \times n$
$\Rightarrow \dfrac{V}{n} = K$
$\Rightarrow \dfrac{{{V_1}}}{{{n_1}}} = \dfrac{{{V_2}}}{{{n_2}}} \to (1)$
Using equation (1) we will find the volume of the heavy gas occupied.
$\Rightarrow \dfrac{{{V_1}}}{{{n_1}}} = \dfrac{{{V_2}}}{{{n_2}}}$
$\Rightarrow \dfrac{{20}}{1} = \dfrac{{{V_2}}}{2}$
We have the put given values in the equation (1) and we have to calculate ${V_2}$
(Here V $=$ volume of the gas occupied and n $=$ number of moles)
$\Rightarrow {V_2} = \dfrac{{2 \times 20}}{1}$
After calculating we get the value of ${V_2}$
$\Rightarrow {V_2} = 40$
Therefore, the volume occupied by the two moles of a heavy gas is 40 lit.
Hence, the correct option is (B).

Note:
Gas molecules do not occupy fixed positions and are widely separated.
Gas molecules possess very high energy.
Since the particles of gases are not held in fixed positions and move freely, gases neither have definite shapes nor definite volumes.
Due to the large separation of molecules, gases have a large volume and thus low densities.
Gases diffuse very readily due to the free movement of the molecules.
Gases can be compressed readily due to the presence of large empty spaces between the molecules.