64 mL of an unknown gas diffuses in the same time as 128 mL of methane gas under identical conditions. The molar mass of unknown gas is

Hint: Molar mass is regarded as the mass of a material in relation to a certain quantity. This gives the number of molecules, atoms, or compounds contained in one mole of material. The SI unit for molar mass is g/mol.

Complete Step by Step Solution:
Mole enables the chemists to weigh different substances, say iron and sulphur, and acquire an equal quantity of iron and sulphur atoms. A mole of a substance is defined as a material mass containing exactly 12,000 g of 12C and the same number of fundamental units as atoms.

Given in the question: 64ml of an unknown gas diffuses in the same time as 128 ml of methane gas under identical conditions.

To find out: The unknown gas's molar mass

Rate of diffusion of unknown gas is equal to 64ml
$\Rightarrow $${{r}_{1}}=64$
Rate of diffusion of methane is equal to 128ml
$\Rightarrow $${{r}_{2}}=128$

We know that the molar mass of methane i.e. CH4 is 16
Therefore, ${{m}_{2}}=16$
Formula to be used in this question is,
$\Rightarrow \dfrac{{{r}_{1}}}{{{r}_{2}}}=\sqrt{\dfrac{{{m}_{2}}}{{{m}_{1}}}}$

Now, substituting the values mentioned above in the given equation
$\Rightarrow \dfrac{64}{128}=\sqrt{\dfrac{16}{{{m}_{1}}}}$
$\Rightarrow \dfrac{1}{2}=\sqrt{\dfrac{16}{{{m}_{1}}}}$

Now, squaring both the sides, we get,
$$ $\dfrac{1}{4}=\dfrac{16}{{{m}_{1}}}$
$\Rightarrow {{m}_{1}}=64$
Therefore, the molar mass of the unknown gas is 64g/mol.

Note: We must be extremely clear about the substance's molar mass and molecular mass. Both of these values are distinct in that molar mass refers to the mass of one mole of the supplied material, whereas molecular mass is the sum of the atomic masses of all atoms in the molecule.