Question

The rate of diffusion of hydrogen is about:
a.) One half that of He
b.) 1.4 times that of He
c.) Twice that of He
d.) Four times that of He

Answer 1

Hint: In order to solve this problem we will use the concept of chemistry as the rate of diffusion is inversely proportional to the square root of molar mass. Further we will compare the rate of diffusion by the help of molar masses of hydrogen and helium.

Formula used- $\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{{{r_{{H_2}}}}}{{{r_{He}}}} = \sqrt {\dfrac{{{M_{He}}}}{{{M_H}}}} $

Complete step by step answer:
Hydrogen gas exists in the form of a diatomic molecule ${H_2}$ . However helium gas exists in the form of monatomic He.
Let us assume the rate of diffusion of hydrogen as ${R_1}$ .
And the rate of diffusion of helium as ${R_2}$ .
As we know that the rate of diffusion is inversely proportional to the square root of molar mass.
So we can write it as
$\dfrac{{{R_1}}}{{{R_2}}} = \sqrt {\dfrac{{{M_2}}}{{{M_1}}}} $
Where M is molar mass of compound

So the relation between the rate of diffusion of hydrogen and helium will become as:
$\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{{{r_{{H_2}}}}}{{{r_{He}}}} = \sqrt {\dfrac{{{M_{He}}}}{{{M_H}}}} $
Now let us substitute in the values in the place of the mass of atoms.
\[
   \Rightarrow \dfrac{{{R_1}}}{{{R_2}}} = \sqrt {\dfrac{4}{2}} \\
   \Rightarrow \dfrac{{{R_1}}}{{{R_2}}} = \sqrt 2 \\
   \Rightarrow \dfrac{{{R_1}}}{{{R_2}}} = \dfrac{{{r_{{H_2}}}}}{{{r_{He}}}} = 1.414 \\
  \therefore {r_{{H_2}}} = 1.414{r_{He}} \\
 \]
Therefore the rate of diffusion of hydrogen is about 1.4 times that of helium.
So, the correct answer is “Option B”.

Note: In order to solve such types of problems students must remember the formula relating the rate of diffusion and the mass of the atom. Also the students must remember the mass of some of the generally used elements and should remember the method to find out the molar mass from the periodic table.