Question

A quantity of 2g of hydrogen diffuses from a container is 10 min. How many grams of oxygen would diffuse through the same container in the same time under similar conditions?
A.5 g
B.4 g
C.6 g
D.8 g

Answer 1

Hint:In this question to find the molecular weight of the oxygen diffused through the container when $2g$ of hydrogen is diffused; the formula used is the ratio of the molecular mass of oxygen to the molecular mass of hydrogen\[\dfrac{{n{H_2}}}{{n{O_2}}} = \sqrt {\dfrac{{M{O_2}}}{{M{H_2}}}} \], here M is the molecular and n is the given mass weight of the gas.

Complete step by step answer:
According to the question;
The weight of hydrogen that diffuses through the container is = $2g$
Time taken to diffuse through the container is = $10\min $

\[\dfrac{{n{H_2}}}{{n{O_2}}} = \sqrt {\dfrac{{M{O_2}}}{{M{H_2}}}} \]
\[\dfrac{{\dfrac{{\dfrac{2}{2}}}{{^w{O_2}}} = \sqrt {\dfrac{{32}}{2}} }}{{32}}\]
$\sqrt {16} $
$ = 4$
\[^w{O_2} = \dfrac{{32}}{4} = 8g.\]
Therefore, the molecular weight of the oxygen that is diffused through the container is: \[8g\]
Thus the correct option is D.

Additional information : The diffusion rate of the gas can be calculated according to Graham's law, which states that the rate of diffusion is directly proportional to the molecule’s weight square roots.
The formula is;
$\dfrac{{{r_1}}}{{{r_2}}} = \sqrt {\dfrac{{{m_1}}}{{{m_2}}}} $; m1 is the mass of the gas that is not known, m2 is the mass of known gas, r1 is the rate of diffusion of known gas and the r2 is the diffusion of known gas.

Note:
Diffusion can be defined as the net movement of solute or solvent from its higher concentration region to the region of its low concentration. It is the simplest approach through which several processes take place in the environment. It is a process which does not have an energy requirement; it occurs spontaneously in nature.
The molecular mass formula is used to calculate the mass of the compound formed from the mass combination of its constituents.