Question

In a given time 8 grams of O2 are diffused.Calculate the mass of H2 diffused under identical condition.

Answer 1

Given

• In a given time interval, 8 grams of $O_2$ is diffused.

To Find

Mass of $H_2$ diffused under identical condition.

Concepts

$\boxed{\green{Rate\:of\:diffusion\:=\: \frac{AP}{\sqrt{2\pi \: RMT}}}}$

Where,

• A = Area of orifice, P = Pressure , R = gas constant, M = molar mass and T = temperature

Hence, For two gases of molecular mass $M_1\:and\:M_2$ , ratio of ratio of diffusion will be

$\frac{r_1}{r_2} \: = \: \sqrt{ \frac{M_2}{M_1} }$

Solutions

Let

• the time interval be t seconds in which given mass of $O_2$ is diffused.

• the rate be expressed be in $gram\: s^{-1}$

• x gram of $H_2$ is diffused.

We know, Molar mass of $O_2\:and\:H_2$ is 32 gram and 2 gram respectively. Now, putting the values in the formula.

$\frac{ r_{H_2} }{r_{O_2}} \: = \: \sqrt{ \frac{32}{2} }$

=> $\frac{ \frac{x}{t}}{ \frac{8}{t}} \: = \: \sqrt{ 16}$

=> $\frac{x}{8} \: = \: 4$

=> $x\: =\:32\:gram$

Hence, 32 gram of $H_2$ will be diffused in same time interval.