If 30cm\(^3\) of oxygen diffuses through a porous pot in 7 seconds, how long will it take 60cm\(^3\) of chlorine to diffuse through the same pot, if the vapour densities of oxygen and chlorine are 16 and 36 respectively?
- 9.3 sec
- 14 sec
-
21 sec
- 28 sec
- 30.3 sec
The correct answer is: C
Explanation
According to Graham's law of diffusion of gases,the rate of diffusion of a gas is proportional to the square root of the density.
From the question, the given parameters are:
Volume of Oxygen, V\(_o\) = 30cm\(^3\), Time of diffusion of Oxygen, t\(_o\) = 7s, Vapour density of Oxygen, d\(_o\) = 16
Volume of Chlorine, V\(_c\) = 60cm\(^3\), Time of diffusion of chlorine, t\(_c\) = ?, Vapour density of Chlorine, d\(_c\) = 36
\(\frac{t_o}{t_c}\) = \(\sqrt{\frac{d_o}{d_c}}\)
\(\frac{7}{t_c}\) = \(\sqrt{\frac{16}{36}}\)
\(\frac{7}{t_c}\) = \(\frac{4}{6}\)
t\(_c\) = \(\frac{7}{4}\times {6}\)
t\(_c\) = \(\frac{21}{2}\)
Recall that the volume of Chlorine is twice that of Oxygen. Hence, t\(_c\) = 2t\(_o\)
t\(_c = 2\times \frac{21}{2}\)
t\(_c\) = 21sec - Option C